THE ORIGIN 
 OF SPECTRA 
 
 . BY 
 
 PAUL D. FOOTE 
 
 Physicist, U. S. Bureau of Standards 
 AND 
 
 F. L. MOHLER 
 
 Physicist, U. S. Bureau of Standards 
 
 American Chemical Society 
 Monograph Series 
 
 BOOK DEPARTMENT 
 The CHEMICAL CATALOG COMPANY Inc. 
 
 19 EAST 24ra STREET, NEW YORK, U. S. A. 
 1922 
 
f 
 
 COPYRIGHT, 1922, BY 
 The CHEMICAL CATALOG COMPANY, Inc. 
 
 All Rights* Reserved 
 
 Press of 
 
 J. J. Little & Ives Company 
 New York, U. S. A. 
 
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4 GENERAL INTRODUCTION 
 
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GENERAL INTRODUCTION 5 
 
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PREFACE 
 
 Although several accounts of the quantum theory of spectra from 
 the mathematical standpoint have appeared in the past year, the experi- 
 mental aspect of the problem has been greatly subordinated. 
 
 In this book the authors have endeavored to present the subject 
 from the experimental side. However, in order to do this, it was found 
 necessary to briefly discuss the theoretical developments. In this 
 regard, the important assumptions involved are enumerated, and only 
 the essential steps in the mathematical analysis are presented. The 
 reader will find the detailed mathematical treatment in the papers 
 given as references, especially in the works of Bohr and Sommerfeld. 
 
 The experimental phase of the quantum hypothesis as applied to 
 spectroscopy was given its first impetus by the pioneer work of J. 
 Franck whose later important researches have contributed much to 
 the development of the subject. The theoretical deductions of Sommer- 
 feld on fine structure have been beautifully verified by the precision 
 spectroscopic work of Paschen. The most recent contributions of Bohr 
 on atomic structure have removed many of the objections of the chemist 
 to the physicist's conception of a planetary structure with revolving 
 electrons. At the same time Bohr's viewpoint has necessitated the re- 
 vision of some of the conceptions of the physicist. 
 
 The subject matter is recognizedly in a transitional stage and the 
 theoretical interpretation of experimental phenomena here given is in 
 no sense complete or final. However, the experimental facts will remain 
 and no time is more opportune for their systematic correlation than the 
 present moment. 
 
 This book is incomplete in many respects. For example, consider- 
 ation of the extensive experiments on the Stark and Zeeman effects and 
 on band spectra has been omitted, in part because their adequate treat- 
 ment seemed to require more space than was deemed advisable to devote 
 to these subjects, and in part because of the authors' inexperience in these 
 fields of spectroscopy. 
 
 7 
 
8 PREFACE 
 
 The title of the book was suggested by a lecture of Prof. J. C. McLen- 
 nan whose many experiments in this field of physics are considered in 
 the text. 
 
 The authors desire to acknowledge the helpful cooperation and 
 advice of their colleague Dr. W. F. Meggers. Many of their "experi- 
 ments have been undertaken with Dr. Meggers as co-worker and he has 
 very kindly prepared most of the photographic prints of spectra repro- 
 duced here as half-tones. Dr. K. T. Compton furnished the advance 
 manuscript of his paper on Cumulative lonization, a synopsis of which 
 is given in Chapter VI. Dr. R. C. Tolman, Dr. C. A. Skinner and Mr. 
 Arthur E. Ruark have very generously given much of their time in 
 reading the manuscript, and have offered many suggestions which have 
 been incorporated in the text. 
 
 The authors wish to express their appreciation of the interest with 
 which the late Dr. C. W. Waidner, former Chief of the Heat Division 
 of this Bureau, followed the course of their work until within a few days 
 of his death. The authors also desire to thank Dr. S. W. Stratton for 
 placing at their disposal every means and facility which could advance 
 their own experimental work in this subject. And finally, the authors 
 are especially grateful to the Monograph Committee of the American 
 Chemical Society, its Chairman, Prof. W. A. Noyes, and Prof. A. A. 
 Noyjs, for making possible the publication of this volume. 
 
 P. D. F. 
 
 Bureau of Standards, May 22, 1922. F. L. M. 
 
TITLES OF CHAPTERS 
 
 CHAPTER PAGE 
 
 I. THE QUANTUM THEORY OF SPECTROSCOPY .... 15 
 II. ENERGY DIAGRAMS 51 
 
 III. lONIZATION AND RESONANCE POTENTIALS FOR THE ELE- 
 
 MENTS 60 
 
 IV. LINE ABSORPTION SPECTRA OF ATOMS 78 
 
 V. LINE EMISSION SPECTRA OF ATOMS 109 
 
 VI. CUMULATIVE IONIZATION 148 
 
 VII. THERMAL EXCITATION 157 
 
 VIII. THERMOCHEMICAL RELATIONS ........ 177 
 
 IX. X-RAY SPECTRA 192 
 
 X. PHOTO-ELECTRIC EFFECT IN VAPORS 216 
 
 XI. DETERMINATIONS OF h INVOLVING LINE SPECTRA . . 223 
 
 APPENDICES 
 
 APPENDIX 
 
 I. COMPUTATIONAL DATA 227 
 
 PERIODIC TABLE 231 
 
 II. BOHR'S THEORY OF ATOMIC STRUCTURE 232 
 
 INDEX OF SUBJECTS 243 
 
 INDEX OF AUTHORS 249 
 
TABLE OF CONTENTS 
 
 HAPTEK 
 
 I. THE QUANTUM THEORY OF SPECTROSCOPY . . . .15 
 
 The Simple Theory of Hydrogen and Ionized Helium . 16 
 Ratio of Mass of Hydrogen Nucleus and Hydrogen 
 
 Atom to Mass of Electron, and Value of elm . . 18 
 
 Elliptical Orbits 19 
 
 Relativity of Mass 24 
 
 The Principle of Selection . 26 
 
 Experimental Verification by Fine Structure Analysis. 27 
 
 Atoms with Many Electrons 30 
 
 Derivation of the Ritz Equation 32 
 
 Application of the Ritz Equation .34 
 
 Fine Structure, Doublets and Triplets 37 
 
 Nuclear Defect of a Ring of Electrons 37 
 
 Spark Spectra '....... 39 
 
 Spectroscopic Tables 43 
 
 X-Rays 46 
 
 II. ENERGY DIAGRAMS 51 
 
 III. lONIZATION AND RESONANCE POTENTIALS FOR THE ELE- 
 
 MENTS 60 
 
 Group I 63 
 
 Group 1 1 63 
 
 Group III 63 
 
 Group IV, Group V . 65 
 
 Group VI 66 
 
 Group VII, Groups VIII and 67 
 
 Hydrogen 68 
 
 The Normal Helium Atom ........ 69 
 
 The Hydrogen Molecule 74 
 
 IV. LINE ABSORPTION SPECTRA OF ATOMS 78 
 
 Line Absorption Spectra of Normal Atoms .... 78 
 
 Reversed Lines 82 
 
 Resonance Radiation 86 
 
 The Broadening of Spectral Lines 91 
 
 Doppler Effect 91 
 
 Impact Damping 92 
 
 Line Absorption Spectra of Excited Atoms .... 93 
 
 The Measurement of r (the life of an excited atom) . 93 
 
 Absorption of Subordinate Series Lines 97 
 
 11 
 
12 CONTENTS 
 
 CHAPTER PAGE 
 
 V. LINE EMISSION SPECTRA OF ATOMS 109 
 
 Metals of Group II of the Periodic Table .... 118 
 
 Relation between 1 @ and 1 S 124 
 
 Metals of Group I of the Periodic Table 127 
 
 The Rare Gases 133 
 
 Helium 133 
 
 Neon 136 
 
 Franck and Einsporn's Observations onMercury . . 137 
 Quantitative Spectroscopic Analysis in its Relation to 
 
 the Origin of Spectra 141 
 
 Long Lines 141 
 
 Raies Ultimes 141 
 
 VI. CUMULATIVE IONIZATION . . . . V. 148 
 
 Excitation by Electronic Impact '. 149 
 
 Excitation by Absorption of Radiation . . . . . 150 
 
 Numerical Magnitudes 152 
 
 Arcs below the lonization Potential 153 
 
 lonization by Successive Photo-Electric Action . . 154 
 
 Further Conclusions 155 
 
 VII. THERMAL EXCITATION 157 
 
 Thermodynamic Considerations 157 
 
 Simple lonization ; 159 
 
 Double lonization . . . . . 161 
 
 Thermal Excitation without lonization 163 
 
 Flame Spectra 165 
 
 Spectral Lines Correlated with Temperature . . . 169 
 
 Solar Spectra 170 
 
 Stellar Spectra 172 
 
 VIII. THERMOCHEMICAL RELATIONS 177 
 
 Electron Affinity of Atoms 177 
 
 Grating Energy, lonization Potential and Electron 
 
 Affinity 179 
 
 lonization of Vapors of Compounds 184 
 
 Critical Potentials and Radiation from Elements in the 
 
 Polyatomic State 187 
 
 IX. X-RAY SPECTRA 192 
 
 Introduction 192 
 
 Critical Potentials for X-Ray Excitation .... 193 
 
 Absorption Phenomena 196 
 
 Emission Lines and the Combination Principle . . 204 
 Theoretical Significance of the System of Absorption 
 
 Limits 209 
 
 Conclusion 213 
 
CONTENTS 13 
 
 CHAPTER PAGE 
 
 X. PHOTO-ELECTRIC EFFECT IN VAPORS 216 
 
 XI. DETERMINATIONS OF h INVOLVING LINE SPECTRA . . 223 
 
 Characteristic X-Rays 223 
 
 The Rydberg Number ... 224 
 
 lonization and Resonance Potentials 225 
 
 APPENDIX I 227 
 
 Computational Data '. . . . 227 
 
 Nuclear Defect, Table 44 . 227 
 
 Numerical Magnitudes, Table 45 228 
 
 Velocities of Electrons, Ions and Molecules .... 229 
 Periodic Classification of Elements, Table 46 . . .231 
 
 APPENDIX II. BOHR'S THEORY OF ATOMIC STRUCTURE . . . 232 
 
 1st Period 233 
 
 2nd Period 235 
 
 3rd, 4th and 5th Periods 235 
 
 6th and 7th Periods 235 
 
 X-Ray Spectra . 237 
 
 Superficial Atomic Properties 237 
 
 Arc and Spark Spectra 239 
 
 Conclusion 240 
 
 INDEX OF SUBJECTS 243 
 
 INDEX OF AUTHORS 249 
 

Chapter I 
 The Quantum Theory of Spectroscopy 
 
 The quantum theory of spectra has been concerned mainly with the 
 Rutherford type of atom. This consists of a positive nuclear charge 
 Ze, where Z is the atomic number, surrounded by Z electrons. Practi- 
 cally the entire mass of the atom is concentrated in the positive core, the 
 size of which, however, is much smaller than that of an electron. 1 The 
 electrons are usually considered as revolving about the nucleus in 
 coplanar orbits. Actually there is evidence that the orbits are not 
 coplanar and models have been proposed in which the electrons do not 
 revolve about the nucleus, but with the exception of helium little progress 
 from the quantitative, spectroscopic and mathematical standpoints has 
 been made with such types of atom. 
 
 Even if we really understood the precise structure of a heavy atom, 
 the mathematical analysis of the orbits would be hopeless a problem 
 of n bodies where n is large. Hence the exact interpretation of spec- 
 troscopic phenomena is a problem for the far-distant future. For the 
 present bold simplifying assumptions must needs be made for the purpose 
 of obtaining results. Postulates are proposed, the only apparent 
 justification of which lies in the applicability of the conclusions to ex- 
 perimental facts. When necessary, the fundamental principles of 
 classical dynamics are temporarily abandoned and apparently illogically 
 accepted for later steps in the analysis of the problem. In spite of such 
 inconsistency the quantum theory of spectra is the only satisfactory 
 attempt so far made toward interpreting spectral series and, already, 
 by predictions from theory, has led to experimental verifications of 
 the greatest moment. This is the goal of any theory; not necessarily 
 to explain nature but to aid in a systematic search for new phenomena. 
 
 l The mass is of electromagnetic nature. As appears later, the ratio of the mass of the 
 hydrogen nucleus to that of a slow-moving electron is about 1846. Since the diameter of a 
 spherical charge is inversely proportional to its mass, the hydrogen nucleus should have 
 1/1846 the diameter of an electron. The best guess is probably 10~ 16 cm for the diameter 
 of this nucleus, but any estimate involves questionable conjectures. 
 
 15 
 
16 ! ORIGIN OF SPECTRA 
 
 THE SIMPLE THEORY OF HYDROGEN AND IONIZED HELIUM 
 We shall first consider simple atoms containing the nucleus and a 
 single electron. Such an atom is hydrogen, ionized helium, or doubly 
 ionized lithium. Merely by way of introduction we shall postulate that 
 the electron of charge e for hydrogen revolves in a circular orbit 
 about the nucleus of charge -\-e. Since the mass of the electron is small 
 compared to that of the nucleus, we may readily derive from simple 
 mechanics the total energy W of the revolving electron (the sum of the 
 kinetic and potential energies). 
 
 W = _ *. I - 2 (1) 
 
 2a> a e* ' 
 
 where a is the radius of the circular orbit, m the mass of the electron and 
 v its linear velocity. 
 
 So far as ordinary mechanics is concerned a may have any value 
 whatever, depending upon "initial conditions ". Bohr, 2 however, postu- 
 lates that only certain definite sizes of orbits are permissible stationary 
 states, so determined that 
 
 2 TT X angular momentum = nh, (2) 
 
 where h is Planck's universal constant of action and n may assume 
 integral values only. Whence : 
 
 2 Trmav = nh. 
 
 Substituting this in the relation ma?v z = e*/2W obtained from (1) 
 we find for W n the total energy of the electron in the nth orbit : 
 
 In order for this to be a stationary state, no energy can be radiated. 
 On the basis of classical dynamics, however, an accelerated electron 
 emits radiation and hence the electron should spiral in toward the 
 nucleus instead of remaining in the nth orbit. We accordingly postulate 
 that on the basis of the quantum theory the nth orbit is a stationary 
 state and that no energy is radiated so long as the electron remains in 
 this orbit. If, however, it should jump to the n'th orbit Bohr further 
 postulates that radiation is suddenly emitted of such frequency v that 
 
 W n - W n . = hf. (4) 
 
 The quantity hv is known as a quantum of energy of frequency v . 
 Hence in any interorbital transition a single quantum of radiation is 
 
 See general reference 1 at end of chapter. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 17 
 
 emitted (n > ri) or absorbed (n < w'), the magnitude of which (ex- 
 pressed in ergs for example) is equivalent to the difference in total ener- 
 gies of the electron in the two orbits concerned. This fact is simply an 
 application of the principle of the conservation of energy. Substituting 
 the values of W from Equation (3) in the above, we obtain: 
 
 2 Tr 2 m 
 
 h* 
 
 In general it is desirable to express our values in terms of wave 
 number v, i.e. the reciprocal of the wave-length in cm in vacuo. Whence, 
 since v = v/c where c is the velocity of light : 
 
 /.r 
 
 R ' 
 
 in which 
 
 _ 2 ,,n _ N ,-^ 
 
 ch* *>' W ? 
 
 The subscript <x> is sometimes added to call attention to the fact 
 that we have assumed the mass of the electron as negligible compared to 
 that of the core. Formula (6) gives to a high degree of precision all the 
 series lines of the hydrogen atom. With n' = I, n = 2, 3, etc., we have 
 the Lyman ultra-violet series; with n' 2, n= 3, 4, etc., the Balmer 
 series; and with n' = 3, n 4, the Paschen series of infra-red lines. 
 
 If we consider the effect 3 of the finite mass M of the nucleus we 
 find that the constant N in (6) must be replaced by : 
 
 NX = M N . (8) 
 
 This is appreciably different from N& for hydrogen as well as for other 
 light elements. The observed value of N H obtained from an empirical 
 consideration of the series lines agrees well with that computed by (8) 
 and (7) from the known physical constants m, e, c and h. For ionized 
 helium we may derive in the above manner: 
 
 The factor 4 enters because of the nuclear charge Z = 2 which occurs in 
 the derivation as Z 2 . This formula again represents important series 
 lines, formerly attributed to hydrogen but now known to be due to 
 ionized helium, for example the series n' = 3, n = 4, 5, etc., also n' =4, 
 n = 5, 6, etc. 
 
 3 Both nucleus and electron revolve around the common center of mass. In this and 
 following developments we are concerned with the energy, momentum, etc., of the entire 
 
 system, not of the electron alone. The substitution of "*jf" for in the above equations 
 . takes account of this. 
 
18 ORIGIN OF SPECTRA 
 
 RATIO OF MASS OF HYDROGEN NUCLEUS AND HYDROGEN ATOM TO 
 MASS OF ELECTRON, AND VALUE OF e/m 
 
 From empirically determined values of A H and A r He it is possible 
 to obtain the ratio of the mass of the hydrogen atom to that of an 
 _ electron. Paschen finds empirically: 
 
 N H = 109677.691 ] 
 A r He = 109722.144 (10) 
 
 and through Equation (8) N* = 109737.11 
 
 mass of helium atom _ M' He _ 4.00 
 mass of hydrogen atom ~~ M' H 1.0077 
 
 from atomic weight determinations. 
 
 mass of helium nucleus _ M He _ 
 mass of hydrogen nucleus M H 
 
 From Equation (8) it follows that: 
 
 M H _ mass of hydrogen nucleus x 
 
 m ~ mass of slow-moving electron AHC A H 
 
 But ^|~5? = ^ e "t 2 ^ m = 3.969. 
 
 ' Hence x = 1.969 ^- + 3.969. 
 
 Assume 1900 > > 1800. Then x = 3.970. 
 m 
 
 Accordingly, from Equations (10) and (11), 
 
 M H mass of hydrogen nucleus _ .. _ 
 
 m mass of slow-moving electron 
 
 A H -^TH _ mass of hydrogen atom _ M H + m _ | 
 
 m mass of slow-moving electron m 
 
 This value agrees well with that obtained by other methods. 
 
 Mi / / 
 
 H / in e/m 
 Furthermore - = ,.., = 7- , 
 
 m e/M' H f 
 
 where / is the value of the Faraday. VinaPs 4 most recent work shows 
 
 * Vinal, Bur. Standards Sci. Papers, 218 and 271. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 19 
 
 that this is not known with quite the precision ordinarily assumed, his 
 extensive experiments giving / = 96500 10 coulombs. Accordingly 
 
 _e m jMj* = (96500) (1846.5) = 1.7819 - 10 8 coulombs/g 1 
 
 (12) 
 
 = 1.7819- 10 7 e.m.u./g 
 = 5.343 10 17 e.s.u./g. J 
 
 These values should be good to 1 part in 2000 so that the method affords 
 one of the most precise means 5 for determining e/m. 
 
 ELLIPTICAL ORBITS 
 
 The possibility of elliptical orbits for the revolving electron greatly 
 complicates the problem by the introduction of a second degree of 
 freedom, viz. variation in the length of the radius vector, but leads to 
 results of the most fundamental nature. 
 
 In general, let us consider a system having k degrees of freedom. 
 For the description of its configurations we require k independent co- 
 ordinates, q\, q* ' q*. These may be, for example, the Cartesian or 
 the polar coordinates of the various particles of the system. Cor- 
 responding to each q there will be a quantity p which plays the same 
 mathematical role in the expression for the kinetic energy of the system 
 
 as the components of momentum, m -^- , m -j- , m-^ play in the formula 
 
 dt o/t dt 
 
 for the kinetic energy of a single particle. Thus for a particle, in Carte- 
 sian coordinates, the kinetic energy, 
 
 where p x , p y , and p z are the components of momentum. It will be 
 noted that if we write -^ = v x , etc., then 
 
 dT dT m 
 M = to, = 2 
 
 and similarly for p v and p z . 
 
 5 This statement is based on Paschen's estimate of the precision with which N H and 
 A 7 He may be empirically determined. - Birge, Phys. R. 17, pp. 589-607 (1921), in a very 
 thorough consideration of the measurements on the hydrogen lines, has concluded that 
 iV H = 109677.7 =t 0.2. An uncertainty of 0.2 in N H gives rise to a possible error of 
 =*= 0.5% in JV He N H of Equation (11), which is carried over directly in the final compu- 
 tation of dm. A similar error in -ZV He would still further increase the uncertainty in the deter- 
 mination of elm. 
 
20 ORIGIN OF SPECTRA 
 
 Likewise for any dynamical system we define the generalized moment 
 Pt corresponding to the coordinate q t to be 
 
 Let us choose such generalized coordinates that the kinetic energy 
 contains only the squares of the generalized moments p t , so that no terms 
 such as pip 2 occur. In general the square of each moment will be pre- 
 fixed by a coefficient which may be a function of one or more of the 
 coordinates q. For example, the expression for the kinetic energy of a 
 particle of mass m in polar coordinates is 
 
 - = p r = linear momentum in the direction of the radius vector; 
 
 -f p. = angular momentum about the origin. 
 at 
 
 Therefore T = ^(^ + - 2 , 
 
 Let the coordinates also be so chosen that the potential energy of 
 the system consists of a sum of functions each of which depends upon 
 one coordinate only. Thus the potential energy will have the form 
 
 For all the systems with which we shall deal, such a choice of co- 
 ordinates is possible. 
 
 The conditions by which we select discrete or quantized states of 
 steady non-radiating motion for the dynamical system of the atom may 
 be stated in terms of the above generalized coordinates as follows : 
 
 f p t dq t = nji 
 
 dT 
 
 where ^"^ 
 
 and where the integral is taken over a complete period of the coordinate 
 in question. (We shall be concerned only with systems where each 
 coordinate is periodic.) The k equations furnished by the above re- 
 quirements are the quantizing conditions laid down independently by 
 W. Wilson 6 and by Sommerfeld. 7 
 
 W. Wilson, Phil. Mag. 29, p. 795 (1915). 
 
 Sommerfeld, "Atombau," any edition, preferably 3d. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 21 
 
 As an example of the application of Equations (13) let us consider 
 first the simple case, described earlier, of circular orbits. Here we have 
 but one degree of freedom, the azimuth <f>, since the radius vector is 
 fixed in magnitude. The limits of integration are < = and = 2 T, 
 corresponding to one complete revolution of the electron. Thus: 
 
 T = ^ 
 
 dT dT 
 
 a*- a? 
 
 Hence f pdq = f mr^dQ = 2 irmr 2 ^ = n a h 
 
 * 
 
 since <j> is constant. But wr 2 is the angular momentum of the electron. 
 We have accordingly derived Equation (2) by the use of the more gen- 
 eral relation (13). 
 
 The integer n a in this case is known as the azimuthal quantum 
 number since the integral to which it applies contains the azimuth as 
 the independent variable. 
 
 In the case of elliptical motion the quantizing process must be 
 applied in respect to both azimuth and radius as follows : 
 
 2 TT J'TT 
 
 azimuth : nji = f pdq = f - d<j> = 2 TT X angular momentum (14) 
 J J o d<p 
 
 2 TT ^ ^T* 
 
 radius: n r h = f pdq = f -rr dr. (15) 
 
 The integer n r is known as the radial quantum number since the in- 
 dependent variable in Equation (15) is the radius r. If we substitute 
 in this the value of the kinetic energy we obtain from (14) and (15) 
 
 in which e is the eccentricity of the elliptical orbit. Thus not only 
 must the angular momentum of the electron have certain discrete 
 values but at the same tune the shapes of the elliptical orbits are re- 
 stricted in a very definite manner. 
 
 If we now evaluate the total energy W n<J n r of the electron in any 
 particular ,orbit determined by the azimuthal quantum number n a and 
 the radial quantum number n r , we find 
 
 Nhc 
 
22 
 
 ORIGIN OF SPECTRA 
 
 It will be noted that several different orbits exist, depending upon how 
 the total value of n a + n r is obtained, for which the energy has the same 
 value. For example the orbit n a = 1, n r = 2 has the same energy as the 
 orbit n a = 2, n r = 1 since n a + n r = 3 in each case. 
 
 Scale 
 
 FIG. 1. A few of the inner orbits wh : ch may be occupied by the electron of the 
 hydrogen atom. Actually these orbits are perturbed so that they are not 
 exactly closed or cyclic. There is present a slow progressive mot : on of peri- 
 hel on. The illustrat'on represents very closely an ''instantaneous photograph" 
 of the possible states, while a "tims expos are" would give a solid field of ink on 
 account of the progressive motion. 
 
 Proceeding now in the same manner as that in which Equation (6) 
 was derived and putting the difference in the total energies of two orbits 
 W naTlr and W n , an , r equal to h times the frequency of the emitted radi- 
 ation, or he times the wave number v, we obtain the following spectral 
 series formula : 
 
 V = 
 
 (18) 
 
 This again represents the series lines of hydrogen. The Balmer series is 
 obtained when n' a -f ri r = 2 and n a + n r = 3, 4, 5, etc. The physical 
 significance of this more complicated formula will appear later. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 23 
 
 It may be readily shown that all elliptical orbits, for which the total 
 energy, W, of the atom is the same cf. Equation (17) have equal semi- 
 major axes, a, and that the semi-minor axes, 6, have the magnitudes: 
 
 n f , 
 
 n r 
 
 a. 
 
 (19) 
 
 All orbits for which n a are straight lines through the nucleus and 
 are hence excluded as physically impossible. We shall consider the 
 form of the various inner orbits for the hydrogen atom, subject to the 
 condition n a ^ 0. The inmost orbit is obtained when n a + n r = 1, that 
 is, when n a = 1, n r = 0, The next group of orbits is found by making 
 n a + n r = 2. Proceeding in this manner we may by the help of Equa- 
 tion (19) compute the constants of the orbits, as given in Table I, 
 and further illustrated by Figure 1. 
 
 TABLE I 
 ORBITS OF HYDROGEN TO n a + n r = 4 
 
 n a + n r 
 
 n a 
 
 n r 
 
 a 
 
 6 
 
 Form of Orbit 
 
 1 
 
 1 
 
 
 
 di 
 
 ai 
 
 circle 
 
 2 
 
 2 
 
 
 
 4i 
 
 4ai 
 
 circle 
 
 2 
 
 1 
 
 1 
 
 4oi 
 
 20! 
 
 ellipse 
 
 3 
 
 3 
 
 
 
 9ai 
 
 9i 
 
 circle 
 
 3 
 
 2 
 
 1 
 
 9ai 
 
 6ai 
 
 ellipse 
 
 3 
 
 1 
 
 2 
 
 9ai 
 
 3ai 
 
 ellipse 
 
 4 
 
 4 
 
 
 
 I6ai 
 
 16i 
 
 circle 
 
 4 
 
 3 
 
 1 
 
 16ai 
 
 12ai 
 
 ellipse 
 
 4 
 
 2 
 
 2 
 
 16ai 
 
 8ai 
 
 ellipse 
 
 4 
 
 1 
 
 3 
 
 16ai 
 
 4ai 
 
 ellipse 
 
 The line H a is produced by an electron jumping from an orbit n a + n r = 3 
 to an orbit n a -f n r = 2. Since there are three. orbits of equal energy 
 value for which n a + n r = 3 and two orbits for which n a -\-n r = 2, the 
 line H a may be produced in six different ways. Similarly H0 and H 7 
 may be produced in eight and ten different ways respectively. These 
 
24 ORIGIN OF SPECTRA 
 
 conclusions, however, must be considerably modified, as will appear 
 directly. 8 
 
 RELATIVITY OF MASS 
 
 The first modification, due to Sommerfeld 9 , arises in the fact that the 
 mass of the electron in its elliptical orbit is not a constant but depends 
 upon its velocity, v, thus :m = m v 1 /3 2 , where = v/c and m is the 
 mass of a stationary or slow-moving electron. From a mathematical 
 standpoint the character of the orbit is considerably changed thereby, 
 but if the velocity of the electron is moderate compared to that of light, 
 we may consider the path as an ellipse with slowly moving perihelion. 
 Corresponding to Equation (17) we now obtain Equation (20) for the 
 energy of the electron in the n a n r orbit. 
 
 where a = -T- (21) 
 
 In this relation o? is a relatively small quantity being equal to 5.31 10~ 5 ; 
 hence it is sufficient for the present to neglect terms of higher order 
 
 s It is of interest to note that there exists a perfectly general relation between the fre- 
 quency of revolution of the electron about the nucleus and the wave number or the frequency 
 of the radiation emitted when the electron falls from one orbit to another. 
 
 It may be readily shown that the frequency of revolution, L. of the electron moving in 
 an elliptical orbit about the positive cha'rge E is given by the relation 
 
 where a= 
 
 On replacing a in the first equation by its equivalent, we obtain 
 
 (by Equation 7) 
 or, for hydrogen, / = z _f c for the initial orbit 
 
 (Tla -f- nr) * 
 
 and /' = ,., / 2 f 7 f /xt for the final orbit. 
 
 Replacing the terms (na + nr) 2 and (n'a + n'r) of Equation (18) by the values from the 
 above relations we find directly 
 
 If this is expressed in terms of the total quantum number n no + n r and frequency v 
 ( = cv) instead of v, we obtain 
 
 Hence the frequency of the emitted radiation is one-half the difference of the products of 
 the total quantum number and the frequency of revolution of the electron in each of the 
 orbits concerned in the transfer. This is a general law immediately applicable to any spec- 
 truin of the hydrogen type, such as that of ionized helium, doubly ionized lithium, etc. If 
 n n' = 1 where both n and n' are large v ~ f, that is, the frequency of the emitted light is 
 approximately equal to the frequency of revolution of the electron in its orbit. This approxi- 
 mation of the quantum theory to the classical dynamics for small frequencies or long wave- 
 lengths has an analogy in the law of the spectral distribution for black-body emission, where 
 the Planck relation approximates the classical Rayleigh equation for long wave-lengths. 
 See general reference 3 at end of chapter. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 25 
 
 than a 2 . The first term of this general equation is identical with Equa- 
 tion (17) (for hydrogen, Z = 1). The second and succeeding terms are 
 the corrections introduced by the relativity considerations. We note that 
 whereas in Equation (17) n a and n r occurred together as a sum, in the 
 correction term of Equation (20). they also occur as a quotient. The 
 energies of the various " elliptical" orbits in Figure 1, for the same total 
 quantum number accordingly depend upon how this number is obtained. 
 For example the energy is slightly different for the orbits characterized 
 by n a + n r = 1 + 2 = 3; n a + n r = 2 + 1 = 3 and n a + n r = 3 + 
 = 3. Thus the six possible transfers from n a + n r = 3 to n a + n r = 2 
 will produce six slightly different frequencies. These frequencies or 
 wave numbers may be computed from Equation (22) which is analogous 
 to Equation (18) derived without relativity considerations. 
 
 
 Hence the line H which represents an interorbital transfer from 
 total quantum numbers 3 to 2, when resolved by a high power spectro- 
 scope such as an echelon grating, should show fine structure and should 
 appear as a group of fine lines. The six mathematically possible com- 
 ponents for H a , computed by Equation (22) , where for N is substituted 
 N-B. thus taking into account the finite mass of the nucleus, are given in 
 Table II. 
 
 TABLE II 
 FINE STRUCTURE OF H a 
 
 V 
 
 X 
 Vacuum 
 
 n a n r - n'arir 
 
 An a 
 
 Remarks 
 See page 26 
 
 r 15233.451 
 
 6564.501 
 
 30->11 
 
 - 2 
 
 excluded 
 
 3.415 
 
 .516 
 
 21-+11 
 
 - 1 
 
 
 rj 3.307 
 
 .563 
 
 12-11 
 
 
 
 excluded 
 
 3.086 
 
 .658 
 
 30 -^ 20 
 
 - 1 
 
 
 3.050 
 
 .674 
 
 21 -+20 
 
 
 
 excluded 
 
 2.941 
 
 .720 
 
 12->20 
 
 + 1 
 
 
 In the same manner the fine structure of other Balmer lines and lines 
 of the Lyman and Paschen series may be computed. With Z = 2 in 
 
26 ORIGIN OF SPECTRA 
 
 Equation (22) we may similarly predict the fine structure of the series 
 lines of ionized helium. 
 
 THE PRINCIPLE OF SELECTION 
 
 The second modification of the simple theory consists in the applica- 
 tion of the principle of selection. So far in the analysis we have utilized 
 the principle of the conservation of energy as applying to the coupled 
 action between the ether and matter. The energy lost by the atom 
 when the electron is transferred from an orbit of higher energy level to 
 one of lesser energy is conserved by the ether in the form of radiation of 
 frequency v or wave, number v given by Equation (22) . Keeping the 
 original Bohr postulates which included the principle of conservation of 
 energy we shall now additionally restrict the problem by the condition 
 that we have conservation of moment of momentum. 10 That is, the 
 moment of momentum lost by the mechanical system forming the 
 atom, in any interorbital transition, is conserved by the ether as moment 
 of momentum of radiation. By a simple mathematical analysis Rubin- 
 owicz 11 showed that these assumptions lead to the conclusions that in 
 any interorbital transition of an electron, resulting in radiation, and 
 not complicated by the presence of an electrostatic or magnetic field, 
 the azimuthal quantum number n a may change by 1, or -|- 1 and 
 by no other amount. Bohr 12 has derived a more restricted principle of 
 selection which excludes the zero change of momentum. For the present 
 we shall confine our discussion to the Bohr restricted principle which 
 may be stated as follows: 
 
 A n a = ri a - n a = + 1 or - 1. (23) 
 
 Applying this principle to the analysis of the fine structure of H a , 
 of the six mathematically possible transitions three are excluded as 
 shown in the last two columns of Table II, because for these the change 
 in azimuthal quantum number is not =b 1. Hence we arrive at the 
 final conclusion that the line H a is made up of three components. On 
 account of the difference in energy of the two final orbits, n a -f n r = 1 -f- 1 
 and n a + n r = 2 + 0, these three lines may be considered as a doublet 
 one component of which has a satellite. Similarly with H^ for which, 
 of the 4X2 = 8 mathematically possible transitions, all but three are 
 excluded by the selection principle. The interorbital transitions result- 
 ing in H and H0 are shown by dotted lines in Figure 1 . 
 
 10 For a concise statement of the conceptions here involved, see Sommerfeld, "Atombau," 
 3d Ed., pp. 310-39. 
 
 11 Rubinowicz, Physik. Z. 19, pp. 441, 465 (1918). 
 
 12 See general reference 2. Also Dushman, J. Opt. Soc. Am. & R. S. I., 6, p. 235 (1922). 
 
THE QUANTUM THEORY OF SPECTROSCOPY 27 
 
 EXPERIMENTAL VERIFICATION BY FINE STRUCTURE ANALYSIS 
 
 The experimental verification of the above deductions in the case 
 of the hydrogen atom is probably as satisfactory as could be expected 
 at the present time. Referring to Table II it is seen that the entire fine 
 structure of H a should cover a spectral range of only 0.2 A. Now the 
 width 13 of a spectral line, assuming it may be accounted for by the 
 Doppler-Fizeau effect, may be shown 14 to be 
 
 A = 0.86 ao~ 6 \VTYM; 
 
 where T is the absolute temperature and M the molecular weight of the 
 radiating gas. 
 
 Since M = 1 for the hydrogen atom it is readily apparent that the 
 precision of measurement of fine structure will be seriously affected 
 by the Doppler effect. Even with the discharge tube immersed in 
 liquid air the theoretical width of each component of H a is 0.051 A. 
 However, the component of longest wave-length should be weak, and it 
 may be shown that the separation of this component and the central 
 component should be only about 4/10 the separation of the central 
 component and the one of shortest wave-length. This results in the 
 obervation of the triplet as a doublet with fairly wide components arising 
 from the Doppler effect. The observed separation of this doublet 
 is obviously not the theoretical doublet separation shown by the braces 
 in the first column of Table II, which has the computed magnitude 
 A*> H = 0.365 cm" 1 . It is possible to compute from the theoretical distri- 
 bution of the lines what magnitude of the doublet separation should be 
 observed. Or conversely, the observed separations when corrected 
 should afford a check upon the theoretical deductions. We have, how- 
 ever, in addition to the distribution of intensity produced by the Doppler 
 effect, in any laboratory experiment, broadenings of each component 
 arising in the Stark effect, imperfect focus upon the plate, spreading 
 of the image on the emulsion, and mechanical difficulties. These 
 effects combine in producing an apparent narrowing of the observed 
 doublet. The following table summarizes the data on H by several 
 observers where we are not certain of the methods employed in deter- 
 mining these various correction factors. In fact, some of these cor- 
 rections have not been applied to the first three values given. * 
 
 13 Measured at the point where the intensity has decreased to 1 !e of its maximum value. 
 
 14 The method of derivation of this and similar formulae is summarized by Nagaoka, 
 Proc. Math. Phys. Soc. Tokyo, 8, pp. 237-43 (1915). 
 
 
28 
 
 ORIGIN OF SPECTRA 
 
 AVB. 
 
 Observer 
 
 Reference 
 
 .34 cm- 1 
 .29 
 .36 
 .35 
 
 Merton 
 Gehrcke and Lau 
 McLennan and Lowe 
 Oldenberg 
 
 Proc. Roy. Soc. 97, p. 307 (1920) 
 Physik. Z. 21, p. 634 (1920) 
 Proc. Roy. Soc. 100, p. 217 (1921) 
 Ann. Physik, 67, p. 453 (1922) 
 
 It is seen that the agreement between the observed and computed 
 values is fairly satisfactory. However, when the measurements are 
 extended to other lines in the Balmer series there appears to be a slight 
 systematic decrease in the doublet separation, measured in cm" 1 , as one 
 proceeds to the higher terms of the series. It is doubtful whether the 
 above-mentioned disturbing effects are adequate to account completely 
 for existing observations on H0, H 7 , and Hj. Ruark has suggested to 
 the authors that there still remain to be considered disturbances arising 
 in (1) finite size of nucleus 15 and (2) possible magnetic moment of 
 nucleus. Any correction arising from a consideration of retarded po- 
 tentials has been shown by Darwin 16 to be less than 0.001 A and to 
 affect all components of a given line in the same mariner. 
 
 The real experimental verification of the theory lies in Paschen' s 
 analysis of certain lines of ionized helium. 17 Since for helium M = 4 
 the Doppler effect is considerably decreased, and since Z = 2 we have 
 a more open scale of v, as is apparent from Equation (22) . The helium 
 line X 4686 is produced by a transfer of the remaining electron in the 
 ionized atom from orbits of total quantum number 4 to orbits of total 
 quantum number 3. Twelve lines are thus mathematically possible, 
 but the application of the Bohr principle of selection reduces this number 
 to five. Figure 2, adapted from SommerfekTs "Atombau," 2d ed., p. 
 350, shows, below, the wave-lengths observed by Paschen, the heights 
 of the shaded portions representing intensity. Above the observed 
 wave-lengths are those computed by means of Equation (22), using the 
 selection principle. At the top, shown by dotted lines, are the mathe- 
 matically possible lines computed directly from Equation (22). The 
 entire wave-length scale covers an interval of only 0.8 A. or about 
 of the distance between the two D-lines of sodium, and yet the theoreti- 
 cally predicted fine structure is well confirmed by the experimental 
 
 14 Silberstein, Phil. Mag. 39, p. 46 (1920), has given the method of computing correc- 
 tions for an aspherical nucleus, 
 is Phil. Mag. 39, p. 537 (1920). 
 i? Paschen, Ann. Physik, 50, pp. 901-40 (1916). 
 
THE QUANTUM THEORY OF SPECTROSCOPY 29 
 
 data. The two lines marked d, while mathematically possible, involve 
 a change in the azimuthal quantum number of two units and hence by 
 the principle of selection should not exist. However, this principle was 
 established conditionally upon the absence of an electrostatic or electro- 
 magnetic field. On the other hand such a field is present in a high 
 voltage discharge tube. A thorough consideration of the phenomena 
 in the presence of disturbing fields requires the application of the quan- 
 tum theory to the Stark and Zeeman effects, 18 quite beyond the scope 
 of the present work. Suffice to say that as a result of such analysis 
 it may be shown that the lines marked d should appear in a weak elec- 
 trostatic field, and still other lines should be excited with higher poten- 
 tials, in agreement with further observations of Paschen. 19 
 
 X 4686.0 5.8 5.6 5.4 
 
 FIG. 2. Fine structure of the helium line X 4686. 
 
 In the case of H a we have seen that the fine structure consists of a 
 fundamental doublet with a satellite. The doublet separation AJ/ H 
 is due to the difference in energy of the two final orbits 1 + 1 = 2 and 
 2 + = 2. This value of A*/ H is readily obtained from Equation (22) 
 by putting AJ> = PI v%, where *>i refers to ri a = 1, n' r = I and any 
 value of n a and n r and where v% refers to n' a = 2, ri r = with the same 
 values of n a and n r . Hence since Z = 1 for hydrogen, we obtain 
 
 (24) 
 
 r =0.365 cm' 1 
 lo 
 
 18 Kramers, Copenhagen Acad., 1919. See also general references 2, 3, 4, 6, 7, at end of 
 chapter. 
 
 19 Paschen, loc. clt. 
 
30 ORIGIN OF SPECTRA 
 
 Now Equation (22) may be rewritten with Na 2 replaced by 16 Av H and 
 the new formula used for estimating the separation of the components 
 of the helium lines in terms of AJ> H - Or conversely, these separations 
 may be determined experimentally for helium and used to compute the 
 value of AJ> H for hydrogen. In this latter manner Paschen found experi- 
 mentally 
 
 AI/H = 0.3645 db 0.0045 cm" 1 , 
 
 in agreement with the theoretical value of Av H given by Equation (24). 
 
 ATOMS WITH MANY ELECTRONS 
 
 Evidence from various sources, both physical and chemical, enables 
 us to derive some information in regard to the distribution of electrons 
 about the nucleus. The periodic table of chemical elements furnishes 
 an important clue as to the electron arrangement. The present view- 
 point is that the intervals between rare gases, and not the rows of the 
 table, give the true periods of the atomic systems. 
 
 The chemical inactivity of the rare gases suggests that these elements 
 represent completed structures. With the intermediate elements only 
 superficial changes in the electron configuration occur. At each new 
 period a " shell" is added to the original structure. An atom is char- 
 acterized by as many groups or " shells" of electrons as the numerical 
 value of the period which it occupies, viz., He one, A three, etc. The 
 number of electrons in each group when completed has been considered 
 equal to the number of elements in the corresponding period. That is, 
 in successive groups from the center out, the number of electrons, on 
 this hypothesis, follows the distribution law 2, 8, 8, 18, 18, 32. 
 
 The new Bohr 20 theory of atomic structure retains the above concep- 
 tion of groups of electrons corresponding to periods in the chemical prop- 
 erties but postulates the occurrence of changes in inner groups as well as 
 in the outer shell. The resulting distribution for several families is given 
 in Table III, in which K, L, M, etc., follow the usual x-ray notation for 
 successive layers. 
 
 As to the orientation of these electrons, many different theories 
 have been proposed. The Lewis-Langmuir 21 hypothesis postulates 
 for each group a cubical distribution of electrons in which motions are 
 limited to relatively small vibrations about positions of equilibrium. 
 Such a model is not easily reconciled with the viewpoint of the spec- 
 troscopist. 
 
 2 Bohr, Z. Physik, 9, pp. 1-67 (1922). 
 
 21 Langmuir, J. Am. Chem. Soc., 38, p. 762 (1916); 41, p. 868 (1919). 
 
THE QUANTUM THEORY OF SPECTROSCOPY 
 
 TABLE III 
 GROUPING OF ELECTRONS IN ATOMS 
 
 31 
 
 Element 
 
 Z 
 
 K 
 
 L 
 
 M 
 
 N 
 
 
 
 P 
 
 Q 
 
 He.. 
 
 Ne.... 
 A 
 Kr ......... 
 Xe 
 
 Nt . ... 
 
 2 
 10 
 18 
 36 
 54 
 86 
 
 2 
 2 
 2 
 2 
 2 
 2 
 
 8 
 8 
 8 
 8 
 8 
 
 8 
 18 
 18 
 18 
 
 8 
 18 
 32 
 
 8 
 18 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 | Li . 
 
 3 
 
 2 
 
 1 
 
 
 
 
 
 
 Na 
 
 11 
 
 2 
 
 8 
 
 1 
 
 
 
 
 
 K .. 
 
 19 
 
 2 
 
 8 
 
 8 
 
 1 
 
 
 
 
 Cu 
 
 29 
 
 2 
 
 . 8 
 
 18 
 
 1 
 
 
 
 
 Rb 
 
 37 
 
 2 
 
 8 
 
 18 
 
 8 
 
 1 
 
 
 
 Ag 
 
 Cs 
 
 47 
 55 
 
 2 
 2 
 
 8 
 8 
 
 18 
 18 
 
 18 
 18 
 
 1' 
 
 8 
 
 1 
 
 
 Au . . . 
 
 79 
 
 2 
 
 8 
 
 18 
 
 32 
 
 18 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 Be 
 
 4 
 
 2 
 
 2 
 
 
 
 
 
 
 Mg. 
 
 12 
 
 2 
 
 8 
 
 2 
 
 
 
 
 
 Ca. . 
 
 20 
 
 2 
 
 8 
 
 8 
 
 2 
 
 
 
 
 Zn 
 
 30 
 
 2 
 
 8 
 
 18 
 
 2 
 
 
 
 
 Sr 
 
 38 
 
 2 
 
 8 
 
 18 
 
 8 
 
 2 
 
 
 
 Cd . 
 
 48 
 
 2 
 
 8 
 
 18 
 
 18 
 
 2 
 
 
 
 Ba 
 
 56 
 
 2 
 
 8 
 
 18 
 
 18 
 
 8 
 
 2 
 
 
 Hg.. 
 
 80 
 
 2 
 
 8 
 
 18 
 
 32 
 
 18 
 
 2 
 
 
 & 
 - Ra 
 
 88 
 
 2 
 
 8 
 
 18 
 
 32 
 
 18 
 
 8 
 
 2 
 
 
 
 
 
 
 
 
 
 
 The configuration originally proposed by Bohr 22 and generally adopted 
 in the past for the extension of the Bohr theory to atoms with many 
 electrons, consisted of coplanar, concentric rings of electrons revolving 
 about the nucleus. The possibility of elliptical orbits complicates the 
 problem, for while several electrons may be stable in the same circular 
 orbit only one electron may occupy an elliptical orbit. However, it is 
 readily possible to so orient a group of similar, coplanar, confocal ellipses, 
 each containing one electron, that at every instant all the electrons of. 
 any one group lie on a circle concentric with the nucleus. 
 
 The recently proposed theory of Bohr (see Appendix II) on which 
 the distribution of electrons in Table III is based, denies the possibility 
 of the formation of a ring model, in spite of its mechanical stability, 
 
 22 See general reference 1 at end of chapter. 
 
32 ORIGIN OF SPECTRA 
 
 and assumes that each electron moves in an individual orbit and in 
 general in an individual plane. The resulting space configuration 
 through which the chemical properties of the elements may be inter- 
 preted leads to insurmountable difficulties in the mathematical analysis 
 of the motion of the electrons in heavy atoms, except for qualitative 
 deductions. 
 
 Accordingly, while recognizing that the electrons are actually re- 
 volving in elliptical orbits in different planes, orbits such that those of 
 greater quantum number and eccentricity may penetrate nearer to the 
 nucleus than those of lesser quantum number but more nearly circular, 
 we shall for the simplification of the mathematical treatment adopt 
 the Sommerfeld 23 conceptions. 
 
 That the postulating of a ring configuration for the inner electrons 
 frequently is an approximation to fact which is justified as far as the 
 motion of an outer electron is concerned will be evidenced by the striking 
 experimental verification of the conclusions drawn in the following 
 sections. 
 
 DERIVATION OF THE RITZ EQUATION 
 
 The Ritz equation represents the variable term in a spectral series 
 formula for elements containing several electrons. The original deriva- 
 tion of this relation was purely empirical, but Sommerfeld 24 has recently 
 shown that it possesses some physical significance. We note from Ta- 
 ble III that the alkalis have one outer electron. As an approximation 
 Sommerfeld assumed that all the other electrons could be considered 
 to be in a single circular orbit. In general then we assume a core of 
 positive charge Ze surrounded by a circular ring of radius ao containing 
 p = Z k electrons, in turn surrounded by the coplanar, and in general 
 elliptical, orbits of the single remaining electron. The outer electron is 
 responsible for the emission pf the ordinary spectral lines. Such an 
 atom resembles the simple structure for hydrogen except that the outer 
 electron is no longer in a Coulomb field, on account of the disturbing 
 action of the ring of electrons. In assuming elliptical orbits we intro- 
 duce two degrees of freedom, requiring as in the general case for hydro- 
 gen, the application twice of the quantizing integral J*pdq = nh. 
 The ring of electrons may be considered as a ring of uniform distribution 
 of charge of total value (Z k)e, and of radius a . We desire the 
 total energy W na n r of the electron in the orbit having as azimuthal and 
 
 ""Atombau." 
 
 " Atombau." 2d ed., Appendixes. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 33 
 
 radial quantum numbers the integers n a and n r respectively and radius 
 vector of length r. This is equal to the sum of the potential energy E P 
 and the kinetic energy T for the same orbit. We find: 
 
 *,--+g+3+..., - (25) 
 
 where ci = j \Z k J e z a Q 2 and c% = ^j [Z k J e 2 a 4 , (26) 
 
 Applying the first quantizing integral: 
 
 r 2 " 
 J pifc = 2 irpt = n a ft. (28) 
 
 Substituting this value of p^ in (27), adding (27) and (25), equating 
 to the total energy W, and solving for p r we obtain for the second quantiz- 
 ing process : 
 
 2 rafce 2 1 n 2 /i 2 2 mci 2 mc2 , , /onN 
 
 -- - 2 ^ 2 53 --- 7S -dr = n r h. (29) 
 
 This complicated integral, evaluated over a complete period, gives: 
 
 JVftcfc 2 
 
 nn W\ 2 > (30) 
 
 - 
 
 The constants a and a in this equation are complicated, but to 
 terms of the first order are as follows: 
 
 _ (2 
 
 
 
 a = - 3 (2 '^'~ 1 * (32) 
 
 ' 
 
 Putting, as heretofore, the difference in total energies of two orbits 
 Wn a n r and W n > an , r equal to he times the wave number of the emitted 
 radiation we obtain the following spectral series formula. 
 1 
 
 v = 
 
 f + fl _ ac(w> a)]2 J (33) 
 
 m = n a -\- n n (m, a) W /he. 
 
 This is the familiar Ritz equation, originally derived empirically. 
 
34 ORIGIN OF SPECTRA 
 
 APPLICATION OF THE RITZ EQUATION 
 
 There are four important series in the arc spectra of the alkalis 
 known as the Principal, 1st Subordinate, 2d Subordinate and Berg- 
 mann Series. Developed empirically these series are represented as 
 follows, where s, o-, p, IT, d, 6, b and |8 are constants. 
 
 Principal : 
 
 N N 
 
 K + s + <r s)] 2 [m + p + TrK p)] 2 
 
 m' =1, m = 2, 3, 4, etc. 
 1st Subordinate: 
 
 * N (35) 
 
 [m' + p + Tr(m',p)] 2 [m + d + (w, d)] 2 
 
 m' = 2, m = 3, 4, 5, etc. 
 2d Subordinate : 
 
 V = K + P + 7rp)] 2 ~ [m + s + <r(m,s)] 2 ' 
 
 m ' = 2, m = 2, 3, 4, etc. 
 Bergmann : 
 
 A T AT 
 
 (37) 
 
 d)] 2 [m + 6 + 0(w, 6)] 2 
 7 r = 3 m = 4, 5, 6, etc. 
 
 The first term in each of the above formulae has a fixed value of m' 
 and is accordingly constant. In shorthand notation these series rela- 
 tions may be written: 
 
 Principal v = 1 s - mp, m = 2, 3, 4 (38) 
 
 1st Subordinate v = 2 p - md, m = 3, 4, 5 (39) 
 
 2d Subordinate v = 2 p - ms, m = 2, 3, 4 (40) 
 
 Bergmann i/ = 3 d ?^6, m = 4. 5, 6 (41) 
 
 On comparing Equations (34) to (37) with Equation (33) we identify 
 a successively with the constants s, p, d and b and ac with the con- 
 stants <T, TT, 5 and ]8. By definition of k we have A; = 1 for the alkalis. 
 Referring to Equation (31) we note that a is proportional to l/n a 3 , i.e. 
 a function of the azimuthal but not of the radial quantum number. 
 Hence in order that a = s be a constant for all the ms terms, such terms 
 must be characterized by a constant azimuthal quantum number, the 
 variation in m = n a + n r being due to the radial quantum number alone. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 35 
 
 Similar conclusions are necessary for the mp, md and mb terms. These 
 conclusions are again substantiated by the fact that a in Equation (32) 
 likewise is a function of n a but not of the variable n r . 
 
 Equation (34) shows that the lowest value 25 of m for the ms terms 
 is 1. Since m = I = n a + n r , and since n a j because this gives the 
 impossible rectilinear vibration through the nucleus, we conclude that 
 n a = 1 for all ms terms. All the ms terms are therefore characterized 
 by an azimuthal quantum number 1 and by a radial quantum number 
 from to oo . The principal series involves combinations of ms and mp 
 terms. By the Bohr principle of selection the azimuthal quantum num- 
 ber n a may change by only + 1 or 1. Hence in the transition from 
 the mp orbit to the ms orbit, since n a cannot be zero, the electron must 
 go from an orbit where n a = 2 to an orbit where n a 1. All mp orbits 
 are therefore characterized by an azimuthal quantum number 2 and 
 by a radial quantum number from to oo . 
 
 We see accordingly a common property in that the radial quantum 
 numbers for both terms may assume any positive integral value includ- 
 ing zero, the latter value referring to a circular orbit. The minimum 
 value of m for the md terms is 3 and for the mb terms 4. Hence if these 
 terms likewise refer to circular orbits, that is if n r can become zero, we may 
 conclude that all md terms are associated with the constant azimuthal 
 quantum number 3 and the mb terms with the azimuthal number 4- 
 These conclusions are summarized in Table IV. 
 
 TABLE IV 
 AZIMUTHAL AND RADIAL QUANTUM NUMBERS 
 
 Variable Term 
 
 Quantum Number 
 
 Azimuthal 
 
 Radial 
 
 ms 
 
 1 
 2 
 3 
 4 
 
 Oto oo 
 to oo 
 Oto oo 
 Oto oo 
 
 mp 
 
 md 
 
 mb 
 
 
 It is now seen why series of the type given by Equations (38) to (41) 
 should predominate and not other combinations. The old Ritz princi- 
 ple of combination stated that any pair of series terms could be used in 
 
 25 Obviously in discussing numerical values of series terms, the symbols m and m', which 
 respectively distinguish initial and final states, are interchangeable: thus 2s = 2's. 
 
36 ORIGIN OF SPECTRA 
 
 combination to give a spectral line. We now associate a definite azimu- 
 thal quantum number with each of the s, p, d and b terms and by the 
 Bohr principle of selection only such combinations may occur for which 
 n a 1 or + 1. Hence we should not expect lines such as v m's 
 nib since these involve a change of three units in the azimuthal quan- 
 tum number. The change in azimuthal quantum number for each of the 
 four series, Equations (38) to (41), is An a = 1. Since the minimum 
 value of n a + n r occurs when n r = 0, we see why these four series begin 
 with peculiar, fixed values of m, the minimum or initial value being 
 determined by the azimuthal quantum number associated with the 
 variable term (except for the 2d subordinate series where m min 
 n a + n r = 1 + D. 
 
 Exceptions to these deductions may be found. A similar excep- 
 tion has been noted with helium where certain components for which 
 An a = 2 appear in a high voltage discharge. Thus with the alkalis we 
 find lines such as v = 2 p mp, Is ms, 3 d md for which the 
 change in azimuthal quantum number is zero. This fact, however, 
 would not be contradictory to the less restricted Rubinowicz principle of 
 selection. A more serious exception occurs in such lines as v = Is md 
 where the change in azimuthal quantum number is two units. All of 
 these exceptions have been, as with helium, attributed to the disturbing 
 effect of the electrostatic exciting field, under which condition their 
 presence is in accord with the theory. Foote, Mohler and Meggers, 26 
 on the other hand observed 1 s 3 d for sodium and potassium in a 
 discharge tube completely shielded from any applied field. The above 
 conclusions are, however, in general well confirmed, and even though 
 the theory is not completely satisfactory, still it contains much of great 
 value and interest. 27 
 
 Since we are concerned in this book only with the more important 
 general principles we are not able to extend the theory to doublet and 
 triplet spectra, 28 which at present is in a less satisfactory state of develop- 
 ment. The spectra of the alkalis are characterized by close doublets, 
 as for example the two D-lines of sodium. The mp terms are associated 
 with double p orbits pi and p 2 of slight energy difference. Hence the 
 lines of the principal series are designated by 1 s mpi and Is mp 2 - 
 Similarly with the metals of the second group of the periodic table which 
 are characterized by rather widely separated triplets arising in the 
 
 26 Phil. Mag., 43, pp. 659-61 (1922). 
 
 27 Probably all of these exceptions can be explained by the electrostatic field arising in 
 neighboring atoms and ions. 
 
 28 Sommerfeld, " Atombau," 3d ed., Chap. 6, Section 5. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 37 
 
 threefold p orbits, pi, p 2 and p s . The latter family also has many single 
 lines grouped in series. Single lines are designated in the same notation 
 except that capital letters are used, as for example 1 S mP, which 
 represents important fundamental lines. We also find for these ele- 
 ments combination series, one term, belonging to the single line group 
 and the other to a triplet group, as for example 1 S mp 2 , another 
 fundamentally important series. 
 
 FINE STRUCTURE, DOUBLETS AND TRIPLETS 
 
 It must be emphasized that the fine structure of hydrogen and of 
 ionized helium has nothing in common with the fine structure, doublets, 
 triplets, satellites, etc., of the more complex elements. It appears rather 
 that the disturbing action of the inner groups of electrons in the complex 
 atoms opens out into several series what would otherwise have been true 
 fine structure. Or put conversely, the components in the fine structure 
 of the Balmer lines of hydrogen are really terms of its principal and 
 subordinate series, which, because of the strictly Coulomb field, are not 
 widely separated. Thus on considering the interorbital transitions 
 involved we may by analogy with the alkalis orient the Balmer lines 
 as shown in Table V. 
 
 TABLE V 
 FINE STRUCTURE OF BALMER LINES 
 
 Line 
 
 n 
 
 'a-i 
 
 - n 
 
 ',- 
 
 J+ 
 
 * 
 
 Series Notation 
 
 Ha 
 
 2 
 
 4. 
 
 
 
 4-3 
 
 + 
 
 
 
 2 
 
 P 
 
 - 3 
 
 d 
 
 1st Sub. 
 
 
 2 
 
 + 
 
 
 
 4-1 
 
 + 
 
 2 
 
 2 
 
 P 
 
 - 3 
 
 s 
 
 2d Sub. 
 
 
 1 
 
 + 
 
 1 
 
 4-2 
 
 
 1 
 
 2 
 
 s 
 
 -3 
 
 P 
 
 Prin. 
 
 H, 
 
 2 
 
 + 
 
 
 
 4-3 
 
 + 
 
 1 
 
 2 
 
 p 
 
 4 
 
 
 1st Sub. 
 
 
 2 
 
 + 
 
 
 
 4-1 
 
 + 
 
 3 
 
 2 
 
 p 
 
 - 4 
 
 s 
 
 2d Sub, 
 
 
 1 
 
 + 
 
 1 
 
 4-2 
 
 + 
 
 2 
 
 2 
 
 s 
 
 4 
 
 p 
 
 Prin. 
 
 etc. 
 
 
 
 
 
 
 
 
 
 
 
 
 NUCLEAR DEFECT OF A RING OF ELECTRONS 
 
 In succeeding discussions it is necessary to consider the shielding 
 action on the nucleus by a ring of several electrons. From purely 
 geometrical considerations, assuming the inverse square law, it may be 
 shown that the force, which is radial, acting on any one of n electrons, 
 
38 ORIGIN OF SPECTRA 
 
 symmetrically distributed in a ring, of radius a , with the charge + Ze 
 at the center, is: 
 
 Ze* e 2 *"f ' irk ,, ON 
 
 = --- I *>**- 
 
 = 2 (Z-s n ), (43) 
 
 - t=re-l , 
 
 where s = I 2 cosec- (44) 
 
 t-i 
 
 The quantity s n is called the nuclear defect of the ring of n electrons and 
 Z' = Z s^the " effective" core charge. For large values of n, above 
 10 to 20, we may represent s n approximately by the simple formula: 
 
 s n = - (nat In n + 0. 12) . (45) 
 
 & 7T 
 
 The radius of a single ring of n electrons about a nuclear charge Ze is as 
 follows : 
 
 h &h fAa\ 
 
 a = z^ a = z 
 
 where a h is the radius of the hydrogen atom. From Equations (1) 
 and (3) we find for an azimuthal quantum number 1 : 
 
 h 2 
 
 In case the electrons are distributed in two concentric rings, in 
 accordance with our interpretation of the quantum theory, we assign 
 to each electron in the inner ring one unit of angular momentum and to 
 each electron in the outer ring two units. Hence for a ring of radius ai 
 containing p electrons and an outer ring of radius a 2 containing q electrons 
 we find: 
 
 The total energy of the p electrons in the inner ring and that of the q 
 electrons in the second ring may be shown to have the values : 
 
 ,,, Nhc,~ /F ^v 
 
 wp 9 * -P -rr ( z ~ S P) > ( 5 ) 
 
THE QUANTUM THEORY OF SPECTROSCOPY 39 
 
 & ~ P ~ s) 2 . (51) 
 
 AJ 
 
 It should be noted in Equations (49) and (51) that the inner ring is 
 considered to be sufficiently close to the nucleus so that, as far as the 
 outer ring is concerned, its nuclear defect is p, these p electrons simply 
 decreasing the core charge by their total value pe. Similarly in Equa- 
 tions (48) and (50) the effect of the outer ring is neglected. It is 
 accordingly evident that in considering the orbits of a single electron 
 revolving outside of other rings of electrons, the number of electrons in 
 the outer ring is a predominant factor, the exact distribution in the inner 
 rings being of minor importance. 
 
 SPARK SPECTRA 
 
 Spectral lines which arise in ionized atoms are called enhanced or 
 spark spectra. Formerly they could be produced in the laboratory 
 only by high voltage condenser discharge whence the terminology 
 " spark" spectra. We have already considered the enhanced spectrum 
 of ionized helium and shall now discuss the spectra of the ionized alkali 
 earths. Referring to Table III, we note that the normal atoms in this 
 group all contain two electrons in the outer ring. We shall assume that 
 one of these has been removed by the process of ionization. The struc- 
 ture then becomes identical with that of the alkali of next lower atomic 
 number except that the core charge is one unit greater. This is equivalent 
 to putting k z = 4 in Equation (33). The enhanced spectrum of ionized 
 magnesium, accordingly, should resemble the arc spectrum of sodium, 
 and similarly for the other pairs of elements in these two groups. The 
 variable series term for these enhanced lines should by Equation (33) 
 take the form : 
 
 = !# ( <m 
 
 v rt i u ) T M i I * ..* / ~*MO \y*/ 
 
 We note that since k = 2, the factor k*N (= 4 N = A) appears in 
 the variable term of the enhanced spectra instead of simply N. This 
 fact is fairly 'well substantiated by empirical computation 29 as shown 
 in Table VI. 
 
 29 Since this was written, Fowler's book on "Series in Line Spectra" has appeared. He 
 has recomputed these series, using A - 4N as predicted by theory. Table VI is accordingly 
 of historical interest only. See section on " Spectroscopic Tables." 
 
40 
 
 ORIGIN OF SPECTRA 
 
 TABLE VI 
 CONSTANT IN ENHANCED SERIES FORMULAE 
 
 Element 
 
 Series 
 
 Constant = A 
 
 A/N 
 
 Me: 
 
 1st Sub 
 
 423377 
 
 3.9 
 
 Sr 
 
 2d Sub. 
 1st Sub 
 
 413202 
 410836 
 
 3.8 
 3.7 
 
 Ca 
 
 2d Sub. 
 1st Sub. 
 
 415157 
 423416 
 
 3.8 
 3.9 
 
 Ba 
 
 2d Sub. 
 1st Sub. 
 
 421559 
 390431 
 
 3.8 
 3.6 
 
 
 2d Sub. 
 
 397795 
 
 3.6 
 
 We shall now discuss the relation between the constants a* for 
 enhanced spectra of the alkali earths and the constants a for the arc 
 spectra of the alkalis. In order to approximate physical conditions 
 more closely, as shown by Table III, we shall consider two rings of elec- 
 trons about the core, besides the orbit of the valence electron, the outer 
 ring of radius a 2 containing, according to Table III, q = 8 electrons and 
 the inner ring of radius a\ containing p = Z q k electrons. The 
 remaining valence electron revolves about this entire structure. More 
 rings could be assumed, for example four with strontium, but as already 
 pointed out, these are unnecessary refinements as far as the orbits of the 
 valence electron are concerned. 
 
 The expression for a as derived by Sommerfeld for a single ring 
 (radius a ) of electrons is given by Equation (31) where k = 1. The 
 value of a* is likewise determined by (31) where k = 2. This relation 
 involves Ci which is by Equation (26) proportional to a 2 . We see, how- 
 ever, by Equation (46) that a depends upon the nuclear charge and hence 
 is different for Mg and Na, and other corresponding pairs of elements. 
 This shrinkage of the ring when the nuclear charge increases by one 
 unit must be considered in determining the ratio a* /a. Now the addi- 
 tion of a second ring simply alters the value of c\ in Equation (31). 
 
THE QUANTUM THEORY OF SPECTROSCOPY 
 
 41 
 
 Taking this into account as well as allowing for changes in the radii of 
 the two rings as determined by Equation (48) we find: 
 
 P 
 
 16 
 
 (q + 2 - s.y 
 
 P 
 
 16 
 
 (53) 
 
 (Z - s p )* ' (q + 1 - Sq )* 
 
 where Z* = Z + 1 is the atomic number of the alkali earth and Z is 
 the atomic number of the alkali. For the doublet system of enhanced 
 lines we use precisely the same formulae Equations (38) to (41) as for 
 the arc spectra of the alkalis except that we replace s, p, d and 6 by the 
 letters @. $, $) and 23 respectively. Table VII shows the values of the 
 empirically determined series constants. The last column gives the 
 ratio a* /a computed by Equation (53) . This agrees with the empirical 
 ratios, again substantiating our theory. 
 
 TABLE VII 
 
 RELATION BETWEEN a* AND a 
 
 
 
 * 
 
 
 
 
 a* -T- a 
 
 
 Elements 
 
 a* = 
 
 a = s 
 
 a* = 9) 
 
 a = p 
 
 <5/s 
 
 %/P 
 
 Com- 
 puted 
 
 Mg/Na 
 
 .93 
 
 .65 
 
 30 
 
 15 
 
 1 43 
 
 200 
 
 148 
 
 Ca/K 
 
 1.20 
 
 .82 
 
 .50 
 
 .29 
 
 1 46 
 
 1.72 
 
 1.49 
 
 Sr/Rb 
 
 1 32 
 
 81 
 
 61 
 
 36 
 
 1 63 
 
 1 70 
 
 1 66 
 
 Ba/Cs 
 
 1.43 
 
 95 
 
 75 
 
 45 
 
 1 50 
 
 * 
 
 1 66 
 
 1.66 
 
 
 
 
 
 
 
 
 
 We may therefore conclude that in all detail the enhanced spectrum 
 of an alkali earth resembles the arc spectrum of the alkali of next lower 
 atomic number. This relation may be extended to other pairs of ele- 
 ments. If we remove the valence electron from sodium the configura- 
 tion is similar to that of neon, as seen from Table III. Hence the spark 
 spectrum of sodium should resemble the arc spectrum of neon, and 
 similarly for the other pairs of elements in these two groups. Such is 
 observed, qualitatively, to be the case. Quantitative evidence is not 
 at hand, since the series relations are as yet unknown for the spark 
 
42 
 
 ORIGIN OF SPECTRA 
 
 spectra of the alkalis and are not known at all completely for the rare 
 gases. But both are alike in their complexity of structure. With 
 these and a few other facts Kossel and Sommerfeld 30 proposed a general 
 ''displacement law" for spectra as summarized in Table VIII. 
 
 TABLE VIII 
 
 RELATION OF ARC AND SPARK SPECTRA 
 
 Group 
 
 VIII, 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 V 
 
 VI 
 
 VII 
 
 Arc.... 
 Spark. . 
 
 complex 
 and 
 triplets 
 ? 
 
 doublet 
 
 complex 
 (and 
 triplets?) 
 
 triplet 
 doublet 
 
 doublet 
 triplet 
 
 triplet? 
 doublet? 
 
 doublet? 
 triplet? 
 
 triplet 
 doublet 9 
 
 ? 
 
 triplet? 
 
 Where a question mark appears, the series relations have not been as yet 
 untangled in the maze of spectral lines. The displacement law states 
 that the spark spectrum of any simply ionized element resembles the 
 arc spectrum of the element of next lower atomic number. 
 
 If an element loses two electrons its spectrum should be similar 
 to the arc spectrum of the element of second lower atomic number. 
 There is some indication of this second type of enhanced spectra in the 
 spark spectra of carbon and' of silicon, but nothing definite has been as 
 yet established. The doubly ionized lithium atom should give a spec- 
 trum identical to hydrogen except that the important lines should lie in 
 the extreme ultra-violet. The wave numbers should obey the approxi- 
 mate relation, analogous to Equation (9) : 
 
 v q AT 
 
 v - y/v 
 
 The series for which n' 1, converges at 9 N or about X 101 A, a spectral 
 region of soft x-rays. Lines in series for higher values of n', which lie 
 in the neighborhood of the visible spectrum, have at times been thought 
 to have been detected in stellar spectra, but the evidence is not conclu- 
 sive. 
 
 The spectrum of a negatively charged atom, one which has attached 
 an extra electron, should resemble the arc spectrum of the element of 
 next higher atomic number. 
 
 so Kossel and Sommerfeld, Verh. d. Phys. Ges., 21, pp. 240-59 (1919). 
 
THE QUANTUM THEORY OF SPECTROSCOPY 43 
 
 From the foregoing discussion it appears that the behavior of the 
 elements as regards their spectra is analogous to that in radioactive 
 transformations where the emission of an alpha particle gives rise to an 
 element two steps to the left in the periodic table and the emission of a 
 beta particle, an element one step to the right. 
 
 SPECTROSCOPIC TABLES 
 
 Until recently there have been but three tables of wave-lengths 
 available in which the lines have been correlated in series according 
 to formulae of the Ritz or similar type; that of Dunz, 31 a supplement to 
 Dunz's tables prepared by Lorenser 32 and these same tables arranged 
 with a different notation in a book by Konen. 33 In these tables the 
 numerical values of all the variable terms in series formulae are con- 
 veniently tabulated. 
 
 The notation employed by Dunz and Lorenser is that of Paschen. 
 Paschen originally proposed for all the ms terms, half integer values for 
 m such as 1.5 s, 2.5 s etc. Later it was found that the J possessed no 
 physical significance and hence more recent writers have included this 
 factor in the series constant a of Equation (33). Whole numbers are 
 therefore assigned to n a + n r = m, viz. I s, 2 s etc., just as has been 
 always done with the mp and other variable terms. Also the variable 
 term mAp used by earlier writers for the Bergmann series has been 
 changed to mb. Accordingly the only modification necessary to the 
 tables of Dunz and Lorenser, excluding errors, is the subtraction of J 
 from each value of m which refers to a ms or mS term and the substitu- 
 tion of mb for raAp. However, since these tables were printed much more 
 precise spectroscopic data have become available, especially in enhanced 
 spectra which have been materially revised, and the entire subject has 
 been brought up to the date April, 1921, by Fowler 34 in a book of nearly 
 200 pages, published March, 1922. 
 
 The vast quantity of data in this book was computed before the 
 physical significance of the revised Paschen notation was appreciated. 
 A notation is employed which is just enough different from the now 
 generally preferred notation to be confusing to the beginner in this 
 subject. The following table lists the essential differences between the 
 revised Paschen notation which is employed in this book and Fowler's 
 notation. One should familiarize himself with both notations; with 
 the first in order to appreciate the physical significance on the basis of 
 
 31 Dunz, Tubingen Dissertation, 1911. 
 
 32 Lorenser, Tubingen Dissertation, 1913. 
 
 33 Konen, "Das Leuchten der Gase und Dampfe. " 
 
 34 See general reference 5 at end of chapter. 
 
44 
 
 ORIGIN OF SPECTRA 
 
 Sommerfelpl's interpretation, with the second in order to obtain readily 
 the numerical values from Fowler's tables. 
 
 Revised Paschen Notation 
 
 Fowler 
 
 Notation 
 
 1 
 
 5, 
 
 2 
 
 S 
 
 1 
 
 S 
 
 2 
 
 S 
 
 
 
 
 2P, 
 
 3 
 
 P 
 
 1 
 
 p 
 
 , 2 
 
 P 
 
 
 
 
 3 
 
 D. 
 
 4 
 
 D 
 
 2D 
 
 , 3 
 
 D 
 
 
 
 
 1 
 
 s, 
 
 2 
 
 s 
 
 1 
 
 s, 
 
 2 
 
 s 
 
 or 
 
 I'f. 
 
 2(7 
 
 2 
 
 P 
 
 3 
 
 P 
 
 1 
 
 
 2 
 
 P 
 
 or 
 
 ITT, 
 
 2-7T ' 
 
 3 
 
 d, 
 
 4 
 
 d 
 
 2 
 
 
 
 3 
 
 d 
 
 or 
 
 26, 
 
 35 
 
 4 
 
 5 
 
 5 
 
 b 
 
 3 
 
 */ ? 
 
 4 
 
 f 
 
 or 
 
 o (p 
 
 4 <f> 
 
 1 
 
 > 
 
 2 
 
 (5 
 
 1 
 
 
 2 
 
 <T 
 
 
 
 
 2 
 
 ro 
 
 3 
 
 ? 
 
 1 
 
 7T, 
 
 2 
 
 7T 
 
 
 
 
 3 
 
 ^ 
 
 4 
 
 5) 
 
 26, 
 
 3 
 
 6 
 
 
 
 
 4 
 
 , 
 
 5 
 
 33 
 
 3 
 
 <t> 
 
 4 
 
 4> 
 
 
 
 
 In Fowler's notation, singlet, doublet and triplet series are dis- 
 tinguished respectively by capital, Greek and small letter abbreviations. 
 The ordinal numeral m, however, may be different from that in the revised 
 Paschen notation. The following examples serve as illustrations. 
 
 Series 
 
 Notation 
 
 Revised Paschen 
 
 Fowler 
 
 Principal series of doublets of alkalis 
 
 1st subordinate (diffuse) series of 
 doublets of alkalis 
 
 2d subordinate (sharp) series of 
 doublets of alkalis 
 
 Bergmann (fundamental) series of 
 doublets of alkalis .... 
 
 Principal series of triplets of alkali 
 earths 
 
 1st subordinate series of triplets of 
 alkali earths 
 
 2d subordinate series of triplets of 
 alkali earths 
 
 Principal series of singlets of alkali 
 earths , 
 
 Combination series of singlets of al- 
 kali earths 
 
 Principal series of doublets of ionized 
 alkali earths. . 
 
 1st subordinate series of doublets of 
 ionized alkali earths 
 
 2d subordinate series of doublets of 
 ionized alkali earths . . . 
 
 Is mp, m = 2, 3 
 
 2 p md, m = 3, 4 
 
 2 p ms, m = 2, 3 
 
 3d w6, m = 4, 5 
 
 Is mp, m = 3, 4 
 
 2 p md, m = 3, 4 
 
 2 p ms, m = 1, 2 
 
 1 mP, m = 2, 3 
 
 1 /S mpa, m = 2, 3 
 
 1 - m9>, m = 2, 3 
 
 2 9) - m, m = 3, 4 
 2 9) m, m = 2, 3 
 
 Iff 
 
 I 7T 
 
 ITT 
 25 
 Is 
 lp 
 Ip 
 IS 
 IS 
 Iff 
 ITT 
 ITT 
 
 mir, m 
 
 md, m 
 
 mff, m 
 m <f>, m 
 mp, m 
 md, m 
 ms, m 
 
 mP, m 
 mp 2 , m 
 mw, m 
 md, m 
 mff, m 
 
 1,2 
 2,3 
 2,3 
 3,4 
 2,3 
 2,3 
 1,2 
 1,2 
 1,2 
 1,2 
 2,3 
 2,3 
 
THE QUANTUM THEORY OF SPECTROSCOPY 45 
 
 These are merely some of the more striking differences in the nota- 
 tions. For the minor differences in the many combination series, refer- 
 ence must be made to the original tables. Throughout this book we 
 shall refer to fundamental lines as those belonging to series converging 
 at 1 s, 1 S or 1 @. They are lines concerned with interorbital transitions 
 for which one orbit represents the normal state of the unexcited atom. 
 They are accordingly fundamentally important lines from the standpoint 
 of atomic structure. Fowler and some other English and American 
 writers use the term " fundamental" in reference to what we have called, 
 following the German custom, the Bergmann series. While the latter 
 nomenclature undoubtedly gives unwarranted credit to Bergmann it is 
 preferred to the nomenclature " fundamental," since physically this 
 series is quite remote from fundamental. 
 
 In the computation of series limits and variable terms Fowler em- 
 ploys the Hicks instead of the Ritz formula as follows : 
 
 , N 
 
 K O) jTT 2 ' ( A) 
 
 Referring to Equations (33) to (37), the variable term of the Ritz formula 
 takes the form 
 
 Carrying out the expansion involved by (m, a) in the denominator and 
 dropping terms beyond m which are relatively small, especially when m 
 is large, we obtain: 
 
 (*>- _ N a cNf- (C) 
 
 On comparing this to (A) we note that since in (A) the ordinal number m 
 occurs as the first power in the third term of the denominator while in 
 (C) it occurs as the square, a' is not identical with acN and a may differ 
 somewhat from a'. 
 
 Since Fowler also uses different values of m, the numerical values of 
 all variable series terms (m, a) will be very slightly different when com- 
 puted by the two formulae. Fortunately the third term in the de- 
 nominator is small, a correction term, so that these discrepancies are of 
 little importance. A series line is always made up of the difference of 
 two terms and is so computed that the difference is practically the same 
 with each system of notation, since it must give the observed line. Limits 
 
46 ORIGIN OF SPECTRA 
 
 however are not observed, but are computed values, and accordingly 
 depend somewhat upon the type of formula chosen. We may therefore 
 expect to find small differences in series limits in tables computed in 
 different manners. While these computed frequencies may be known to 
 six significant figures on the basis of a specified formula, different formulae 
 may disagree in the fifth figure or to even 10 parts in 50,000, and in 
 certain cases where but few series terms are known, the differences 
 may be very much greater. 
 
 In this book we are not concerned with computation of series limits 
 but as will appear later we are interested in the actual physical value 
 of convergence wave numbers regardless of the method whereby they 
 are obtained. From this standpoint many of the limits listed in our 
 tables are probably not certain by ten units. However, this small un- 
 certainty is of negligible significance when referred to ionization po- 
 tentials, energy levels in the atom, etc. 35 
 
 In applying deductions from the theoretical derivation of the Ritz 
 equation to values of the spectral series constants a and ac of Equation 
 (B) as was done for example in Table VII, one should use the constants 
 determined by the Ritz rather than by the Hicks equation. Even here 
 however the differences are usually trivial when one considers that the 
 theory in its present state is only qualitatively verified. 
 
 X-RAYS 
 
 One of the greatest successes of the quantum theory of spectroscopy 
 is its application to the interpretation of x-ray spectra. 36 The char- 
 acteristic x-ray spectra of an element may be grouped in series designated 
 as the K, L, M, etc., series. The K radiation, which is of the shortest 
 wave-length, is produced by an interorbital transfer where the final 
 orbit is the inmost one in the atom. Figure 3 shows schematically how 
 the various prominent x-ray lines are excited. Ka, the line of longest 
 wave-length in the K series, is produced by an electron falling from the 
 L ring to the K ring. La, the line of longest wave-length in the L 
 series, is produced by an electron falling from the M ring to the L ring. 
 The second line of the K series, K&, arises in a transition between the 
 M and K rings. The limit of any series is the frequency determined 
 by an electron falling from outside the atom into a vacant space in the 
 
 35 Inconsistencies between the data given in the illustrations and tables, in this book, 
 amounting to 5 or less units, may occur occasionally, since the latter have been revised in the 
 proof to fit the latest available figures. These differences, however, are of little significance. 
 
 36 See Chapter IX for detailed discussion. 
 
THE QUANTUM THEORY OF SPECTROSCOPY 47 
 
 corresponding ring. Since, as seen from Table III, the inner rings con- 
 cerned with the production of x-rays all contain several electrons, the 
 spectral series relations cannot be given by a simple formula of the 
 Balmer type. It is necessary to consider the modifying effect of the 
 other electrons in the various rings. 
 
 M 
 
 Limit 
 
 FIG. 3. Simple diagram showing prominent x-ray lines. 
 
 The Ka line, for elements of atomic number 10 or greater, is probably 
 the result of an interorbital transition represented as follows, where the 
 figures and letters denote numbers of electrons in the groups specified 
 
 K-r'mg L-ring M-ring 
 
 initial condition 1 8 r 
 
 final condition 2 7 r 
 
 By aid of Equations (50) and (51) we shall compute the total energy of 
 the rings in the initial and in the final conditions. 
 
 Initial Condition: W p = - NhcZ\ (54) 
 
 W q = - 2Nhc(Z - 3.80) 2 , (55) 
 
 rNhc 
 
 W r = - 
 
 (56) 
 
48 
 
 ORIGIN OF SPECTRA 
 
 Final Condition: W p = - 2Nhc(Z - 0.25) 2 , 
 
 W q = - l.75Nhc(Z - 4.30) 2 , 
 
 W T = - 
 
 (57) 
 (58) 
 
 (59) 
 
 Subtracting the value of the total final energy from that of the total 
 initial energy and equating this to hcv we obtain : 
 
 For Ka i = Z 2 (p - i) - 0.85 Z + 3.6. (60) 
 
 The first term in this expression is the simple formula representing the 
 transition of an electron from orbit 2 to orbit 1, analogous to Equation 
 (6) for hydrogen. The second and third terms are due to the disturbing 
 action of the other electrons. While a formula derived in the above 
 manner is of great interest if in only qualitative agreement with experi- 
 ment, unfortunately this equation leaves much to be desired from the 
 quantitative standpoint. The introduction of relativity considerations 
 does not alter materially the computations for elements of low atomic 
 number and the effect, here neglected, of the electrons in the outer 
 rings on the energy of the inner rings, is also of a small order of 
 magnitude. It is of interest to note that if in Equation (57) instead of 
 s p = 0.25 we arbitrarily put s p = 0.45 we obtain : 
 
 For Ka jj = Z * 0* ~ &) ~ 1 ' 65 Z + 3 ' 88 ' (61) 
 
 This relation agrees excellently with experiment as shown by Table IX. 
 
 TABLE IX 
 
 COMPUTATION OF v/N FOB THE LINE Ka FOB ELEMENTS OF Low 
 
 ATOMIC NUMBEB 
 
 Element 
 
 Z 
 
 Computed v/N 
 
 Observed v/N 
 
 Na. . 
 
 11 
 
 76.5 
 
 76.6 
 
 Mg.. 
 
 12 
 
 92.1 
 
 92.0 
 
 Al 
 
 13 
 
 109.2 
 
 109.3 
 
 Si 
 
 14 
 
 127.8 
 
 1280 
 
 P 
 
 15 
 
 147.9 
 
 148.0 
 
 s 
 
 16 
 
 169.5 
 
 170.0 
 
 Cl 
 
 17 
 
 192.6 
 
 193.4 
 
 K 
 
 19 
 
 243.3 
 
 243.8 
 
 Ca 
 
 20 
 
 270.9 
 
 271.3 
 
 
 
 
 
THE QUANTUM THEORY OF SPECTROSCOPY 49 
 
 Just as is the case with hydrogen and ionized helium where we find 
 each line made up of several components, so with x-rays. Instead of the 
 simple structure schematically indicated by Figure 3, many other x-ray 
 lines are observed. A two-quantum L electron may move in either a 
 circle or an ellipse. Likewise the M orbits of quantum number three 
 may be either a circle or two types of ellipses. Hence we obtain doublet 
 separations in the K and L spectra, due to the two forms of L orbits. 
 The fine structure of x-ray lines, which is still more complicated than 
 that just indicated, will be described in detail in Chapter IX. It is 
 of interest here merely to mention the Sommerfeld derivation of the 
 magnitude of the L-doublet separation as obtained, from relativity 
 considerations. The method is analogous to that used in deriving 
 Equation (24) for the hydrogen doublet. Employing Equation (20) 
 we compute the energy of a single electron for the orbit n a + n r = 1 + 1 
 and for the orbit n a + n r = 2 + 0. The difference in these energies is 
 equal to hckv. One point must be noted, however, in that instead of 
 the atomic number Z, we use Z' = Z z. This is simply another 
 method of correcting for the effect of the other electrons in the atom. 
 For most of the elements z = 3.50, empirically determined, but it is 
 evident that this is only an approximate method for representing nuclear 
 defect and cannot be applied to elements of very low atomic number. 
 
 We accordingly obtain from Equation (20) the following relation 
 in which the development is carried as far as the sixth power of the 
 constant a. 
 
 A, = ATZ'l + z' + -+ . . . . (62) 
 
 Replacing Na 2 by 16 AJ> H , Equation (24), we may compute the L-doub- 
 let separation for any element in terms of the separation of the hydro- 
 gen doublet. As an example, for uranium, Z f = 92 3.50, we find 
 
 A^ = 8.17 10 7 Av H = 2.98 10 7 cm- 1 . 
 
 The observed doublet separation for uranium is 3.02 10 7 cm" 1 , in excellent 
 agreement with the above computed value which represents an extra- 
 polation of eighty million-fold. We here see that the fine structure of 
 the hydrogen Balmer lines is carried throughout the entire range of 
 elements, appearing in their K and L x-ray spectra, on an increasingly 
 greater scale of magnification as the atomic number progresses. 
 
50 
 
 ORIGIN OF SPECTRA 
 
 GENERAL REFERENCES 
 
 (1) Bohr, Phil. Mag., 26, pp. 1, 476, 857 (1913); idem., 27, p. 506 (1914); idem., 
 29, p. 332 (1915); idem., 30, p. 394 (1915). 
 
 (2) Bohr, The Quantum Theory of Line Spectra, Parts I and II, Danish Academy 
 of Science, 100 pp. (in English). 
 
 Series Spectra of the Elements, Zeit. Physik, 2, pp. 422-69 (1920). 
 Structure of Atoms and the Physical and Chemical Properties of the Elements, 
 Zeit. Physik, 9, pp. 1-67 (1922). 
 
 (3) Sommerfeld, Atomic Structure and Spectral Lines, 3d Edition, 764 pp. (1922). 
 
 (4) Silberstein, Report on the Quantum Theory of Spectra, 42 pp. (1920). A 
 splendid synopsis of the theoretical development to this date. 
 
 (5) Fowler, Report on Series in Line Spectra, 183 pp. (1922). The most com- 
 prehensive catalog of series spectra ever published. 
 
 (6) Adams. The Quantum Theory, Bull. Nat. Res. Coun., 1, pp. 301-81 (1920). 
 
 (7) Page, Dynamic Theories of Atomic Structure, Bull. Nat. Res. Coun., 2, 
 pp. 356-95 (1921). 
 
Chapter II 
 Energy Diagrams 
 
 It is convenient to represent the various stationary states of a 
 radiating atom by schematic diagrams. For" example, in the case of 
 hydrogen the total energy of the atom is a minimum when the electron 
 is in the inmost orbit, total quantum number 1, as is evident from 
 Equations (3), (17) or (20). When the electron is displaced to infinity, 
 or just outside the sphere of influence of the core, which practically is a 
 very small distance, the total energy is all potential and is a maximum. 
 Between these two positions we have many orbits where the electron 
 assumes intermediate values of the total energy corresponding to the 
 total quantum numbers n = 2, 3, 4, etc. In general it is more con- 
 venient to consider instead of the total energy of the electron, the amount 
 of work required to displace it from an inner to an outer orbit. Hence 
 to the inmost orbit is ascribed the largest numerical value of the work, 
 this being the work necessary to displace the electron to infinity. Such 
 a diagram for hydrogen is shown in Figure 4. The first orbit, n = 1, 
 corresponds to 215.6 X 10~ 13 ergs; the second to 53.9; the third to 23.95, 
 etc. That is, it requires 215.6 X 10 ~ 13 ergs to completely remove the 
 electron from its inmost stable position in the hydrogen atom, and 53.9 
 X 10~ 13 ergs to remove it from the second orbit, etc. The various 
 series lines of hydrogen are shown on this diagram. For example H a 
 represents a transition from orbit 3 to orbit 2. Referring to the energy 
 scale on the right we accordingly find that this represents an energy 
 change of 3 X 10" 12 ergs. (This value is obtained by taking the differ- 
 ence between the energy values corresponding to the head and tail of 
 the arrow marked a. Note that logarithms of energy are plotted on the 
 left in order to obtain an open scale.) Similarly the energy required to 
 produce an emission of one quantum of any frequency represented by 
 'the series lines of hydrogen may be read from this plot. On the com- 
 pressed scale of the diagram the fine structure of the various lines is not 
 indicated. Actually orbit 2 is double and orbit 3 triple, as explained 
 earlier in the text, cf. page 27. 
 
 51 
 
52 
 
 ORIGIN OF SPECTRA 
 
 Usually in such diagrams we are more concerned with the wave 
 number v of the radiation. It is accordingly desirable to plot instead 
 of log energy the equivalent value of log v. In this case the difference 
 
 - oo 
 
 
 
 
 ! ErgsxlO 13 
 
 
 0.6 
 0.8 
 1.0 
 
 r-i 
 
 __ 
 
 
 
 i 
 i 
 
 n ^ rrrt 
 
 W 
 
 
 > ' 
 J_) 
 
 co 
 
 
 
 
 
 0Fi OO 
 
 
 
 ( 
 
 ! 
 
 
 
 
 
 (4 i^.WW 
 
 C 
 
 + 
 
 - 
 
 
 
 1 
 "i 
 
 / 
 
 
 
 
 
 
 
 fi - 
 
 - 
 
 
 
 / 
 
 $ 
 
 
 
 
 
 
 
 
 u 
 o 
 
 X 
 
 &1.4 
 
 
 
 
 
 
 
 
 
 
 
 
 L 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 Paschen 
 
 X3 
 
 0) 
 
 
 
 
 
 a 
 
 
 
 
 
 
 
 ^ 
 
 
 be 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C 
 
 
 J ! - 6 
 
 1.8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 E 
 
 3 
 
 2c R* 7 on 
 
 
 - 
 
 
 
 
 
 Balmer 
 
 3 
 
 Or 
 
 
 
 2.0 
 
 - 
 
 
 
 
 
 
 
 
 
 1 
 efl 
 
 c- 
 
 o 
 
 00 
 
 > 
 2 
 
 
 2.2 
 2.4 
 
 ~ 
 
 
 
 
 
 
 
 
 
 1 
 
 1 jMR fin 
 
 2 
 
 
 Lyman 
 
 
 FIG. 4. Energy diagram for hydrogen. 
 
 in wave numbers corresponding to the initial and final orbits gives di- 
 rectly the wave number of the emitted radiation. Such a diagram for 
 sodium is shown in Figure 5. All of the p-orbits are really double, but 
 their separation is indistinguishable on this small scale of wave numbers. 
 
ENERGY DIAGRAMS 
 
 53 
 
 Each D-line is represented by a transition from the initial 2 p orbit 
 to the final 1 s orbit, and its wave number is given by the difference 
 in wave numbers corresponding to these two energy levels 24472 or 
 24489 to 41449. Similarly for all other lines as far as shown on the 
 
 
 - 4149 
 
 
 
 4386 
 
 
 
 
 
 4412 
 
 
 ^ 7 
 
 
 5074 
 
 
 
 
 
 
 
 6403 
 
 
 
 
 
 
 
 6859 
 
 
 _ 
 
 
 
 
 
 
 
 6897 
 
 
 3.9 
 
 
 
 
 
 
 8248 
 
 
 4.0 
 
 
 
 
 
 
 
 
 
 
 
 en 
 
 T > 
 
 
 
 
 
 
 
 
 11,175 
 
 ;> 
 
 
 
 
 
 
 
 
 
 
 
 12,274 
 
 4.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C\J 
 
 
 
 
 
 
 
 
 
 
 
 
 in 
 
 4.2 
 
 
 
 
 
 
 
 
 
 
 15,706 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4.3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 24,472 
 
 
 4.4 
 
 *"* 
 
 
 
 
 B 
 
 s 
 
 24,489 
 
 
 4.5 
 
 - 
 
 
 
 1 
 S 
 
 11 1? If 1 
 
 <go, . Si. *4 o 
 
 
 
 
 
 
 
 
 
 t-H O3 n 
 
 3 f^ J 
 
 J) tO m 
 
 
 4.6 
 
 - 
 
 
 
 0, 
 
 ?-i co 
 
 ^ 41,449 n 
 
 (SI 
 
 FIG. 5. Schematic representation of the arc spectrum of sodium. 
 
 5p 
 
 5b 
 5d 
 
 4s 
 
 4p 
 4b 
 4d 
 
 3s 
 
 3p 
 3d 
 
 2s 
 
 2p 
 
 Is 
 
 plot (to the term 5 p). The first four lines of the principal series are 
 indicated by arrows terminating at the convergence frequency 1 s, the 
 electron falling from 2 p, 3 p, 4 p, 5 p respectively to 1 s. The first lines 
 of the 1st and 2d subordinate series are indicated by arrows terminating 
 at the convergence frequency of these two series, etc. 
 
54 
 
 ORIGIN OF SPECTRA 
 
 90U9IBA OMJ, < 
 
 
 
 CO II -' 
 
 - 1 ' 
 
 
 Ni" 
 
 
 
 o 
 
 o 
 
 ^ 
 
 
 
 ^^ 
 
 s 
 
 
 
 
 II 
 
 
 
 
 
 
 
 c?" 3 
 
 o [0 tO c\J 
 
 1 
 
 
 
 
 cog r 
 
 ^ u, * 
 
 CO 
 
 ID 
 
 
 
 5r< r- 
 
 \ 5 
 
 s 
 
 ^' 
 
 h ^* 
 
 
 
 
 
 
 22 w 
 
 
 
 
 
 ^J 
 
 5 o 
 
 IS Q) 
 
 
 
 
 
 <* 
 
 'c ^ 
 
 
 
 
 
 
 O CO 
 
 B 
 
 
 
 
 
 10 
 
 
 
 
 f 
 
 .<* 
 
 
 
 
 o 
 
 ID 
 
 
 O j^ 
 
 
 
 
 
 
 ^ ^ 
 
 
 
 
 J 
 
 N 
 
 ^D ^MlO 
 
 ^ r o ^-, 
 
 
 Q 
 to 
 
 
 
 ^ 
 
 
 
 
 X. 
 
 " 
 
 1 
 
 
 
 r- 
 
 o 
 
 
 
 <M 
 
 dT ^H 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 CO 
 
 
 
 00 
 
 
 to 
 
 
 
 to 
 
 
 CO 
 
 
 
 
 1 
 
 
 
 
 
 I 
 
 
 j 
 
 
 
 1 
 
 8 
 
 tf J 
 
 H 
 
 o 
 
 P? 
 
 d 
 o -j 
 
ENERGY DIAGRAMS 55 
 
 Figure 6 shows a similar diagram for the arc spectrum of magnesium, 
 with several of the fundamental lines indicated by arrows. Making 
 use of the quantum relation hc*v = eV 10 8 , we may express wave number 
 in terms of the potential difference V through which an electron must 
 freely fall in order to accumulate an amount of kinetic energy equivalent 
 to a quantum of radiation of wave number v. Expressed in volts we / 
 find: 
 
 Volts = V = 1.2345 v 1(T 4 ) ,. ON 
 
 or v =81007 T 
 
 Expressed in terms of wave-length X measured in Angstrom units, we 
 find: 
 
 V = 12345/X. (64) 
 
 The terminology "volts" by universal custom is used to signify a 
 variety of meanings where the more precise statement of fact requires 
 several words and is inconvenient. For example, instead of stating 
 precisely that we refer to the velocity of an electron which has been 
 accelerated through a potential difference of x volts, we may express 
 this fact by stating that the electron has a velocity of x volts. Similarly, 
 we may use the expression "an energy of x volts" meaning the value of 
 the kinetic energy of the electron referred to above. With the quantum 
 relation hc 2 v eV-10 8 tacitly understood, we may speak of frequencies, 
 wave numbers and wave-lengths of x volts, meaning for example the 
 wave number derived by substituting x for V in Equation (63) , etc. 1 
 
 In Figure 6, for example, a displacement of one electron to the left 
 from 1 S to 2 p 2 requires 2.70 volts work. The electron in returning to 
 1 S gives up this energy as a quantum of radiation of wave-length 4573 A. 
 The arrow-head shows the direction and end of the displacement in each 
 case. 
 
 Figure 7 is a schematic representation of the enhanced lines of 
 magnesium. It is noted that one of the valence electrons is absent, 
 which fact greatly alters the values of the different energy or wave 
 number levels. The first pair of each of the three series. Prin., 1 @ 
 m $, 1st Sub., 2 <P - m S>, and 2d Sub., 2 $ - m @, is indicated by 
 arrows. 
 
 The above examples illustrate the usefulness of such energy diagrams. 
 All mathematically possible series and combination lines are given by 
 the frequency differences of pairs of energy levels. The various levels, 
 
 i Language serves two purposes; one in a definitional sense, where preciseness is requisite; 
 the other for the conveyance of ideas, where conciseness is essential. It is in the latter sense 
 that the above inexact yet unambiguous notation is justifiable. 
 
56 
 
 OF SPECTRA 
 
 4- 
 
 1 
 
 !- 
 
 ^ suoiioeig ;^ 
 
 
 
 
 1 
 
 
 u> 
 
 
 . 
 
 m 
 
 
 
 suoj-^oai g 
 
 8 
 
 a 
 
 
 
 
 
 ^ '8 
 
 
 
 
 
 in 
 
 
 
 6 
 
 
 8 
 
 
 
 .3 
 
 
 
 *~ 
 
 m 
 
 
 
 CD 
 
 
 -2 
 
 eo 
 
 
 
 CX 
 
 ^~~ 
 
 n 
 
 
 
 od 
 
 
 2 
 
 
 
 
 
 i 
 
 
 
 ^ 
 
 
 CO 
 
 
 
 
 
 115 1 
 
 3 
 
 
 
 g 
 
 1 
 
 s 
 
 UOJP913 33U9IBA I 
 
 S tf 2 
 
 U -8 
 
 J 
 
 
 (8 
 
 
 
 CO CO 
 0^ ^D 
 
 ^"* CO 
 
 
 a 
 o 2 ^ 
 
 "T 
 
 
 
 
 ~~~~~ 
 
 o D ^ 
 
 <4 
 
 J 
 
 
 
 
 %9 
 
 t-) 
 
 
 
 SV N 1 
 
 
 } 
 
 j 
 
 
 a 
 
 B 
 
 OJ 
 
 \ 1- 
 
 <^ m <u 
 
 3| - 
 
 
 | I ?5 SS __ 
 
 ^ ^ 
 
 OD ^ 2 
 
 
 -*-* 1 
 05 i> < 
 
 "S 5^ 
 
 ^ T 
 
 - 1 5 1 
 
 J C" 
 
 M CKNI 
 
 4.7 4 
 
 Loo 
 
 epresentatio 
 
 r s 
 
 
 
 
 . 03 p|^ 
 
 
 CO o 
 
 
 
 S c rt 
 
 
 "* 
 
 
 
 'Sco 
 
 
 g 
 
 
 
 ^o 
 
 
 
 S 
 
 
 
 ? ' ^ 
 
 
 1> 
 
 "* 
 
 ^ C5 
 
 
 
 
 
 E- 
 
 
 
 
 10 
 
 
 
 
 
 . 
 
 
 
 
 
 , 
 
 
 
 1 
 
ENERGY DIAGRAMS 
 
 57 
 
 CM 
 
 2 
 I 
 
 a 
 
 cd 
 
 
58 
 
 ORIGIN OF SPECTRA 
 
ENERGY DIAGRAMS 59 
 
 however, are concerned with only the total quantum number. No 
 differentiation between azimuthal and radial quantum numbers is 
 made. The so-called Grotrian diagrams remedy this difficulty. These 
 possess the additional advantage that the fine structure, doublets, etc., 
 may be readily indicated. 
 
 Figure 8 is such a diagram for hydrogen. Three coordinates are 
 employed: as abscissa, logarithm of the wave number; as ordinate, the 
 azimuthal quantum number; and a third system, indicated by dotted 
 lines, the sum of the azimuthal and radial quantum numbers. Each 
 point shown by a small circle represents a wave number or equivalent 
 energy level which may be computed from Equation (20) by the proper 
 assignment of azimuthal and radial quantum numbers. A spectral 
 frequency is indicated by a straight line between two points and its 
 numerical value is given by the difference in the wave numbers corre^ 
 spending to each end of this line. By the Bohr principle of selection the 
 change in azimuthal quantum number = 1. Hence all straight lines 
 representing spectral frequencies must terminate in adjacent horizontal 
 lines of constant azimuthal quantum number. The group terminating 
 at the upper right-hand point represents the Lyman series, each member 
 -of which is a singlet. The plot shows H a and H^ of the Banner series, 
 each member being a triplet and hence appearing three times. The 
 first line of the Paschen series, which is a quintuplet, appears five times 
 on the chart, and is designated by the letter P. 
 
 In a similar manner the spectra of the heavier elements may be 
 illustrated. Figure 9 represents sodium. The double mp terms, all 
 having the same azimuthal quantum number 2, are shown by mpi and 
 mp 2 . All lines representing the principal series terminate at the upper 
 right-hand point and each occurs twice on account of the double-p 
 values. The two D-lines are marked with their proper wave-lengths. 
 The straight lines representing the 1st and 2d subordinate series all 
 terminate at 2 p and again occur twice because of the double values of 
 mp. The above discussion illustrates the use and construction of these 
 diagrams for representing series relations. We shall have occasion to 
 refer to them subsequently. 
 
Chapter III 
 lonization and Resonance Potentials for the Elements 
 
 When electrons are accelerated through gas or vapors there are, 
 especially for monatomic gases having a small electron affinity and the 
 metallic vapors, well-defined critical velocities at which a large transfer 
 of energy takes place between electrons and atoms. For velocities 
 below this minimum critical value the collision is elastic, the electron 
 rebounding from the atom with usually an alteration in its direction 
 of path but with the same kinetic energy. In general two types of 
 inelastic collision occur, one in which an outer electron of the atom 
 undergoes an interorbital transition, and the other in which an outer 
 electron is completely removed. In the latter case the atom is " simply" 
 ionized, having a total net charge + e> The potential through which an 
 electron must fall in order to accumulate just sufficient velocity to 
 produce the first type of inelastic collision has been termed by Tate and 
 Foote the resonance potential. The corresponding value for a collision 
 resulting in ionization is known as the ionization potential. In general 
 there may be several ionization potentials corresponding to the removal 
 of 1, 2, 3, etc. electrons, but only simple ionization will be considered in 
 the present section. Experimental evidence has shown that the loss 
 in kinetic energy of the impacting electron during a collision of the 
 " resonance" type is equal to the resonance potential, ' whether the 
 initial energy be exactly equal to or greater than that corresponding 
 to the resonance potential. Whether or not this be true in the case of 
 ionization remains to be demonstrated, for it is possible that the ejected 
 electron may leave the atom with any velocity whatever, depending 
 upon the nature of the impact. 
 
 Since energy is abstracted from the impacting electron and absorbed 
 by the atom, the total energy of the atom, following a collision, is in- 
 creased by an amount equivalent to either the resonance or ionization 
 potential. When the atom subsequently returns to its normal state this 
 energy is emitted in the form of radiation. In the case of ionization the 
 electron may return by a variety of interorbital transitions, each resulting 
 
 60 
 
IONIZATION AND RESONANCE POTENTIALS 61 
 
 in an emission of a quantum of wave number v k) subject to the conserva- 
 
 fon of energy condition: 
 
 energy condition: 
 
 eV t - 10 8 , 
 
 where V t is the ionization potential. With numerous atoms and elec- 
 trons returning to equilibrium in different manners, we have as the 
 composite result an emission of the complete arc spectrum. If an elec- 
 tron returns to the normal orbit directly without passing through inter- 
 : mediate states of equilibrium, but one frequency is emitted, which is 
 j the highest frequency in the arc spectrum. This frequency, as is evident 
 ] from a consideration of the energy diagrams Figures 4 to 9 and Equations 
 I (34) to (37), is the highest convergence frequency of any series of the 
 I arc spectrum, the wave numbers 1 s for the alkalis and 1 S for the metals 
 of Group II. of the periodic table. In the normal unexcited atom, ac- \ 
 cordingly, the outer electron concerned with emission of spectral lines lies J 
 in the 1 s or 1 S orbit. 
 
 The energy absorbed by the atom at the resonance potential is not 
 great enough to completely eject an electron, but rather is just sufficient 
 to displace it to a neighboring orbit of higher energy value. We have v 
 found experimentally that the alkali metals possess a resonance potential } 
 corresponding exactly to the amount of work required to displace an/ 
 electron from the 1 s orbit to the 2 p orbit, the first energy level above^ 
 1 s. For sodium, as illustrated by Figure 5, the energy absorbed by 
 the atom is 2.10 volts. The electron accordingly in returning to its 
 normal orbit releases this amount of energy as a quantum of radiation, 
 of wave number v = 1 . s 2 p; that is, the D-lines and no other lines 
 of the sodium spectrum are emitted. Since both D-lines are emitted 
 it may be expected that two resonance potentials exist, but if so the 
 difference in their values would be many times less than our errors of 
 measurement. It is doubtful whether any conclusion in this regard may 
 be drawn from the fact that we found a single resonance potential for 
 caesium where the doublet separation is considerably larger. There is 
 on the other hand a vague possibility that the component of higher 
 frequency is the determining factor for the resonance potential, in 
 rather superficial analogy to the excitation of the K series at the mini- 
 mum potential corresponding to Ka. 
 
 In the case of the metals of Group II of the periodic table the authors 
 have found that two resonance potentials exist. One of these cor- 
 responds to the energy required to displace an electron from its normal 
 position in the 1 S orbit to the neighboring orbit 2 p 2 . The electron in 
 
62 
 
 ORIGIN OF SPECTRA 
 
 returning to the 1 S orbit gives up this energy as a quantum of radiation 
 of wave number v = 1 S 2 p 2 . Only the single line is emitted. In 
 fact the corresponding frequencies IS 2pi and IS 2 p 3 are absent 
 even in the complete arc spectra of these metals. The reason for these 
 missing terms is explained, not at all satisfactorily , however, by Sommer- 
 feld's theory of " internal quantum numbers" and is beyond the scope of 
 the present book. 1 
 
 TABLE X 
 RESONANCE AND IONIZATION POTENTIALS, GROUP I 
 
 Element 
 
 z 
 
 Series 
 Notation 
 
 V 
 
 Volts 
 
 Computed 
 
 Observed 
 
 Li 
 
 3 
 11 
 19 
 29 
 37 
 47 
 55 
 79 
 
 Is 
 ls-2 Pl 
 
 Is 
 ls-2 Pl 
 
 Is 
 ls-2 Pl 
 
 Is 
 
 Is - 2 Pl 
 
 Is 
 1 s - 2 pi 
 
 Is 
 la-2p, 
 
 Is 
 1 s - 2 pi 
 
 Is 
 ls-2 pl 
 
 43,486 
 14,903 
 
 41,449 
 16,973 
 
 35,006 
 13,043 
 
 62,308 
 30,784 
 
 33,689 
 12,817 
 
 61,096 
 30,473 
 
 31,405 
 11,732 
 
 70,000? 
 41,174 
 
 5.368 
 1.840 
 
 5.116 
 2.095 
 
 4.321 
 1.610 
 
 7.692 
 3.800 
 
 4.158 
 1.582 
 
 7.542 
 3.762 
 
 3.877 
 1.448 
 
 8 to 9? 
 5.1 
 
 5.13 
 2.12 
 
 4.1 
 1.55 
 
 4.1 
 1.6 
 
 3.9 
 1.48 
 
 Na .. ... 
 
 K 
 
 Cu 
 
 Rb . . 
 
 Ag.. 
 
 Cs 
 Au 
 
 
 The second resonance potential corresponds to the energy required 
 to displace an electron from its normal position in the 1 S orbit to the 2 P 
 orbit. If the electron returns directly to the 1 S orbit without passing 
 
 Sommerfeld, " Atombau," 3d Ed., Chap. 6, Section 5. 
 
IONIZATION AND RESONANCE POTENTIALS 63 
 
 through intermediate states of equilibrium, this energy is liberated as a 
 i quantum of radiation of wave number v = 1 S 2 P. These transi- 
 tions are illustrated in the case of magnesium by Figure 6, the resonance 
 potentials being 2.70 and 4.33 volts. 
 
 In general we note that the ionization potential of a monatomic 
 vapor corresponds to the highest convergence frequency in the arc 
 spectrum of the material; to the limit of a series the first line of which 
 corresponds to a resonance potential. Exceptions to this general rule 
 will be given individual attention later. As will be considered in more 
 detail under a separate section 2 these series are absorption lines for the 
 normal atom, so that ionization and resonance potentials in certain 
 cases may be predicted from a knowledge of the prominent absorption 
 lines. 
 
 Group I: Table X shows the ionization and resonance potentials 
 for metals in Group I of the periodic table. The computed values are 
 obtained from the series relationships and are to be preferred to our 
 direct experimental values for all computations in which a consideration 
 of ionization and resonance potentials enters. No satisfactory results 
 have been obtained with copper, silver and gold, although we have made 
 very elaborate and extensive experiments. The difficulty is of a pyro- 
 metric nature, temperatures of 2000 C and a high vacuum being re- 
 quired. However, from series relationships and a consideration of the 
 absorption or " reversed" lines the computed values are probably correct. 
 
 Group II: Table XI shows the computed values of the resonance 
 and ionization potentials for elements of Group II of the periodic table, 
 together with the experimental values obtained by the authors. 3 
 
 Group III: The series relations in this group, which includes alumi- 
 num, gallium, indium, and 4 thallium, should be similar to that of the 
 alkali metals. The arc lines have been beautifully correlated in series of 
 this type, consisting of widely spaced doublets, but the convergence 
 frequency of the principal series is smaller than that of the subordinate 
 series a fact not easily reconciled with the quantum theory unless 
 the observed principal series is of a second type converging at 2 s instead 
 of 1 s. This would indicate that the most important principal series 
 which converges at 1 s is as yet undiscovered. If so most of the lines 
 except the first term should lie in the extreme ultra-violet. It is of 
 interest that several lines supposedly of the arc spectrum have been 
 observed which have a greater wave number than the highest known 
 
 a Cf. Chapter IV. 
 
 8 For data by other observers, see general references at end of chapter. Several of the. 
 experimental values in Tables X and XI were obtained by Tate and Foote. 
 
64 
 
 ORIGIN OF SPECTRA 
 
 convergence frequency, again indicating that 1 s remains to be dis- 
 covered. 4 
 
 TABLE XI 
 RESONANCE AND IONIZATION POTENTIALS, GROUP II 
 
 Element 
 
 Z 
 
 Series 
 
 V 
 
 Vc 
 
 >lts 
 
 
 
 Notation 
 
 
 Computed 
 
 Observed 
 
 Be 
 
 4 
 
 
 > Mg ? 
 
 > Mg? 
 
 
 Mg 
 
 12 
 
 IS 
 
 61,672 
 
 7.613 
 
 7.75 
 
 Ca 
 
 20 
 
 !S-2p 2 
 IS-2P 
 
 IS 
 
 21,871 
 35,051 
 
 49,305 
 
 2.700 
 4.327 
 
 6.087 
 
 2.65 
 4.42 
 
 6.01 
 
 Zn 
 
 30 
 
 !S-2p 2 
 1S-2P 
 
 IS 
 
 15,210 
 23,652 
 
 75,767 
 
 1.878 
 2.920 
 
 9.353 
 
 1.90 
 
 2.85 
 
 9.3 
 
 Sr 
 
 38 
 
 lS-2p 2 
 1S-2P 
 
 IS 
 
 32,502 
 46,745 
 
 45,926 
 
 4.012 
 5.771 
 
 5.670 
 
 4.18 
 5.65 
 
 Cd 
 
 48 
 
 lS-2p 2 
 1S-2P 
 
 IS 
 
 14,504 
 21,698 
 
 72,539 
 
 1.791 
 2.679 
 
 8.955 
 
 8.92 
 
 Ba 
 
 56 
 
 !S-2p 2 
 1S-2P 
 
 IS 
 
 30,656 
 43,692 
 
 42,029 
 
 3.784 
 5.394 
 
 5.188 
 
 3.95 
 5.35 
 
 Hg. . 
 
 80 
 
 lS-2p 2 
 1S-2P 
 
 IS 
 
 12,637 
 18,060 
 
 84,178 
 
 1.560 
 2.230 
 
 10.392 
 
 10.2 
 
 Ra 
 
 88 
 
 !S-2p 2 
 1S-2P 
 
 IS 
 
 39,413 
 54,066 
 
 40-50000? 
 
 4.866 
 6.674 
 
 5-5.5? 
 
 4.76 
 6.45 
 
 
 
 !S-2p 2 
 IS-2P 
 
 12,500? 
 20,700? 
 
 1.5? 
 2.6? 
 
 
 4 These are conveniently summarized in tables by Fowler, " Report on Series in Line 
 Spectra," Chap. 17. 
 
ION I Z AT ION AND RESONANCE POTENTIALS 65 
 
 The only critical potentials known for this family are our measure- 
 ments on thallium, which are rather unsatisfactory. We found a reso- 
 nance potential 1.07 volts and an ionization potential 7.3 volts. The 
 resonance potential corresponds closely to the component of higher 
 frequency of the first pair of Paschen's principal series usually given as 
 P = 1 s 3 pi but which more likely should have the notation v 2 s 
 3 pi = 8683.3 o 1.07 volts. This exact agreement with experiment 
 is accidental, and in case this frequency is 2 s 3 pi, it probably has no 
 physical significance whatever, as the determining wave number then 
 should be 1 s 2 pi. The observed ionization potential corresponds 
 to a value of 1 s of about the magnitude to be expected but greater than 
 
 | any convergence frequency known at present. More observations on 
 critical potentials for this group should be made; our work on thallium 
 should be repeated with greater care; and the spectral series relations 
 should be further investigated with the object of finding higher con- 
 vergence frequencies for the principal series of all the metals of this 
 family. 
 
 Group IV: The series relations for this family are in a very un- 
 satisfactory state, 5 and there is little hope for directly determining the 
 
 j critical potentials of such highly refractory elements, except lead, unless 
 an entirely new method of experimentation should be devised. We have 
 tried without success the vaporization of such refractory materials in a 
 high vacuum, using a small crucible and projecting an approximately 
 
 j unidirectional stream of the vapor through the ionization chamber. 
 
 i The problem is most difficult both from the standpoint of electrical 
 
 : measurements and of pyrometry. Our results with lead by the usual 
 
 ' method gave for the resonance potential 1.26 volts and for the ionization 
 potential 7.93 volts. The first point coincides with an isolated group of 
 infra-red lines, observed by Randall, the shortest wave-length of which 
 
 is X = 10291 =0= 1.30 volts. 
 
 Group V: Series relations are unknown 6 and it is questionable 
 whether measurements on critical potentials of polyatomic vapors 
 give any direct indication of spectral frequencies of line series since 
 
 , the work of ionization, for example, may include that of dissociation 
 of the molecule into atoms. 7 It is even possible that the band spectra 
 of polyatomic vapors are more closely related to the values indicated 
 by critical potentials. In Table XII the potentials for antimony and 
 
 * Fowler summarizes the present meager knowledge of the series spectra of these elements 
 in two pages, loc. cit., pp. 163^. 
 
 Fowler, loc. cit., p. 164. 
 
 i See latter part of Chap. VIII. 
 
66 
 
 ORIGIN OF SPECTRA 
 
 bismuth are unreliable. Although we have made numerous deter- 
 minations each one of which appeared satisfactory by itself, the different 
 observations showed wide deviations, possibly accounted for by the 
 formation of polarization films on the electrodes. It should be pointed 
 out that observations on ionization potentials without corresponding 
 data on resonance, for velocity corrections, are of little value with non- 
 metallic vapors, as surprisingly large errors arise in " initial velocities" 
 determined by the usual velocity distribution curves. Such is not the 
 case with metallic vapors and the rare gases. 
 
 TABLE XII 
 RESONANCE AND IONIZATION POTENTIALS, GROUP V 
 
 Element 
 
 Z 
 
 Observed Potential, 
 Volts 
 
 Remarks 
 
 Resonance 
 
 Ionization 
 
 N 
 
 7 
 
 15 
 33 
 51 
 83 
 
 8.18 
 
 5.80 
 4.7 
 ? 
 2.0 
 
 16.9 
 
 13.3 
 11.5 
 
 7.8-8.5 
 8.0-8.5 
 
 Lines at X 1494.8 and 
 \1492.8o 8.27 volts. 
 Ionization at 17.75, 
 25.4, 30.7 observed 
 by Brandt. 8 
 
 Uncorrected for initial 
 velocity. 
 
 P.... 
 
 As 
 
 Sb 
 
 Bi 
 
 
 Group VI: Our knowledge of the spectral series of these elements 9 
 is confined to oxygen, sulphur and selenium. Principal, 1st and 2d 
 subordinate series of both single lines and triplets are known for oxygen, 
 and a similar triplet structure for sulphur and selenium. There is no 
 apparent relation between the values of the series terms and the observed 
 critical potentials. For example, Fowler lists 1 S and 1 s for oxygen 
 as v 33043 and v 36069 respectively, corresponding to roughly 
 four volts, whereas the ionization potential is nearly sixteen volts. This 
 
 Brandt, Z. Physik, 8, pp. 32-44 (1921). 
 Hughes, general references at end of chapter. 
 Fowler, loc. cit., p. 166. 
 
 For data on nitrogen by other observers see 
 
IONIZATION AND RESONANCE POTENTIALS 
 
 67 
 
 lack of agreement might be due to the fact that the wave number v 
 33043 is really 2 S instead of 1 S and that 1 S is as yet unknown.- On 
 the other hand it is more probable that the ionization potential is char- 
 acteristic of the molecule, as above mentioned, and hence has only a 
 remote relation to spectral frequencies for the atom. Table XIII 
 summarizes our data on several of the polyatomic elements in this 
 group. The values for selenium and for tellurium are questionable. 
 
 TABLE XIII 
 RESONANCE AND IONIZATION POTENTIALS, GROUP VI 
 
 Element 
 
 Z 
 
 Observed Potential 
 Volts 
 
 Remarks 
 
 Resonance 
 
 Ionization 
 
 o 
 
 8 
 16 
 34 
 52 
 
 7.91 
 4.78 
 3.0-3.5 
 2.3-2.9 
 
 15.5 
 12.2 
 12-13 
 ? 
 
 See Hughes 10 for data 
 by other observers. 
 
 (12.7 observed by 
 Udden.)" 
 
 s 
 
 Se 
 
 Te 
 
 
 Group VII: Spectral relations unknown. 12 Hughes and Dixon 13 
 observed a critical potential in chlorine at 8.2 volts and in bromine at 
 10.0 volts, but whether these are ionization or resonance potentials is 
 uncertain. For iodine we have found a resonance potential of 2.34 
 0.2 volts and an ionization potential of 10.1 0.5 volts. Smyth and 
 Compton 14 observed ionization of molecule at 9.4 volts, ionization of 
 atom at 8.0 volts and ionization of fluorescing molecule at 6.8 volts. 
 
 Saha, Nature, 107, p. 683 (1921), states that Catalan in some unpub- 
 lished work has found 1 S for manganese. His value gives 7.38 volts^ 
 for the computed ionization potential, which is consistent with the 
 behavior of the element in the solar spectrum, as mentioned on page 172. 
 
 Groups VIII & 0: Table XIV summarizes mainly the work of Horton 
 and Davies 15 on the rare gases, work which has been done apparently 
 
 10 See general references at end of chapter. 
 
 "Udden, Phys. R., 18, p. 385 (1921). 
 
 12 Fowler, loc. cit., p. 173, summarizes some data on manganese triplets. 
 
 " Hughes and Dixon, Phys. R., 10, p. 495 (1917). 
 
 14 Smyth and Compton, Phys. R., 16, pp. 501-13 (1920). 
 
 15 Horton and Davies, Proc. Roy. Soc., 95, p. 408 (1919); 97, p. 1 (1920); 98, p. 121 
 (1920); Phil. Mag., 39, p. 592 (1920). 
 
68 
 
 ORIGIN OF SPECTRA 
 
 with high precision and the greatest experimental skill. The data 
 of these and other observers are tabulated by Hughes. 
 
 TABLE XIV 
 RESONANCE AND IONIZATION POTENTIALS, GROUP 
 
 Element 
 
 Z 
 
 Observed Potential Volts 
 
 Resonance 
 
 lonization 
 
 He 
 
 2 
 
 10 
 
 18 
 
 20.4 
 21.2 
 
 11.8 
 
 17.8 
 
 11.5 . 
 
 25.6 
 (25.4 
 
 (25.5 
 
 16.7 
 20.0 
 
 22.8 
 
 15.1 
 
 Franck and Knipping 16 
 later 25.3) 
 Compton 17 ) 
 
 Ne 
 
 A 
 
 
 No data on the metals exist either in regard to spectral series 18 
 or critical potentials. 
 
 Hydrogen. Hughes lists the work of eleven groups of experimenters. 
 In Table XV we summarize the values obtained by Horton and Davies 19 
 and by ourselves. 20 
 
 TABLE XV 
 RESONANCE AND IONIZATION POTENTIALS, HYDROGEN 
 
 Resonance 
 
 lonization 
 
 
 
 
 Observers 
 
 1st 
 
 2d 
 
 1st 
 
 2d 
 
 
 10.5 
 
 13.9 
 
 14.4 
 
 16.9 
 
 Horton and Davies 
 
 10.4 
 
 12.0 
 
 13.3 
 
 16.0 
 
 Mohler and Foote (Revised 
 
 
 
 
 
 from more recent data. 
 
 
 
 
 
 Earlier published values 
 
 
 
 
 
 were 12.2 and 16.5) 
 
 " Franck and Knipping, Zeit. Physik, 1, p. 320 (1920). 
 
 " Compton, Phil. Mag., 40, p. 553 (1920). 
 
 18 Constant difference groups are known, suggesting that series relations exist. 
 
 19 Proc. Roy. Soc., 97, p. 23, 1920. 
 
 20 Mohler and Foote, Bur. Standard Sci. Paper, 400; Phys. R., 19, pp. 419-20 (1922). 
 
ION I Z AT ION AND RESONANCE POTENTIALS 69 
 
 THE NORMAL HELIUM ATOM 
 
 While the quantum theory yields results of the greatest precision in 
 the case of ionized helium, a satisfactory interpretation of the normal 
 helium atom with two electrons proves to be very difficult. The simple 
 Bohr theory assumed that the two electrons revolved in a single circular 
 orbit about the nucleus of charge + 2 e. By Equation (50) we obtain 
 accordingly for the total energy of the atom: 
 
 W = - 2 (2 - 0.25) 2 = - 1.321 - KT 10 ergs =c= - 83.0 volts. (65) 
 
 The energy of the simply ionized atom is obtained by the same equation 
 or by Equation (20) and gives directly the value 54.2 volts concerning 
 which there can be no question, as it is derived from the solution of the 
 simple problem of two bodies which has been amply developed and 
 verified in the earlier part of this book. The difference in these two 
 values, 83.0 54.2 = 28.8 volts, should give the ionization potential 
 of helium, whereas by direct experiment we find about 25.5 volts, a 
 sufficiently unsatisfactory agreement to warrant the rejection of this 
 structure for the normal helium atom. Furthermore it is not in accord 
 with the known diamagnetic properties of helium. 
 
 Helium 21 possesses two independent groups of series in its arc spec- 
 trum, a single line and a doublet system, between which no combinations 
 whatever occur. This peculiar behavior immediately suggests that the 
 systems arise in two entirely different configurations of the helium atom. 
 In fact it was once thought that helium must be a mixture of two gases, 
 for convenience called orthohelium and parhelium, names now retained 
 to denote the two types of atomic configuration. 
 
 Figure 10 shows the series relations for helium. The upper half 
 represents the single-line system ascribed to parhelium. The lower 
 half of the figure shows the doublet system of orthohelium. The doub- 
 lets are exceedingly close and hence do not appear resolved in this dia- 
 gram. In the notation we represent, as usual, singlet series by capital 
 letters and doublet series by lower case letters. The highest convergence 
 limits 2 S and 2 s for these two groups correspond respectively to 3.954 
 and 4.747 volts. If either of these states represented the normal atom, 
 one of the values named should be the ionization potential, and the 
 stability of the atom would be but 1/7 the observed stability. The 
 most obvious step accordingly is to identify the normal state with 
 either 1 S or 1 s, to which should correspond the experimental value for 
 the ionization potential. 
 
 21 Fowler, loc. cit., p. 89. 
 
70 
 
 ORIGIN OF SPECTRA 
 
 Nedotiv* Enerdies on Wave Number S 101* 1 10 (TVrm Values) 
 
 FIG. 10. The series relationships for helium. (From Kemble, Phil. Mag. 42, p. 124; 
 
 1921.) 
 
 FIG. 11. The normal helium atom. 
 
 
ION I Z AT ION AND RESONANCE POTENTIALS 71 
 
 1 he first electron bound to the helium nucleus revolves in a 1 quan- 
 tum circular orbit. The second electron cannot in the normal state 
 revolve in a coplanar orbit which surrounds the first because (a) the 
 readily computed energy relations are not in agreement with ionization 
 potential measurements and (b) the configuration would resemble 
 lithium and should have a positive valence. As already mentioned 
 (cf. discussion of Equation (65)), the two electrons cannot revolve in 
 the same orbit, and as Bohr points out there is no type of transition con- 
 ceivable between a state^where the electrons occupy different orbits and 
 that state in which the same orbit is occupied. 
 
 Bohr 22 concludes that in the normal state both electrons move in 
 1 quantum paths which make an angle of 120 degrees with each other 
 as shown in Figure 11. To a first approximation these are circular 
 orbits. On account of the mutual action of the two electrons, however, 
 there is a slight deviation from the true circle, and the two orbits rotate 
 slowly about the fixed axis of angular momentum of the atom. Bohr 
 states that while the mathematical analysis of this three-body problem 
 is not yet complete, preliminary computations indicate that it will give 
 the correct value of the ionization potential. 
 
 Lande 23 has shown that the single-line system belongs to a crossed- 
 orbit configuration, where one of the electrons undergoes interorbital 
 transitions, while the doublet system arises in transitions of the outer 
 electron in a coplanar configuration. We accordingly assign the singlet 
 spectra to parhelium and the doublet spectra to orthohelium. Normal 
 helium is therefore the 1 S state of parhelium. In the 2 s state of ortho- 
 helium the inner electron revolves in a 1 quantum circular orbit, while 
 the outer electron, according to Bohr, moves in a coplanar elliptical 
 orbit of total quantum number 2 and azimuthal quantum number 1. 
 The 1 s state should therefore require two electrons in the same circular 
 orbit at opposite ends of a diameter. Although this is the most stable 
 type of configuration, Bohr, as stated above, concludes it cannot be 
 formed, and accordingly we have no term 1 s in the helium spectrum, a 
 hypothesis also advanced by Franck and Reiche 24 from other consider- 
 ations. 
 
 Since Bohr's mathematical computations on the dynamics of these 
 systems have not been published, we shall, following Franck and Knip- 
 ping, 25 compute 1 S from their observation on the ionization potential. 
 
 22 Bohr, Z. Physik, 9, pp. 1-67 (1922). 
 
 "Physik. Z., 20, pp. 228-34 (1919); 21, pp. 114-22 (1920). 
 
 24 Z. Physik, 1, pp. 154-160 (1920). 
 
 2 'Z. Physik, 1, p. 320 (1920). 
 
72 ORIGIN OF SPECTRA 
 
 One obtains 1 S 202910 =0= 25.3 volts. Using the spectroscopically 
 determined values of 2 S and 2 s, as shown in Figure 10, we find 
 
 '1S-2S = 202910 - 32031 = 170880 =c= 21.1 volts 
 1 S - 2 s = 202910 - 38453 = 164460 o 20.6 volts 
 
 These potentials correspond to the resonance potentials of helium, 
 the observed values of which are 21.2 and 20.4 volts, as given in Table 
 XIV. It therefore appears that a 21.1 volt impact ejects an electron 
 from the normal 1 S state to the 2 S state of parhelium, while a 20.6 volt 
 impact ejects an electron from the normal 1 S state of the crossed orbit 
 system to the 2 s state of the coplanar system, orthohelium. 
 
 The existence of the wave number 1 S immediately suggests the 
 presence of a principal series of the form 1 S wP.the first few terms 
 of which may be computed from the known values of mP as follows : 
 
 
 Notation 
 
 V 
 
 X 
 
 1 ,S 
 
 - 2P 
 
 175 730 
 
 569 A 
 
 1 S 
 
 -3P 
 
 190,810 
 
 524 
 
 1 fi 
 
 -4P 
 
 196 100 
 
 510 
 
 
 
 
 
 Spectroscopic measurements have not as yet shown the presence of this 
 series. Fricke and Lyman 26 observed only the single line at X 585. This 
 apparently has the notation 1 S 2 S, for the computed value, cor- 
 responding to the resonance potential 21.1 volts, is exactly this wave- 
 length. The excitation of 1 S 2 Sis contrary to the Bohr principle of 
 selection, but the line was emitted in a strong spark where, on account 
 of the presence of the electrostatic field, the selection principle is not 
 applicable. The line would not be absorbed by the surrounding un- 
 excited gas, as for this the selection principle would hold. Lines of the 
 series 1 S mP, on the other hand, should show very great absorption. 
 This probably explains why Fricke and Lyman could detect in their 
 experiments the emission of only the line 1 S 2 S. If one could devise 
 a continuous source of ultra-violet radiation in this extreme spectral 
 range, it might be possible to obtain the series 1 S mP as absorption 
 lines, analogous to Wood's work with sodium, page 80. Possibly 
 "exploded wires" 27 could be employed to advantage in this respect. 
 
 2 Phil. Mag., 41, p. 814 (1921). See footnote 39, page 77. 
 27 Anderson, Astrophys. J., 51, pp. 37-48 (1920). 
 
ION I Z AT ION AND RESONANCE POTENTIALS 
 
 73 
 
 Using the photo-electric method described on page 137 Franck and 
 Knipping 28 have obtained in helium at very low pressure some evidence 
 for the presence of the lines 1 S 2 P and 1 S 3 P. Their results 
 expressed in volts are as follows: 
 
 
 Notation 
 
 Volts computed 
 
 Volts observed 
 
 1 fi 
 
 -2P 
 
 21.85 
 
 21.9 
 
 1 S 
 
 - 3P . 
 
 23.7 
 
 23.6 
 
 
 
 
 
 The method is not conclusive, but merely suggestive. 
 
 If electrons are ejected to the 2 s or 2 S orbits of trie helium atoms 
 by low voltage electronic bombardment, it would appear that they 
 should have difficulty in returning to the normal state. The return 
 to 1 S from 2 s is prevented by the general law that intercornbination 
 lines between the crossed and coplanar orbital systems do not take place. 
 The return from 2 S is contrary to the selection principle and should 
 therefore require the presence of a disturbing field. Hence the 2 s and 
 2 S states should represent metastable forms of helium, at least capable of 
 existing for an appreciable length of time which is much greater than 
 the life of the 2 P state, for example. 29 This is evidenced by experi- 
 mental work on the absorption of helium excited by a mild electric 
 discharge. Paschen 30 observed that the gas very readily absorbed 
 the lines 2 S - 2 P, X = 20582 and 2 s - 2 p, X = 10830. These lines 
 were also reemitted as resonance radiation (see page 86). From the 
 fact that the scattered or resonance radiation for 2 s 2 p was probably 
 greater than that for 2 S 2 P, Franck and Reiche concluded that 
 only the state 2 s should be considered as a metastable modification of 
 helium. In the 2 s state with one electron revolving about the other in a 
 
 2 8 Loc. cit. 
 
 29 Since the above was written a paper more directly bearing on this point has been 
 published by Kannenstine, Astrophys. J., 55, p. 345 (1922). A two-electrode Wehnelt arc in 
 helium was excited by an alternating potential and the current- voltage characteristics were 
 observed by use of a Braun-tube oscillograph. Operations were so controlled that after the 
 arc had struck at a potential above the normal ionization point, it could be maintained at 
 voltages as low as 4.8 volts. This voltage corresponds to the wave number 2s and accord- 
 ingly represents the ionization potential of the helium atom in its 2s state. Now with a 60 
 cycle, applied potential, the arc was extinguished with each cycle, and was struck again only 
 when the potential was greater than 25 volts. However, when the frequency of the applied 
 potential was increased to between 200 and 220 cycles, the arc both struck and broke at 4.8 
 volts. This is interpreted to mean that the average life of the metastable helium atom in 
 the 2s state is about one-half of the cycle, or of the order 0.002 seconds. As will appear in 
 the section on "The Measurement of T," Chap. IV, the time during which an outer orbit, 
 not constituting a metastable configuration, may be occupied, is very much smaller, of the 
 order 10" 8 sec. 
 
 3 <> Ann. Physik, 45, pp. 625-56 (1914). 
 
74 ORIGIN OF SPECTRA 
 
 coplanar orbit, helium should resemble lithium and might therefore be 
 expected to be capable of forming compounds. Franck and Reiche 
 have suggested several means, some involving processes of this type, by 
 which the electron once in the 2 s orbit can return to normal without 
 emitting the monochromatic wave number 1 S 2 s. At the present 
 time, however, most of these hypotheses are highly speculative and 
 admitting the above general conclusions, the transitions from either 
 2 s or 2 S to normal, in the absence of a strong field, are not satisfactorily 
 explained. 
 
 Kemble 31 and more recently Van Vleck 32 have questioned the possibil- 
 ity of identifying the 1 S state with the crossed orbit system described, 
 so that Bohr's new computations of such orbits will be awaited with 
 the greatest interest. 
 
 THE HYDROGEN MOLECULE 
 
 Bohr 33 proposed a model of the hydrogen molecule consisting of 
 two nuclei each of unit positive qharge, with two electrons revolving 
 in the same circular orbit, the plane of which is symmetrically 
 located perpendicular to the line joining the nuclei. The dimensions 
 are fixed by the electric forces and the condition that each electron 
 has one unit of angular momentum. The total energy of such a 
 configuration is readily found to be 2.20 Nhc ergs. Referring to 
 Equation (3) or (17) the energy of two normal hydrogen atoms is 
 2 Nhc ergs. The difference in these two values accordingly should 
 give the work necessary to dissociate a hydrogen molecule into neutral 
 atoms. This amounts to 0.20 Nhc ergs or 2.7 volts. Bohr shows that a 
 configuration for the molecular positive ion, consisting of the two nuclei 
 and a single electron revolving about the line between them, is unstable 
 and hence the removal of one electron from the molecule may result in 
 its dissociation and the production of a neutral atom and an ionized 
 atom. The total energy for the latter state is 1.00 Nhc ergs. The 
 work required to ionize the molecule in this manner is accordingly (2.20- 
 1.00) Nhc, which is equivalent to 16.2 volts. 
 
 This configuration of the hydrogen molecule must be rejected for 
 the following and other reasons. 
 
 (1) Such a molecule would be paramagnetic, while hydrogen is 
 known to be diamagnetic. 
 
 Phil. Mag., 42, p. 123 (1921). 
 a* Phys. R., 19, pp. 419-20 (1922). 
 Phil. Mag., 26, pp. 857-75, (1913). 
 
IONIZATION AND RESONANCE POTENTIALS 
 
 75 
 
 (2) Langmuir's 34 experimental determination of the heat of dis- 
 sociation is 84000 cal/mol or 3.6 volts per molecule. 35 
 
 (3) Positive ray analysis shows the existence of positive molecular 
 ions. 
 
 The Bohr-Sommerfeld theory of the structure of the hydrogen atom, 
 on the other hand, is satisfactory, as the many remarkable experimental 
 confirmations of the series spectra and fine structure testify. As illus- 
 trated by Figure 4, the ionization potential of the atom should be 13.54 
 volts and the resonance potential 10.16 volts, corresponding to the 
 convergence frequency and first line respectively of the Lyman series. 
 
 Measurements of the critical potentials for hydrogen by different 
 observers show wide divergence both in the experimental values and in 
 their interpretation. The results of Horton and Davies and of the 
 authors, given in Table XV, are somewhat more consistent, showing 
 two resonance potentials at 10.5 and 12 to 13 volts, a trace of ionization 
 at a slightly higher point and strong ionization at 16 to 17 volts. Our 
 values would immediately suggest the following interpretation, on the 
 basis of Bohr's theory. 
 
 Volts 
 Observed 
 
 Type of Collision 
 
 Volts 
 Com- 
 puted 
 
 Observed 
 
 Theoretical 
 
 10.4 
 12.0 
 13.3 
 16.0 
 
 Strong resonance 
 Faint resonance 
 Very faint ionization 
 Strong ionization 
 
 Atom: 1st line of Lyman Series 
 Atom : 2d line of Lyman Series 
 Convergence of Lyman Series 
 Molecule: Bohr's configuration 
 
 10.2 
 12.0 
 13.5 
 16.2 
 
 In spite of this apparent agreement between theory and experiment 
 it is doubtful that the above table represents the correct analysis of the 
 data, the difficulty being in the accounting for the presence of the 
 quantity of monatomic hydrogen necessary to give such a pronounced 
 indication of a resonance potential at 10.4 volts. In experiments where 
 a hot cathode is employed there will be only a slight amount of thermal 
 dissociation even for a wire operated at 2500 C. There is possibly 
 
 " J. Am. Chem. Soc., 34, p. 860 (1912). 
 
 35 Relation between volts per molecule and calories per gram moL The kinetic energy m 
 ergs of an electron which has fallen through a field of x volts is given by Equation (66) : 
 1.592 X lO-i 2 x volts (66) 
 
 ergs 
 
 one 20 calorie = 4.183 10 7 ergs 
 number of molecules per gram mol = 6.06 
 Hence cal. /mol = 23070 x volts /molecule 
 and kg cal. /mol = 23.07 x volts /molecule 
 
 1Q23 
 
 (67) 
 (68) 
 (69) 
 (70) 
 
76 ORIGIN OF SPECTRA 
 
 sufficient dissociation, however, to account for the weak ionization 
 observed at 13.3 volts. Using pressures of about 0.1 to 0.2 mm Hg 
 in a discharge tube where the collisions occur over a space of 1 cni, it is 
 found that about half of the electrons lose 10.4 volts velocity at this 
 resonance potential. Now if J% of the gas at any instant had been 
 dissociated by the hot wire, a very liberal estimate, only one collision 
 in one hundred would have taken place with an atom. Hence one would 
 conclude that half of the electrons collided some 100 times elastically 
 in this small distance before encountering an atom responsible for the 
 energy loss of 10.4 volts, a conclusion at variance with probability 
 considerations. Thus it appears likely that the observed resonance 
 potential of 10.4 volts, as well as 12.0 volts, is due to the molecule. 
 
 We have made experiments using a potassium hvdride and potassium 
 surface as a photo-electric source of electrons, 36 instead of a hot cathode. 
 Precisely the same results were obtained, with the exception of ioniza- 
 tion at 13.3 volts, in regard to which no conclusion could be drawn, as 
 the sensitivity was not sufficient to detect this critical potential. It is 
 doubtful whether monatomic hydrogen could have been present in 
 such an apparatus, operated cold. 
 
 The possibility of dissociation by electron impact below the resonance 
 potential is still an open question, but even so, this could scarcely 
 account for a sufficient amount of atomic hydrogen to explain our 
 results. 
 
 The agreement between the observed value of 16.0 volts for the 
 ionization of the molecule and that predicted by Bohr's theory again 
 must be of no significance. Ef ionization of the molecule results in a 
 neutral atom and an ionized atom, the ionization potential should be 
 13.5 + 3.6 = 17.1 volts, on the basis of Langmuir's determination of 
 the work of dissociation. This disagreement with experiment suggests 
 the possibility that a molecular ion is formed at this low voltage. In 
 support of such argument we have found that the secondary spectrum 
 of hydrogen predominates over the Balmer series below 20 volts, and 
 the secondary spectrum is usually ascribed to vibrations of the molecule 
 or molecular ion. 
 
 It is possible that the ionization potential of the molecule represents 
 the work of dissociation plus the work of ionization of one atom minus 
 the electron affinity E of the hydrogen molecule. We then obtain 
 13.5 + 3.6 E-n = 16.0 or E u = 1.1 volts. Bohr's theoretical com- 
 putation, based on the configuration which we have shown to be 
 
 3Mohler, Foote, and Kurth, Phys. R., 19, p. 414 (1922). 
 
ION I Z AT ION AND RESONANCE POTENTIALS 77 
 
 objectionable, gives 1.6 Volts. 37 Further discussion of the question of 
 electron affinity and dissociation is given in Chapter VIII. 
 
 Although we have questioned the ascribing of the 10.4 volt resonance 
 potential, observed by the ordinary methods, to monatomic hydrogen 
 for the reason that we cannot account for a sufficient quantity of the 
 monatomic gas, there has never been any doubt as to the existence of a 
 
 resonance potential corresponding to v = N ( ^ for the atom 
 
 and an ionization potential corresponding to v = N, viz. 10.2 volts and 
 13.5 volts respectively. The well-known series relations require such 
 critical potentials. Duffenback 38 has recently assured the presence of 
 an atmosphere of monatomic hydrogen by operating the ionization 
 chamber in a tungsten tube furnace at 2000 to 2500 abs. At 2500 
 abs and 1 mm pressure 98.8 per cent of the gas is dissociated into atoms . 
 He found that with the furnace operated cold most of the ionization 
 occurred at about 16 volts, but at the higher temperatures the current 
 showed marked ionization at 10.3 and 13.2 volts. As will be discussed 
 in Chapter VI, arcs may be struck at the lowest resonance potential, so 
 that the appearance of the critical potentials 10.3 and 13.2 volts at high 
 temperature where considerable dissociation occurs is a confirmation 
 of the facts to be predicted from the line spectrum of the atom. 
 
 GENERAL REFERENCES 
 
 Hughes, A. L., Bull. Natl. Res. Coun., 2, pp. 127-169 (1921). An excellent tabu- 
 lar summary of the experimental determinations of critical potentials to about 
 March, 1921. As practically all observations by numerous observers are listed, 
 many of which were not made under satisfactory experimental conditions, some 
 judgment must be employed in selecting the most probable value where the range 
 is wide. 
 
 McLennan, J. C., Phys. Soc., London, 31, pp. 1-29, 1918. 
 
 Franck, J., Physik. Z., 22, pp. 388, 409, 441, 466, 1921. 
 
 Gerlach, W., Vieweg's " Tagesfragen" Number 58, pp. 8-52 (1921). This con- 
 tains a bibiliography of one hundred and thirty-three references. A large number 
 of American and English papers published after 1916 are omitted, however, on 
 account of their inaccessibility at that time. 
 
 37 Bohr, Phil. Mag., 26, p. 863 (1913), shows that the total energy of the neutral hydrogen 
 molecule on the above described configuration is W = 2.20Nhc ergs. The total energy for 
 the same configuration with three electrons instead of two in the common orbit, the plane of 
 which is perpendicular to the line joining the nuclei, is shown to be W = - 2.32Nhc ergs. 
 Hence an amount of work (2.32 2.20)Nhc = 0.l2Nhc ergs must be done on the second 
 system to reduce the molecular ion to the normal state. This is equivalent to 1.6 volts, a 
 value which accordingly represents the electron affinity of the normal molecule. 
 
 58 Science 55, pp. 210-211 (1922). 
 
 8 Lyman, Science, 56, p. 167 (1922), finds in helium the folio wing lines: X 584.4, X 537.1, 
 X 522.3, X 515.7, and possibly X 600.5. His paper appeared after this book was in page proof, 
 too late to incorporate in the discussion on page 72. The first four lines are members of a 
 series 1 X mP where 1 X= 198290 and IX 2 So fifth line above (approximately) o first 
 resonance potential. These observations conflict with measurements on ionization potential. 
 
Chapter IV 
 Line Absorption Spectra of Atoms 
 
 LINE ABSORPTION SPECTRA OF NORMAL ATOMS 
 
 In accordance with the classical theories of radiation, as expressed 
 by the usual interpretation of Kirchhoff's law, we should expect all 
 emission lines of an element to appear as absorption lines 1 when a column 
 of the vapor or gas is viewed against a source which emits a continuous 
 spectrum. Experimentally, however, in any particular arrangement 
 of apparatus we find that only for certain types of lines is absorption 
 readily observed. The quantum theory of spectra satisfactorily ac- 
 counts for this fact. 
 
 As a particular example we shall consider first the alkali metals. 
 For the normal unexcited atom the valence or outer electron lies in the 
 1 s orbit. The atom accordingly is capable of absorbing monochromatic 
 radiation in quanta of a frequency or energy value just sufficient to 
 displace the valence electron to an outer orbit. Radiation of frequency 
 corresponding to energy intermediate 2 to two outer orbits leaves the atom 
 unaffected. The atom is unable to resonate to such frequencies; it can- 
 not absorb them because there is no position of equilibrium which the 
 atom could assume and retain the energy. It cannot absorb a portion 
 of the energy just sufficient to reach a stable configuration beqause the 
 incident radiation exists in discrete, indivisible quanta which must be 
 absorbed in toto or not at all. 
 
 By the Bohr principle of selection the azimuthal quantum number 
 in any interorbital transition of an electron must change by it 1 unit. 
 Hence only those frequencies of the incident radiation will be absorbed 
 which result in the ejection of the valence electron to orbits for which 
 the azimuthal quantum number differs by unity from the normal state. 
 This requires that the electron pass from the 1 s orbit to an mp orbit 
 where m may have any value from 2 to <x> . Hence only radiation of 
 
 1 With some exceptions of academic interest. 
 8 For other cases, see Chapter X. 
 
 78 
 
LINE ABSORPTION SPECTRA 
 
 79 
 
 wave number v = 1 s mp is absorbed from the continuous source. 
 The long column of absorbing vapor thus accumulates energy and 
 would continue to increase in energy until the valence electron of every 
 atom finds itself in a p-orbit, but for the following two facts: (1) An 
 atom having its electron in a p-orbit or any other outer orbit is described 
 as an " excited atom" and is capable of absorbing other characteristic 
 radiation. This interesting phase of absorption spectra is treated in a 
 following separate section. (2) The electron once displaced almost 
 instantly resumes its normal 1 s position. 
 
 If the electron displaced to the mp orbit returns to the 1 s orbit in a 
 single jump, the line v 1 s mp is emitted. This emission, however, 
 for the long column of gas is spread over a solid angle 4 TT, whereas the 
 radiation absorbed from the source is confined to the narrow beam 
 passing through the gas. Radiation of frequency v I s mp is 
 accordingly abstracted from the beam of small solid angle and subse- 
 quently, by the above described indirect process, scattered in all direc- 
 tions. The result is that along the line of sight far more radiation is 
 absorbed than is emitted and the lines v 1 s mp stand out as sharp 
 absorption lines against the continuous source and the scattered radi- 
 ation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 58 55 52 50 48 46 
 
 FIG. 12. Principal series lines of sodium from m = 46 to 58, observed as absorpti 
 
 lines. 
 
 In general if 1 s or 1 S represents the normal orbit of the electron 
 in the unexcited atom, we should expect to observe as absorption lines 
 the wave numbers v = 1 s mp for the alkalis; 1 S mp 2 and IS 
 mP for the metals of Group II of the periodic table and similarly for the 
 other groups. Lines in emission series which converge at 1 s or 1 5, 
 when the orbits corresponding to these frequencies represent the normal 
 state, should be absorption lines, characteristic of the normal atom. 
 
 The experimental verifications of this simple theory are conclu- 
 sive. Wood and Fortrat, 3 using in effect a train of thirteen 60 
 quartz prisms, have examined the absorption spectra of a long column 
 (3 meters: 20 meters recommended) of sodium vapor of fairly low den- 
 
 3 Wood and Fortrat, Astrophys. J., 43, pp. 73-80 (1916). 
 
80 ORIGIN OF SPECTRA 
 
 sity. The only absorption lines appearing belonged to the principal 
 series Is mp. These were observed to m = 58, fifty-seven pairs, 
 although the resolution was not sufficient to separate the pairs beyond 
 m = 8. The last thirteen observed members of the series are indicated, 
 on a wave-length scale, by Figure 12. The wave-length corresponding 
 to the convergence frequency lies to the left of the line m = 58 about 
 the distance equal to the length of the portion of the series illustrated. 
 On this scale the D-lines would lie to the right a distance of 1100 feet. 
 Line m = 46 differs in wave-length from line m = 58 by about one 
 Angstrom unit. 
 
 Figure 13 illustrates the line absorption spectrum of sodium. The 
 upper spectrogram is from a negative made by Dr. G. R. Harrison and 
 shows the absorption of the second, third and fourth members of the 
 principal series. At low vapor pressure these lines are very sharp. 
 If the pressure is increased, higher terms are brought out, but the absorp- 
 tion of the first members widens into broad bands, as shown by the 
 lower spectrogram made by Prof. Wood. The central spectrogram, 
 also Wood's, shows the line absorption clearly, nearly to the head of the 
 series. We have marked twenty-one terms, but many more were readily 
 visible in the negative. The emission lines in these illustrations are 
 due to the cadmium or aluminum spark in air employed as a source. 
 
 The exact physical significance of the broadening of the lines at 
 high pressure has not been satisfactorily interpreted by the quantum 
 theory. 4 The necessity for employing high pressure in order to bring 
 out higher terms is to be expected. The chance that an electron be 
 displaced to say the 58th orbit is small when there are so many orbits 
 of nearly identical energy value. By increasing the pressure the number 
 of atoms is increased with a proportionate change in the probability 
 of a displacement to any individual orbit, and the resulting absorption 
 of the corresponding line. The same effect might be produced by in- 
 creasing the length of the column of vapor. The phenomenon at high 
 pressure is, however, complicated possibly by the interpenetration, 
 or certainly by the perturbations, of orbits of electrons in neighboring 
 atoms. 
 
 Wood's work on sodium has been extended to the other alkali vapors 
 by Bevan. 5 In this manner terms of the principal series were obtained 
 as absorption lines to m = 25 for potassium, m = 26 for rubidium, 
 m = 22 for caesium and m = 28 for lithium. 
 
 4 See page 91. 
 
 s Proc. Roy. Soc. Lond., 83, pp. 421-28 (1910), 85, pp. 54-8 (1910). 
 
2680 
 
 Z853 
 
 3303 
 
 FIG. 13. Absorption spectrum of sodium, showing absorption of principal series 
 lines. The bright lines are due to the source of light. 
 
SOB 
 
 215C 
 
 236 
 
 250 
 
 275 
 
 360 
 
 FIG. , 14. Absorption spectrum of mercury showing the absorption line X 2537, 
 1 S 2 p 2 . The emission lines are due to the source of light. 
 
80 C 
 
 FIG. 14A. Absorption of mercury X 2537. The continuous spectrum is produced 
 by an aluminum spark under water. Tungsten electrodes are still better. 
 
 Cs 
 
 8943.46' 
 
 FIG. 15. Reversals of the first pair of the principal series for the alkalis. The illus- 
 trations have been prepared on the same scale of wave-lengths. , 
 
SOD 
 
 * 
 
 FIG. 15A. Illustrating the practically complete absorption of rare mercury vapor for 
 the resonance radiation X 2537. 
 
LINE ABSORPTION SPECTRA 81 
 
 The important series converging at 1 S for the metals of Group II 
 are mainly confined to the ultra-violet. Wood first showed that the 
 mercury line 1 S 2 p%, X = 2537, is strongly absorbed by a column 
 of mercury vapor. Figure 14, by Wood, illustrates this absorption very 
 clearly. At low pressure, the absorption is very sharply defined, but as 
 the pressure of the vapor is increased, by increasing the temperature as 
 indicated, the line widens into a band. The absorption of this line is 
 now a matter of common experience in the operation of a quartz mercury 
 vapor lamp. If the lamp is overheated, as was first pointed out by 
 Wood, its actinic effect is greatly reduced on account of the absorption 
 of X 2537 by the dense vapor. A photograph of the arc under such 
 conditions shows almost complete absence of this line. On account of 
 the continuous spectrum which is produced with strong current and 
 high temperature X 2537 may appear as a strong reversal against the 
 faint background of the continuous emission spectrum. 
 
 Wood and Guthrie 6 found absorption in cadmium vapor for the 
 lines 1 S - 2 p 2 , X 3260 and 1 S - 2 ' P, X 2288. McLennan and Ed- 
 wards 7 have demonstrated that the mercury line 1 S 2 P, X 1849, is 
 entirely absorbed by a column of rare mercury vapor, but did not succeed 
 in obtaining it as a reversal against a continuous background. The 
 experimental difficulty here is in producing a suitable continuous source 
 of ultra-violet light. The best method so far devised 8 is the use of an 
 aluminum or preferably tungsten spark gap immersed in water and 
 excited by a very high voltage, using a Tesla coil, auxiliary air gap and 
 capacity. This gives a continuous spectrum throughout the visible 
 and in the ultra-violet at least to the limit of the quartz spectrograph. 
 It is obviously not suitable however for work with the vacuum spectro- 
 graph. For this range the Lewis 9 method employing hydrogen offers 
 a little hope, but its use is necessarily restricted. One will readily 
 appreciate the almost insurmountable difficulties in the determination 
 of absorption spectra of metallic vapors below X 2000. 
 
 McLennan and Edwards besides corroborating Wood's work ob- 
 served absorption and complete reversal against a brighter background, 
 
 6 Astrophys. J., 29, p. 211 (1909). 
 
 7 Phil. Mag., 30, pp. 695-700 (1915). 
 
 8 The electrical arrangement is described by Howe, Phys. R., 8, p. 681 (1916). Fig. 14A 
 shows the beautiful continuous spectrum which is easily obtained. If only the central portion 
 of the spark is employed practically no trace of emissidn lines is present. In this spectrogram 
 Dr. Meggers and the authors were endeavoring to obtain the line absorption spectrum of 
 arsenic vapor. This was unsuccessful, but the absorption of the mercury line X 2537 is very 
 pronounced, arising in the mercury which was present with the arsenic vapor. The mercury 
 emission spectrum is also shown for comparison. More recent descriptions of the spark 
 apparatus are given in " Transmissivity of Food Dyes." Bur. Standards Sci. Paper No. 440. 
 
 9 Science, 41, p. 947 (1915); Phys. R., 16, p. 367 (1920). Hulburt, Astrophys. J., 42, 
 
82 ORIGIN OF SPECTRA 
 
 in rare zinc vapor, of the zinc line 1 S 2 p 2 , X 3076 and complete 
 absorption of 1 S - 2 P, X 2139. 
 
 McLennan 10 using a column of magnesium vapor obtained reversal 
 of the line 1 S 2 P, X 2852, and showed the presence of absorption 
 for 1 S 3 P, X 2026. For some unexplained reason he could not 
 detect absorption of the fundamental line 1 S 2 p 2 , X 4571. 
 
 King's 11 work on furnace spectra shows that fundamentally important 
 lines are readily absorbed and may appear as reversals against the 
 brighter background of the furnace walls, for example X 4227, 1 S 2 P, 
 of calcium. King states that in general, for all metals the strong absorp- 
 tion lines are those which are excited as emission lines at low temperature. 
 Among these latter, as will appear in Chapter VII, are to be found the 
 fundamental lines of series converging at 1 S or 1 s, at least insofar as 
 the spectral region investigated covers that embraced by these series. 
 
 REVERSED LINES 
 
 The spectrum of a material obtained in an ordinary arc is in general 
 composed of emission lines. However, under certain conditions lines 
 are reversed, appearing black against the brighter background. An 
 example of this is shown by Figure 15, prepared by Meggers, for the first 
 pair in the principal series of each of the alkalis. The reversed portion, 
 which appears black, is much narrower than the emission line, showing 
 in the reproduction as a white band. 12 Generally absorption lines are 
 more nearly monochromatic than the corresponding emission line, in 
 part because of the smaller >oppler effect and lesser pressure of the 
 cooler vapor, but also for other reasons which have not been satis- 
 factorily explained. The reversal is due to absorption of the emitted 
 light by the zone of cooler vapor surrounding the arc. In the illus- 
 tration given the emission line for caesium is exceptionally broad. 
 Frequently, however, the emission lines are narrow and the reversal 
 may then almost or even completely cover the emission. Reversals 
 are found even in flame spectra. A narrow reversal of the D -lines 
 against the broader background of the emission spectrum is readily 
 observed in a long train of bunsen burners fed with salt. 
 
 Probably reversals in the arc can be obtained for all lines of series 
 converging at 1 s or 1 S. The observation of a reversal, however, does 
 not indicate that the line belongs to these series. Among the thousands 
 
 "McLennan, Proc. Roy. Soc., 95, pp. 273-9 (1919). 
 " Astrophys. J., 51, pp. 13-22 (1920). 
 
 12 It is of interest that the square root of the doublet separations for the alkalis v 
 plotted against atomic number gives an approximately straight line. 
 
LINE ABSORPTION SPECTRA 83 
 
 of reversals listed in the spectroscopic tables will be found all types of 
 lines, including those belonging to subordinate and combination series, 
 series converging at 2 s, etc., the explanation of which is given in the 
 section on excited atoms and in Chapters VI and VII. On the other 
 hand by careful consideration of reversed lines considerable information 
 may be derived concerning series relations. Thus with copper we 
 find a strong reversal of the pair X 3248 and X 3275, which fact combined 
 with our somewhat unsatisfactory knowledge of the series relations 
 for this element enables us to predict with a fair degree of certainty 
 that this is the pair 1 s 2 p which determines the value of the resonance 
 potential. For the same reason we are led to suspect that X 2428 is a 
 member of the principal series of gold, and is likely the term Is 2 pi, 
 although the series relations are entirely unknown. The fact that all 
 the lines of Paschen's principal series of thallium are so readily reversed 
 in the arc is a strong argument for assigning the notation 1 s to the 
 convergence frequency instead of 2 s, as suggested in the chapter on 
 ionization potential. In this particular case, however, the vapor may be 
 " excited" by the high temperature, as discussed in Chapter VII. Under 
 such conditions the fundamentally important lines should be suppressed 
 both in emission and absorption, especially so since the resonance po- 
 tential is extremely low. The work of Wood and Guthrie 13 on absorp- 
 tion of thallium vapor is suggestive but inconclusive and should be 
 repeated using as long a column of vapor at as low a temperature as 
 practicable. 
 
 McLennan and Young 14 have made an investigation of the arc re- 
 versals for calcium, strontium and barium. They observed the first 
 six lines of the series 1 S mP as reversals in calcium, ten lines of this 
 series in strontium and nine lines in barium. 15 
 
 One finds in the spectroscopic tables that at least the first term of the 
 series 1 S 2 P and 1 S 2 p% has been observed reversed for most of 
 the elements of Group II. In Table XVI are listed several of the early 
 members of these series. A few of these lines are merely computed 
 values, having been unobserved as yet either in emission or absorption. 
 In the last column, A denotes that the line has been observed as an 
 absorption line, using a long column of vapor; R as a reversal in an arc; 
 K as a reversal in furnace spectra, and F as an emission line in flame 
 spectra. It is noted that the wave-lengths of many of the lines are less 
 than 2000 A. These accordingly can be best studied, for absorption, 
 
 13 Astrophys. J., 29, p. 211 (1909). " Proc. Roy. Soc. 95, pp. 273-9 (1919). 
 
 15 Two of these were assigned entirely incorrect wave-lengths, viz., IS - 3P and IS - 4P 
 for barium. 
 
84 
 
 ORIGIN OF SPECTRA 
 
 as reversals in arcs. A suggested method suitable for the vacuum 
 spectograph is to employ a very long vertical tube with a Wehnelt cathode 
 arc at the bottom. The metal is boiled at the bottom and condensed 
 in the upper part of the tube, at the top of which is mounted the spectro- 
 graph, sufficiently distant to prevent contamination. The emission 
 lines will be broad on account of the higher pressure at the bottom of 
 the tube, thus furnishing a background for the absorption lines produced 
 by the long column of rarer vapor. There is, however, still a splendid 
 field for work at wave-lengths longer than 2000 A. especially with 
 elements of other groups of the periodic table. 
 
 TABLE XVI 
 
 IMPORTANT (FROM STANDPOINT OF ATOMIC STRUCTURE) SERIES LINES 
 FOR METALS OF GROUP II. COMPILED BY F. A. SAUNDERS 
 
 Element 
 
 Notation 
 
 i/ 
 
 X (vacuum) 
 
 X (air) 
 
 Remarks 16 
 
 Me . 
 
 18 
 
 61672 
 
 1622 
 
 
 
 
 
 21871 
 
 4572 
 
 4571 
 
 FK 
 
 
 1 <$ _ 3 p 2 
 
 47853 
 
 2090 
 
 
 
 
 1 S 4 pz 
 
 54253 
 
 1843 
 
 
 
 
 1 S 5 pz 
 
 57020 
 
 1754 
 
 
 
 
 1S-2P 
 
 35051 
 
 2853 
 
 2852 
 
 AFRK 
 
 
 1S-3P 
 
 49347 
 
 2026 
 
 
 RK 
 
 
 1S-4P 
 
 54703 
 
 1828 
 
 
 
 Ca 
 
 IS 
 
 49305 
 
 2028 
 
 
 
 
 
 15210 
 
 6575 
 
 6573 
 
 K 
 
 
 1 $ 3 pz 
 
 36555 
 
 2736 
 
 2735 
 
 
 
 1 S 4 pz 
 
 42519 
 
 2352 
 
 
 
 
 1 S 5 7)2 
 
 44962 
 
 2224 
 
 
 
 
 1S-2P 
 
 23652 
 
 4228 
 
 4227 
 
 RKF 
 
 
 1S-3P 
 
 36732 
 
 2723 
 
 2722 
 
 K 
 
 
 1S-4P 
 
 41679 
 
 2399 
 
 2399 
 
 RK 
 
 
 1S-5P 
 
 43933 
 
 2276 
 
 2275 
 
 RK 
 
 Zn . 
 
 1 
 
 75767 
 
 1318 
 
 
 
 
 1 S - 2 pz 
 
 32502 
 
 3077 
 
 3076 
 
 ARFK 
 
 
 1 S 3 2?2 
 
 61274 
 
 1632 
 
 
 
 
 1 >S 4 >2 
 
 68081 
 
 1469 
 
 
 
 
 1 $ _ 5 p 2 
 
 70982 
 
 1409 
 
 
 
 ._.. 
 
 1S-2P 
 
 46745 
 
 2139 
 
 2139 
 
 ARK 
 
 
 1S-3P 
 
 62902 
 
 1590 
 
 
 
 
 1>S-4P 
 
 68608 
 
 1458 
 
 
 
 
 IS -5P 
 
 71215 
 
 1404 
 
 
 
 16 A denotes that the line has been observed as an absorption line using a long column of 
 rare vapor. Continued on page 85. 
 
LINE ABSORPTION SPECTRA 
 
 85 
 
 TABLE XVI Continued 
 
 IMPORTANT (FROM STANDPOINT OF ATOMIC STRUCTURE) SERIES LINES 
 FOR METALS OF GROUP II. COMPILED BY F. A. SAUNDERS 
 
 Element 
 
 Notation 
 
 V 
 
 X (vacuum] 
 
 X (air) 
 
 Remarks 16 
 
 Sr 
 
 18 
 
 45926 
 
 2177 
 
 
 
 
 lS-2p 2 
 
 14504 
 
 6895 
 
 6893 
 
 K 
 
 
 1 S - 3 p 2 
 
 33869 
 
 2953 
 
 2952 
 
 
 
 lS-4p 2 
 
 39426 
 
 2536 
 
 
 
 
 IS -2P 
 
 21698 
 
 4609 
 
 4607 
 
 RFK 
 
 
 1 S - 3 P 
 
 34098 
 
 2933 
 
 2932 
 
 K 
 
 
 1S-4P 
 
 38907 
 
 2570 
 
 2570 
 
 RK 
 
 
 1S-5P 
 
 41172 
 
 2429 
 
 2428 
 
 RK 
 
 Cd 
 
 IS 
 
 72539 
 
 1379 
 
 
 
 
 IS -2p 2 
 
 30656 
 
 3262 
 
 3261 
 
 ARFK 
 
 
 lS-3p 2 
 
 58462 
 
 1711 
 
 
 
 
 !S-4p 2 
 
 65027 
 
 1538 
 
 
 
 
 !S-5p 2 
 
 67842 
 
 1474 
 
 
 
 
 IS-2P 
 
 43692 
 
 2289 
 
 2288 
 
 ARFK 
 
 . 
 
 1S-3P 
 
 59906 
 
 1669 
 
 
 
 
 1S-4P 
 
 65494 
 
 1527 
 
 
 
 
 1S-5P 
 
 68056 
 
 1469 
 
 
 
 Ba 
 
 IS 
 
 42029 
 
 2379 
 
 
 
 
 1 S - 2 p 2 
 
 12637 
 
 7913 
 
 7911 
 
 K 
 
 
 lS-3p 2 
 
 30815 
 
 3245 
 
 3244 
 
 K 
 
 
 1 S - 4 p 2 
 
 35892 
 
 2786 
 
 
 
 
 IS-2P 
 
 18060 
 
 5537 
 
 5535 
 
 RFK 
 
 
 IS-ZP 
 
 32547 
 
 3072 
 
 3072 
 
 RK 
 
 
 1S-4P 
 
 36990 
 
 2703 
 
 2703 
 
 RK 
 
 
 1S-5P 
 
 38500 
 
 2597 
 
 2597 
 
 RK 
 
 Hg. , 
 
 IS 
 
 84178 
 
 1188 
 
 
 
 
 lS-2p 2 
 
 39413 
 
 2537 
 
 2537 
 
 ARFK 
 
 
 !S-3p 2 
 
 69656 
 
 1436 
 
 
 
 
 1 S - 4 p 2 
 
 76464 
 
 1308 
 
 
 
 
 1 S - 5 p 2 
 
 79410 
 
 1259 
 
 
 
 
 IS-2P 
 
 54066 
 
 1850 
 
 
 AK 
 
 
 IS-ZP 
 
 71291 
 
 1403 
 
 
 
 
 1S-4P 
 
 78810 
 
 1269 
 
 
 
 
 1S-5P 
 
 79961 
 
 1251 
 
 
 
 16 (Continued) R denotes that the line has been observed as a reversal in an arc. 
 
 K denotes that the line has been observed as an absorption line in furnace spectra, i.e., 
 reversed against the bright walls of the furnace. 
 
 F denotes that the line has been observed as an emission line in a flame. 
 
 For relation between X (vac) and X (air) see data of Meggers and Peters, Smithsonian 
 Tables, 7th Ed., p. 293. Also Bui. Bur. Standards, 14, p. 731 (1918). 
 
86 ORIGIN OF SPECTRA 
 
 RESONANCE RADIATION 
 
 As stated earlier, the mechanism of line absorption of vapors involves 
 the re-emission of the radiant energy absorbed. This re-emitted light, 
 called resonance radiation, has been studied in considerable detail for 
 sodium and mercury. 17 If a bulb of pure sodium vapor at low pressure 
 is illuminated by a beam of light from a sodium flame or vacuum arc, 
 the vapor will diffusely emit radiation consisting of only the two D- 
 lines, 1 s 2 pi and 1 s 2 p 2 . At very low pressure, less than that 
 corresponding to saturation at 150 C, the entire bulb is filled with a 
 faint glow. As the pressure is increased the diffusely emitted light 
 becomes concentrated near the place of incidence of the exciting beam 
 of radiation, and at 250 C, pressure about 0.01 mm, is confined to the 
 extreme surface. 
 
 These phenomena show that the effective part of the incident radi- 
 ation is absorbed in a very thin layer of the vapor at the higher temper- 
 ature while at lower temperatures and pressures the radiation penetrates 
 the bulb and is passed on from atom to atom throughout the volume. 
 
 Analysis of the emitted light by the interferometer shows that the 
 entire width of the lines, about 0.03 A, may be accounted for by the 
 Doppler effect alone of the vapor at this comparatively low temperature. 
 Only a portion of the exciting D-radiation is absorbed so that the beam 
 passing through the vapor shows a very narrow absorption line in the 
 center of each of the broad, transmitted D-lines. 
 
 Strutt 18 has found that the sodium doublet 1 s 3 p, X 3303, like- 
 wise excites resonance light. In this case the emitted radiation consists 
 of both D-lines and radiation of the frequency absorbed, X 3303. This 
 is in accord with the quantum theory. Absorption of a quantum of 
 radiation of wave-length X 3303 ejects an electron from the 1 s orbit to 
 either the 3 pi or 3 p 2 orbit. This energy may be given up either by a 
 direct return to 1 s with the emission of 1 s 3 p or indirectly by a 
 transition to 2 p and from there to 1 s, the latter step involving the 
 emission of the D-lines.. The Bohr principle of selection shows that, 
 in the absence of a disturbing field, a direct fall from 3 p to 2 p with the 
 emission of 2 p 3p should not occur, a fact confirmed by Strutt. The 
 transition between these two orbits must be made through either the 
 2 s or 3 d orbit as an intermediate stage, as shown by Figure 9. The 
 following table illustrates the various steps involved as a consequence 
 
 17 Cf. Wood's " Physical Optics," 2d Ed. The discovery and a great part of the develop- 
 ment of this subject is due to Wood and his co-workers. 
 "Proc. Roy. Soc., 96, pp. 272-86 (1919). 
 
LINE ABSORPTION SPECTRA 
 
 87 
 
 of the absorption of 1 s 3 pi. A similar table may be prepared for an 
 initial absorption of 1 s 3 p 2 in which all steps from d on are the same 
 as here given. Absorption of 1 s 3 p\ accordingly may be followed 
 by emission through the successive stages b or c, e, i, or d, g, i or d, h, j, 
 etc. With many atoms returning to normal by different paths, all of the 
 lines given in this table may be emitted. Strutt's observation that 
 both D-lines as well as 1 s 3 p are emitted when the exciting radiation 
 is 1 s 3 p is accordingly confirmed by the theory. The reason that 
 Strutt did not observe the other lines listed is because they all lie in the 
 infra-red. 
 
 TABLE XVII 
 
 Step 
 
 Position of Valence 
 Electron 
 
 Radiation 
 
 Wave-length 
 in A 
 
 
 Initial 
 
 Final 
 
 Notation 
 
 Remarks 
 
 
 a 
 
 Is 
 
 3P1 
 
 Is -3 pi 
 
 absorbed 
 
 3302.5 
 
 b 
 
 3pi 
 
 Is 
 
 Is - 3pi 
 
 radiated 
 
 3302.5 
 
 c 
 
 3 pi 
 
 3d 
 
 3d -3pi 
 
 u 
 
 90480. 
 
 d 
 
 3pi 
 
 2s 
 
 2s 3pi 
 
 u 
 
 22056.9 
 
 e 
 
 3d 
 
 2 pi 
 
 2 Pl - 3d 
 
 u 
 
 8196.1 
 
 f 
 
 3d 
 
 2p 2 
 
 2p 2 -3d 
 
 11 
 
 8184.5 
 
 g 
 
 2s 
 
 2pi 
 
 2 pi- 2s 
 
 It 
 
 11404.2 
 
 h 
 
 2s 
 
 2p 2 
 
 2p 2 -2s 
 
 11 
 
 11382.4 
 
 i 
 
 2pi 
 
 Is 
 
 l-2pi 
 
 11 
 
 5890.2 
 
 j 
 
 2p 2 
 
 Is 
 
 1 s - 2 p 2 
 
 It 
 
 5896.2 
 
 If sodium vapor is excited by one of the D-lines alone, we should 
 expect that only this line would appear in the resonance radiation, since 
 a transition from 2 pi to 2 p 2 involving an emission of 2 p 2 2 pi is 
 contrary to the Bohr principle of selection and a transition from 2 p 2 
 to 2 pi requires additional energy. Wood and Dunoyer 19 concluded 
 that resonance radiation excited by one D-line consisted of that D-line 
 alone. Wood and Mohler, 20 however, later, showed that this was true 
 only at extremely low pressure. If the pressure of the sodium vapor is 
 increased or if hydrogen is added, both D-lines appear when the excita- 
 tion is by either DI or D 2 alone. It is possible that the principle of 
 selection is broken down at high pressure by the disturbing field of 
 
 iPhil. Mag., 27, p. 1018 (1914). 
 2 Phys. R., 11, p. 70 (1918). 
 
88 ORIGIN OF SPECTRA 
 
 neighboring atoms. In such case by excitation with 1 s 2 pi the 
 infra-red line 2 p 2 2 p lt \ 590 n (1/17 cm), may be emitted with the 
 subsequent emission of 1 s 2 p 2 - For the same reason excitation by 
 1 s 2 p 2 may be followed by absorption of 2 p 2 2 pi from the con- 
 tinuous emission spectrum, black-body distribution, of the walls of the 
 vessel or room. This would eject the electron to the 2 pi orbit, thus 
 permitting the subsequent emission of 1 s 2 p t . It is also possible, 
 when we are concerned with such extremely minute quantities of energy 
 as are represented by quanta of wave-length 1/17 cm, that atomic 
 collisions may play an important role and .that the transfer of the electron 
 between 2 pi and 2 p 2 is the direct result of slightly inelastic collision. 
 Under such circumstances the principle of selection would not be 
 violated. 
 
 Mercury vapor at low pressure shows resonance radiation for the 
 line X 2537, 1 S 2 p 2 . No investigation has been made with excitation 
 by other fundamental lines, 1 S 3 p 2 , 1 S 2 P, etc., since they lie in 
 an inconvenient spectral region, as. shown by Table XVI. If the width 
 of the resonance line is due entirely to the Doppler effect, we have for the 
 vapor at room temperature: 
 
 width of line = 0.86 10~ 6 X VT/M = 0.0026 Angstrom. 
 
 Hence to observe the absorption of this line or the reversal of such a 
 narrow line against the broad emission spectrum should require high 
 resolving power. The pressure of mercury vapor at room temperature is 
 about 0.001 mm Hg; at 60 C, 0.02 mm; at 100 C, 0.28 mm. This small 
 variation in temperature does not materially change the Doppler effect, 
 yet at even 60 C the absorption of a short column of mercury vapor may 
 be readily observed with a prism spectrograph and a pronounced reversal 
 obtained against a continuous source, similar to the reversals shown in 
 Figure 14. It is an experimental fact that absorption of X 2537 by mercury 
 vapor at 20 C cannot be detected with an ordinary prism-spectrograph, 
 because of the insufficient resolution. Yet a very short column of rare 
 vapor is opaque to a portion of this line, a fact simply and clearly dem- 
 onstrated by Wood. A saucer containing mercury at room temper- 
 ature was photographed with a quartz-lens camera against the resonance 
 radiation emitted by a bulb of mercury vapor, which was excited by a 
 beam of radiation X 2537. The photograph showed the opaque clouds 
 of the vapor rising over the dish. If the photograph is made with an 
 ordinary source of X 2537, many times broader than the absorption line, 
 the vapor above the saucer appears transparent. 
 
LINE ABSORPTION SPECTRA 89 
 
 Figure 15 A obtained by Wood 21 shows the shadow cast by a quartz 
 bulb filled with mercury vapor at room temperature when illuminated 
 by the mercury resonance radiation. The opacity of the extremely 
 rare vapor to this radiation is readily apparent, the entire bulb appearing 
 black. 22 
 
 If a beam of X 2537 from an ordinary mercury arc passes through a 
 column of mercury vapor at low pressure the scattered light is not con- 
 fined to the geometrical boundary of the beam, but as mentioned earlier 
 for sodium, is diffusely radiated throughout the vapor. Wood 23 has 
 measured the rate at which the intensity decreases in mercury vapor at 
 0.001 mm Hg pressure in a direction at right angles to the geometrical 
 boundary of the beam as follows : 
 
 Distance 
 
 Relative Intensity 
 
 0.0 mm 
 
 1/1 
 
 0.5 
 
 1/3 
 
 1.5 
 
 1/6 
 
 2.5 
 
 1/10 
 
 3.5 
 
 1/30 
 
 These data probably give an approximate measure of the absorption 
 coefficient of the vapor for the resonance radiation. For example, 
 0.5 mm of mercury vapor at 0.001 mm Hg pressure may reduce the 
 intensity of a beam of resonance radiation to 1/3 its initial value. It 
 is unfortunate that the value of the absorption constant, the importance 
 of which will appear in Chapter VI, has not been measured by a more 
 direct method, but very likely the experimental difficulties would be 
 considerable. 
 
 An exact definition of resonance radiation is difficult to formulate. 
 Originally the term referred to the radiation of the,same wave-length as 
 that of the exciting source, emitted by a vapor which before the excita- 
 
 21 "Researches in Physical Optics," Part I, Columbia University Press. 
 
 22 In a recent letter R. W. Wood gives the results, as yet unpublished, of experiments 
 on the intensity of mercury resonance radiation. The intensity is increased by the addi- 
 tion of helium or argon, although other gases reduce the intensity of the radiation or de- 
 stroy it entirely. In helium at 33 cm, the radiation is 4 times as strong as in Hg vapor alone 
 at room temperature (.001 mm pressure). The complete explanation of these 'phenomena 
 is probably quite complicated, but it has been shown experimentally that the increase of in- 
 tensity by helium is due to the fact that the spectral range absorbed (out of the middle of 
 the broad 2537 exciting line) is widened, so that more energy is diverted from the primary 
 beam. This was proved by first passing the exciting beam of X 2537 light through a cell of 
 Hg vapor in vacuo. It was thus freed of all frequencies capable of exciting Hg vapor in vacuo ; 
 however, it excited powerfully Hg in helium. 
 
 23 "Researches in Physical Optics, "Part I, p. 54. 
 
90 ORIGIN OF SPECTRA 
 
 tion was in a normal state. Hence the D-lines stimulated by the D- 
 lines may be called resonance radiation, while the excitation of the D- 
 lines by the second pair of the principal series would not fall within this 
 classification. We shall see, however, in the following section that an 
 atom having an electron in an outer orbit y for example the 2 p 2 orbit, 
 is capable of absorbing the first line of a subordinate series and subse- 
 quently may re-emit the line as strictly resonance radiation. Accord- 
 ingly, even if we rigidly restrict the terminology resonance radiation to 
 the emission of the same radiation as that of the stimulating source, 
 any line whatever may be a resonance line depending upon the state of 
 the vapor. If the atoms are in a normal condition, lines of the funda- 
 mentally important series converging at 1 S or 1 s may be resonance 
 lines. If the atoms are "excited, "as explained in the following section, 
 lines of other series may show resonance radiation. The phenomenon 
 is simply a consequence of absorption. Any line which is absorbed, 
 by a monatomic vapor, from a beam of radiation, subsequently may be 
 radiated in all directions, and observed as scattered light. 
 
 It may be that the definition 'of resonance radiation should be re- 
 stricted, as advocated by Franck, to the case where the emitted fre- 
 quency is the only one possible. This would require in general that the 
 first line of a principal series, converging at 1 S or 1 s, or a combination 
 line if of lower frequency, should be a resonance line, for example Is 
 2 p for the alkalis and 1 S 2 p 2 for the alkali earths. Further, since 
 transitions from 2 P to 2 p z in the absence of a disturbing field are con- 
 trary to the Bohr selection principle, tHe line 1 S 2 P should be a 
 resonance line for metals of Group II even upon the above restricted 
 definition. Franck classes the scattered emission of the line 2 s 2 p 
 of helium, X 10830, as resonance radiation because the 2 s state is a 
 metastable configuration and an electron in the 2 p orbit can give rise 
 to the emission of only 2 s 2 p. 
 
 The phenomena of resonance radiation must not be confused with 
 the fluorescence of metallic vapors. Fluorescent spectra are best 
 observed with much greater vapor densities and with intense illumi- 
 nation. The emitted radiation is very complicated and depends upon 
 the wave-length of the exciting source. The stimulus may have an 
 entirely different wave-length from any line in the emission spectrum 
 of the pure vapor. As briefly described in the latter part of this chapter, 
 fluorescence may be generally ascribed to unstable, polyatomic, molecu- 
 lar formations. 
 
LINE ABSORPTION SPECTRA 91 
 
 THE BROADENING OF SPECTRAL LINES 
 
 We have seen that the narrow portion of the line X 2537, represented 
 by the resonance radiation from mercury vapor at room temperature, 
 is almost totally absorbed by a very short column of mercury vapor at 
 0.001 mm pressure, while by increasing the pressure to several mm the 
 entire line is absorbed. On further increase in pressure the line widens 
 into a band. 
 
 The increase in width of an absorption, or emission, line has been 
 considered from the classical dynamical standpoint by Rayleigh, 24 
 Lorentz 25 and others. Rayleigh discusses five different causes for 
 broadening, and Franck 26 has interpreted three of these in relation to 
 the quantum theory. Two causes, the Doppler Effect and Impact 
 Damping, are of particular interest. 
 
 Doppler Effect. From the classical theory, a quasi-elastically bound 
 electron, vibrating with a frequency V Q and moving with a velocity v 
 in a direction making an angle <j> with the line drawn from the atom to 
 the observer gives rise to the frequency 
 
 
 v = v l + -cos<f> 
 
 where c is the velocity of light. In consequence of the Maxwellian 
 distribution of velocities of the atoms of a radiating gas, we have a 
 broadening of the spectral line about the monochromatic frequency VQ, 
 which leads directly to the useful expression given on page 27 for the 
 width of a line. In general v is small compared to c, so that the broaden- 
 ing amounts to only a few hundredths of an Angstrom. In the case of 
 canal rays, however, we have a stream of radiating atoms projected with 
 high velocity in a single direction, so that instead of a broadening we 
 
 have a shift of frequency Aj7 = =F VQ - , according as one looks with or 
 
 c 
 
 against the direction of propagation of the beam, amounting to an 
 easily observable quantity, of the order of an Angstrom unit. 
 
 The above explanation, which is so simple from the classical dynamical 
 standpoint, especially in its relation to familiar acoustical phenomena, 
 is by no means satisfactory on the basis of the quantum theory. Here 
 we give individuality to the quantum and are led to question how the 
 energy of a quantum projected in the direction of the beam may differ 
 
 2 < Phil. Mag., 29, pp. 274-84 (1915). 
 K. Akad. Amsterdam Proc., 18, pp. 134-50 (1915). 
 
 "The Broadening of Spectral Lines," 5 pp., Anniversary Volume of Kais. Wilh. Ges. 
 (1921). 
 
92 ORIGIN OF SPECTRA 
 
 by 2 Mi* ergs from that projected at 180 to this direction. The ex- 
 planation lies in the effect of the radiation pressure. The emission of a 
 quantum projected in the direction of the speeding atom produces a 
 recoil upon the atom and retards it. The quantum thereby abstracts 
 from the kinetic energy of the atom, hkv ergs, so that the frequency of 
 emission is increased by Ay. If the emission takes place in a direction 
 opposite to that along which the atom is projected, the atom is acceler- 
 ated by the emission, its kinetic energy is increased by Mj7 ergs, and 
 the frequency of the quantum is lowered by Ai/. 
 
 The magnitude of the Doppler effect thus remains the same, but 
 the interpretation of the phenomenon is different by the two theories. 
 
 Impact Damping. At high pressure and also in a strong electrical 
 discharge the broadening of lines may be many times greater than that 
 attributable to the Doppler effect. Lorentz considered this phenomenon 
 as due to impacts from neighboring atoms which an atom suffers during 
 the process of emission. If the emission is broken up by the impact, 
 or if a phase change is produced, it may be shown that the emitted 
 radiation will consist of a dispersion of frequencies which is greater 
 the shorter the time of the undisturbed emission. Since the number of 
 impacts increases with increasing pressure, we obtain an increase in 
 broadening of the line, a fact well established by experiment. 
 
 The quantum theory substitutes for impact damping the influence 
 of the electrical fields of neighboring atoms upon the position and energy 
 of the electron in a quantized orbit. Since the energy of any orbit is 
 altered, the energy difference of the two orbits between which an electron 
 jump takes place may be changed, with a resulting modification of hv. 
 
 As will appear in the following section, an electron may occupy an 
 outer orbit in an undisturbed atom for an appreciable length of time r. 
 Franck believes that if such an atom which is in a condition to emit a 
 spectral line, collides with another atom, the time r is immediately 
 altered and the emission is forced to take place while the orbits of the 
 radiating atom are deformed by the electrical field of the impacting 
 atom. Since all types of collision may occur, resulting in different de- 
 grees of orbital deformation, a dispersion of frequencies will be produced 
 with a resulting broadening of the emission line. Also since the number 
 of collisions increases as the pressure is raised, the amount of broadening 
 should increase. An analogous interpretation may be given to the 
 phenomenon of absorption so that probably the remarkable broadening 
 of the absorption lines noted in the foregoing section is mainly due to 
 the disturbance of inter-atomic fields by atomic collision. 
 
LINE ABSORPTION SPECTRA 93 
 
 LINE ABSORPTION SPECTRA OF EXCITED ATOMS 
 
 An excited atom is one having an outer electron in an orbit other 
 than its normal orbit. We shall first consider atoms for which the 
 outer electron is in the orbit of next higher energy level than that of the 
 normal position. For hydrogen this is the second ring; for the alkalis, 
 the orbit 2 pi or 2 p 2 ; and for the metals of Group II of the periodic 
 table, the orbit 2 p 2 . In the latter case we shall neglect consideration 
 for the present of the orbit 2 p 3 which lies between 1 S and 2 p 2 . 
 
 Two means have been already discussed by which the valence electron 
 may be ejected to this second orbit. First, as the immediate result of 
 an electron collision at the resonance potential or as an indirect result of 
 recombination, following ionization, and return toward normal, the 
 electron may temporarily assume a position in the second orbit. Second, 
 the electron may be ejected to the second orbit directly by absorption 
 of radiation of such frequency as Is 2 p or 1 $ 2 p 2 as discussed 
 in the preceding section, or indirectly by the absorption of any radi- 
 ation of the type Is mp followed by subsequent emission of a line 
 in a series converging at 2 p. A third method, which is discussed in 
 Chapter VII, involves a consideration of the effect of elevated temper- 
 atures. There is evidence that merely heating a gas drives a valence 
 electron to an outer orbit. 
 
 The electron once in the second orbit does not in general remain 
 there long, and if undisturbed falls into the normal orbit emitting the 
 first line of the principal series the single-line spectrum as shown 
 in Chapter^. The question as to the length of time r the second orbit 
 is occupied is a most fundamentally important one and will be considered 
 below. 
 
 THE MEASUREMENT OF T 
 
 Suppose in the case of mercury that the atom remains in the excited 
 condition for exactly r sec., and that the time required for a stimulus 
 to thus activate the atom and the time during which radiation is subse- 
 quently emitted is small compared to r. That is, suppose the time 
 required for any interorbital transition were negligibly small compared 
 to the time during which an electron occupied an outer ring such as the 
 2 p 2 orbit. This being true we shall consider what may be done with a 
 unidirectional stream of mercury vapor issuing from a properly designed 
 nozzle, as shown in Figure 16. This stream is illuminated at b by a 
 small diaphragmed beam of radiation of wave-length X 2537, the cross 
 
94 
 
 ORIGIN OF SPECTRA 
 
 section of the beam being represented by c. The atoms are accordingly 
 stimulated at b and for each excited atom a valence electron is ejected 
 to the 2 p 2 orbit, as a result of the exciting radiation. On account of 
 the velocity of translation of the atoms, which may be determined by a 
 measurement of the temperature of the boiling vapor or by other means, 
 the atoms travel to the position b' before returning to the normal state. 
 Accordingly at b' there should be an emission of the line X 2537 and the 
 distance b to b' gives a measure of the time T in the excited state. 
 
 FIG. 16. Unidirectional stream of mercury vapor. 
 
 Unfortunately, although such an experiment yields interesting 
 results which will be considered in the latter part of this chapter, it has 
 no bearing upon the life of an excited atom. That this is true is evident 
 from a consideration of the molecular velocities involved. The most 
 probable velocity, as follows from the kinetic theory of gases, is given 
 by the expression v = 12900 \/T/M where T is the absolute temperature 
 and M the molecular weight of the gas. For mercury at 500 abs we 
 obtain a velocity of 2 X 10 4 cm/sec. Hence in 10-s sec., which, as 
 will appear, is the probable order of magnitude of the result desired, 
 
LINE ABSORPTION SPECTRA 95 
 
 the atoms would have traveled the almost imperceptible distance 
 2 X 10"^ cm. Furthermore, aside from the above and the question 
 of the distribution of velocities in the stream, and the fact that the 
 time r is a mean phenomenon analogous to mean free path, etc., other 
 difficulties may arise which make such an experimental arrangement 
 impossible. For example some of the radiation emitted when an atom 
 returns to the normal state may be absorbed by a neighboring atom so 
 that the original radiation is passed on successively by many atoms, if 
 the pressure is high, before it finally escapes from the stream. Horton 
 and Davies observed that radiation produced at the resonance potential, 
 21.2 volts, in helium, in one side of a well-shielded U-tube was passed 
 on from atom to atom, finally appearing at the other end of the tube. 
 The phenomenon is well known in the study of resonance radiation 
 where the entire bulb is filled with a glow by a narrow beam of exciting 
 radiation. If this effect were predominant, measurements such as the 
 above would simply give the average length of time that the radiation 
 in a particular apparatus may be passed on from atom to atom. 
 
 We define r as the average time during which an electron remains 
 in an outer orbit of an atom. If at a given time t = 0, we have NO 
 excited atoms, then the number N which remain in the excited state 
 after t seconds have elapsed is 
 
 N = N Q e- 2at , - 
 I 
 
 ! where a is a constant. It is at once apparent that the average value of t 
 for all the atoms is given by T = 1/2 a. 
 
 The constant a may be determined experimentally in the following 
 manner, where we shall consider, for simplicity of explanation, the X 
 2537 line of mercury. A canal ray tube is employed which is divided 
 into two chambers, A and B, separated by the cathode through which an 
 extremely small hole or slit is cut. The vapor is excited in chamber A by 
 electronic bombardment at several thousand volts. The resulting 
 positive ions are driven to the cathode and some of these are projected 
 with high velocity through the hole into the chamber B. This latter is 
 maintained at the highest possible vacuum by vapor pumps, liquid 
 air, etc., so that no disturbing collisions will occur here. The cathode 
 acts a shield to the region B, keeping away stray ejectrons. Yet it is 
 found that the atoms in B are neutral. This means that each atom 
 projected through the chamber B, as the result of the velocity which it 
 accumulated while an ion in chamber A, recombined somewhere in A, 
 probably very close to the cathode. Let us assume tentatively that at 
 
96 ORIGIN OF SPECTRA 
 
 
 the instant each now neutral atom penetrates chamber B, it is in a state 
 to emit X 2537; that is, a valence electron lies in the 2 p 2 orbit. At 
 this point, for some few atoms, the valence electron drops to the normal 
 1 S orbit, the process occurring for all the atoms, relative to time, as 
 indicated by the above equation. Since, however, the atoms all have 
 a very high unidirectional velocity, the resumption of the normal condi- 
 tion occurs over a considerable length of space for the entire group of 
 atoms. As each return to normal is accompanied by the emission of a 
 quantum of X 2537, we obtain a streak of emitted radiation, which may 
 be several cm in length for a light element, the intensity of which de- 
 creases, as follows from the above, proportionally to e~ 2ax/v , where x 
 is the distance of penetration in B and v is the velocity of the stream. 
 This velocity may be found by observation of the Doppler effect 
 in the emitted radiation. 27 
 
 Wien 28 has made extensive measurements on hydrogen, nitrogen and 
 oxygen, but at present the experimental difficulties have not permitted 
 the use of vapors such as mercury. 29 In general the theory is not quite 
 as simple as that outlined above. The atoms entering the chamber B 
 are in excited states corresponding to the outermost quantized orbits. 
 They are therefore capable of emitting any of the arc lines. The inten- 
 sity of H0 (for example) representing an interorbital transition between 
 orbits of quantum numbers 4 and 2 first increases slightly and then 
 decreases in accordance with the law already given. Mie 3 ? shows such 
 an effect is to be expected. 
 
 The value of 2 a is found to be of about the same magnitude for 
 different lines even with different elements. For the and 7 lines 
 of hydrogen Wien observed 2 a = 4.35 -10 7 sec" 1 or r = 2.3 -10~ 8 sec. 
 Dempster 31 obtained for H0, T = 5- 10~ 8 sec. 
 
 The conception of the occupancy of an outer orbit for an appreciable 
 time has as an analogue the emission of damped vibrations in accordance 
 with the ideas of classical dynamics. Thus the damping constant for a 
 radiating electron vibrating about its position of equilibrium may be 
 shown to have the form 
 
 8 
 
 3 me 3 
 
 " Wood has described several methods (Proc. Roy. Soc., 99, pp. 362-371, 1921) for the 
 measurement of the very short time interval between the absorption of light by phosphores- 
 cent substances and its re-emission. Possibly the modification of the Abraham and Lemoine 
 method therein described could be applied to the measurement of T for resonance radiation. 
 
 28 Ann. Physik, 60, pp. 597-637 (1919); 66, pp. 229-36 (1921). 
 
 29 In part probably because of the very high voltage necessary to produce a sufficient 
 velocity of the heavy mercury ions. See Fig. 45 (Appendix I) . 
 
 so Ann. Physik, 66, pp. 237-60 (1921). 
 si Phys. R., 15, pp. 138-9 (1920). 
 
96 A 
 
 FIG. 17. Spectrum of Zeta Tauri from H T to limit of Balmer series (last line showing 
 H 3 i) made with 37| inch reflector. These hydrogen lines are all absorption 
 lines, reversed against the continuous background of the stellar emission spec- 
 trum. 
 
 FIG. 18. Reversal of hydrogen alpha in the laboratory. 
 
 J440 
 
 j 1 1 1 1 1. r. 
 
 S+SO 
 
 I 
 
 S470 
 
 iifii iiTiiirhT 
 
 I III I ill i I i Til 1 1 I 
 
 I 
 
 I 
 
 FIG. 19. The upper spectrogram shows the reversal of the mercury line X 5461, 
 2 pi 1 s, against the solar spectrum. The lower spectrogram shows the solar 
 source alone. 
 
LINE ABSORPTION SPECTRA 97 
 
 This gives for the average duration of the emission r = 1/2 a = 2- 10~ 8 
 sec. for H a . In general we may conclude that r is of the order 10~ 8 sec. 
 
 ABSORPTION OF SUBORDINATE SERIES LINES 
 
 It is readily seen by referring to the energy diagrams, Figures 4 to 9, 
 that an atom having an electron in the second or 2 p ring is capable of 
 absorbing any radiation belonging to spectral series which converge at 
 this energy level. The process is identical with that discussed in the 
 preceding section, except all the transitions take place from the second 
 instead of first orbit. This is the explanation of the appearance of the 
 Balmer series of hydrogen as absorption lines or of the frequently ob- 
 served reversals of lines of the subordinate series in the case of the 
 alkalis and alkali earths. Figure 17 shows the spectrum of Zeta Tauri 
 in which lines of the Balmer series from H y to H 3 i appear sharply re- 
 versed. This illustration is from a photograph made by Dr. R. H. 
 Curtiss, University of Michigan, for the authors. The absorption is 
 produced by a stratum of excited hydrogen atoms against the continuous 
 emission spectrum from an interior laye'r in the star. 32 The solar spec- 
 trum also shows as Fraunhofer lines many lines belonging to subordinate 
 series, for example the C line which is H a . The literature abounds 
 with examples of such reversals in the arc. Meggers 33 mentions the 
 reversal of X 8183, X 8195, 2 p - 3 d, the first pair of the 1st Subordinate 
 series of sodium. Many similar cases are to be found in Kayser's tables. 
 The arc reversals, which appear as narrow black lines on the bright, 
 wider background of the emission spectra are readily observed visually 
 in a cored carbon arc. Usually they flash on for only a few seconds: 
 it is very difficult to obtain more than a momentary appearance of a 
 large number of such absorption lines at the same time. This momen- 
 tary character is due to the constant shifting of the envelope of absorbing 
 and excited vapor immediately surrounding: the arc. 
 
 Spectroscopists have in the past made little differentiation between 
 the reversal of a line of a principal series and a line of a subordinate 
 series. In fact the principal series of an alkali has been incorrectly 
 called its Balmer series because its lines are all easily absorbed, giving a 
 spectrum resembling the Balmer lines in the spectra of certain stars 
 (compare Figures 12, 13, and 17). The physical mechanisms, however, 
 producing the Fraunhofer C and D lines are entirely different, a fact 
 readily recognized when one attempts to show in the laboratory the 
 Balmer absorption spectrum of hydrogen. No one has ever produced in 
 
 32 See Chapter VII. Bur. Standards Sci. Paper. No. 312. 
 
98 ORIGIN OF SPECTRA 
 
 the laboratory a subordinate series spectrum at all resembling that given 
 in Figure 17, although it is not difficult to obtain such a spectrum for a 
 principal series. 
 
 The authors have devised many methods for producing this peculiar 
 type of absorption so far without much success. The resonance 
 potential of the hydrogen atom is 10.2 volts. Hence if a hydrogen 
 atom collides with a 10.2 volt electron, it is capable for an instant of 
 absorbing a line of the Balmer series. A similar condition in reference 
 to the subordinate series holds for sodium bombarded by 2.1 volt elec- 
 trons. Another suggested method is to illuminate sodium vapor with 
 intense radiation from a sodium flame. The resulting absorption of the 
 D-lines should activate the sodium atoms so that they would be capable 
 of absorbing the subordinate series. A long train of sodium flames 
 should be capable of showing this absorption. Zahn, 34 from photo- 
 metric measurements and determinations of the quantity of sodium 
 present in a flame, has computed that each sodium atom emits about 
 2000 quanta of D-radiation per second. If the time during which the 
 atom remains in the active state is'10" 8 sec., an atom on the average, 
 per second, has an electron in the 2 p ring for 2000 X 10~ 8 or about 10~ 5 
 sec. In other words at any instant about 1 in 50,000 sodium atoms 
 is capable of absorbing subordinate series lines. This proportion 
 should be sufficient to show some effect in a long train of flames. 
 
 While these experiments bearing directly upon the quantum theory 
 of absorption have not as yet yielded satisfactory results, there are many 
 indirect indications of its validity. It is very difficult to produce a 
 sufficiently long column of vapor heavily bombarded by low speed 
 electrons at the resonance potential. However, with a Geissler tube, and 
 high potential, a very long column of excited vapor may be obtained. 
 The objection to this method of activation is that the atoms are emitting 
 the complete spectrum and hence electrons are to be found in every 
 possible orbit instead of the second orbit only. Since, however, the 
 first fundamental line of the type 1 s 2 p is emitted strongly, the 
 orbit 2 p is occupied to some extent and absorption of the subordinate 
 series should occur. In general the absorption of, for example, 2 p 
 3 d> is obscured by the emission of this line by the gas. but there are 
 methods for detecting it. 
 
 Wood 35 has described a very simple method for observing the absorp- 
 tion of the Balmer line H a in hydrogen. Using a lone- discharge tube 
 arranged for end-on observation it is noticed that the color of the dis- 
 
 * Verh. d. Physik. Ges., 15, pp. 1203-14 (1913). "Physical Optics," 2d Ed. 
 
LINE ABSORPTION SPECTRA 99 
 
 charge is rose-red as viewed through the side of the tube, but is bluish- 
 white when viewed along the axis. In the latter case the red line has 
 been absorbed by the long column of excited vapor. A similar phenome- 
 non may be observed with other gases and vapors. 
 
 Ladenburg 36 has obtained a reversal of H by the following method. 
 Two long discharge tubes are mounted on a common axis and arranged 
 with windows for end-on observation. 37 These are excited in series 
 by an induction coil. The pressure in the rear tube is high so that 
 broad intense emission lines are produced. The vapor in the front tube 
 both emits and absorbs H, but by proper regulation of the pressure a 
 narrow reversal may be obtained, as shown by Figure 18. This illustra- 
 tion is a drawing, as the actual photographs of the phenomenon, though 
 conclusive, were not very satisfactory for reproduction. The band of 
 light is the broad H a line emitted by the rear tube at high pressure. 
 The long narrow line comes from the front tube. A small portion 
 of this is reversed where it crosses the emission band of the rear tube. 
 When a pulsating discharge is used, it is necessary to have both tubes 
 glow at exactly the same instant. If, however, a direct current dis- 
 charge is employed for the absorption tube, a continuous source, such 
 as an electric lamp, may be used for the background. From photometric 
 measurements upon the brightness of (1) the source alone, (2) the glowing 
 absorption tube alone, (3) the two in combination, it is possible to com- 
 pute the absorption coefficient of the gas for the various spectral lines. 
 By employing high dispersion and resolution, Ladenburg and others 
 have determined the absorption curve over the single line H, and 
 find that in general almost complete absorption occurs. None of the 
 light of wave-length H a from the background penetrates through the 
 excited vapor. 
 
 Metcalfe and Venkatesachar, 38 using a tube containing mercury 
 vapor which was excited by a small current above the ionization po- 
 tential, observed, photometrically, absorption of the following and 
 other mercury lines. 
 
 X 
 
 Notation 
 
 Remarks 
 
 5461 
 
 2 Pl -ls 
 
 strong 
 
 4359 
 
 2p 2 - Is 
 
 H 
 
 4047 
 
 2p 3 -ls 
 
 11 
 
 3342 
 
 2pi - 2s 
 
 very strong 
 
 3663 
 
 2 pi - 3d 
 
 strong 
 
 36 Verb. d. Physik. Ges., 12, pp. 54-80 (1910); pp. 549-564 (1910). 
 
 37 This experiment is most beautifully made by use of discharge tubes with windows 
 fused on by the Fairchild method, cf. J. Optical Soc. Am., 4, p. 496 (1920). 
 
 . Roy. Soc., 100, pp. 149-66 (1921). 
 
100 
 
 ORIGIN QF SPECTRA 
 
 They state that the absorption of X 2537, 1 S 2 p 2 , is not increased 
 when the vapor is luminous. It is evident that such should be the case. 
 If any perceptible change could be detected the luminous vapor should 
 show less absorption for this line in proportion to the ratio of the number 
 of excited to normal atoms actually an extremely small quantity. 
 These investigators succeeded in obtaining complete reversal of the 
 lines 2 pi I s and 2 p 2 1 s. The lower spectrogram of Figure 19 
 was obtained by sighting directly on the sun and shows the Fraunhofer 
 lines, while for the upper spectrogram a column of excited mercury vapor 
 was interposed in the line of sight. The reversal of the green mercury 
 line 2 pi I s, \ 5461 A, shows clearly in the upper spectrogram. 
 
 One of the most interesting contributions to this subject has been 
 made recently by Fuchtbauer. 39 He employed a double-walled, long 
 cylindrical tube of quartz between the two walls of which a mercury 
 arc was excited. In the central open space coaxial with the discharge 
 tube was mounted a second closed quartz tube fitted with windows for 
 end-on observation. This second tube contained mercury vapor the 
 pressure of which could be regulated. The emission tube was further 
 jacketed outside with a layer of mercury which acted as a reflector 
 concentrating the radiation on the interior, and the entire system was 
 cooled by an ice bath. When the vapor pressure in the inner tube was 
 adjusted to that corresponding to about 35 C,this vapor became in- 
 tensely luminous, emitting all the arc lines of mercury, although it had 
 no connection whatever with an exciting potential. 
 
 This fact is precisely what one should expect on the basis of the 
 quantum theory of spectroscopy. We shall analyze these results in 
 detail. The atoms in the inner tube are first excited by radiation of 
 some frequency belonging to a series converging at 1 S. There are two 
 such series 1 S mP and 1 S mp 2 . According to the theory an 
 electron would be ejected to an mP or an mpz orbit by absorption of the 
 corresponding spectral line in these two series. The first line of the 
 first series is X 1849. The first two lines of the second series are X 2537 
 and X 1292. The radiation from the enveloping quartz lamp must pass 
 through two quartz walls before it reaches the vapor in the inner tube. 
 Fused quartz is opaque to all lines of these series except X 2537 and to 
 some extent X 1849. Fuchtbauer states that practically no light of 
 wave-length X 1849 was transmitted. Certainly the radiation of this 
 wave-length would be weak compared to X 2537 and we shall omit its 
 consideration. In so doing, however, the bearing of the theory upon 
 
 39 Physik. Z., 21, pp. 635-8 (1920). 
 

 LINE ABSORPTION SPECTRA 
 
 101 
 
 the observed phenomenon is unaltered. A similar analysis may be 
 carried through by the reader, admitting the presence of X 1849. 
 
 FIG. 20. Small portion of energy level diagram for mercury. 
 
 Accordingly the radiation chiefly effective in initially exciting the 
 vapor is 1 S - 2 p 2 , \ 2537. This radiation is absorbed by the vapor 
 and each excited atom has an electron in the 2 p 2 orbit. Before the 
 electron has time to return to the 1 S orbit, with a resulting emission of 
 X 2537, it absorbs a quantum of energy of some frequency belonging to a 
 series converging at 2 p 2 . This radiation is readily transmitted through 
 the quartz. The azimuthal quantum number of the 2 p 2 orbit is 2. 
 Hence since there is no disturbing electrostatic or magnetic field, this 
 absorption, by the Bohr principle of selection, will displace the electron 
 to an orbit where the azimuthal quantum number is either 1 or 3, 
 that is to a ms, mS, md, or mD orbit of higher energy level, and the line 
 absorbed from the exciting radiation will belong to one of the four 
 series which converge at 2 p 2 . The process is illustrated by the energy 
 level diagram, Figure 20, on which &few of these transitions are indicated. 
 
102 *'0&IQlff'Of SPECTRA 
 
 Suppose the atom absorbed the line 2 p 2 - 3 d r , X 3126. The electron 
 is accordingly displaced to the 3 d' orbit and the atom is in a position 
 to absorb lines of the Bergmann series. This process may be continued 
 with a multitude of variations up to the point where the electron is 
 completely removed and the atom is ionized. At any stage in the 
 process the electron if undisturbed may return to normal either directly 
 or by successive steps, emitting various lines of the arc spectrum, some 
 of which are shown by dotted lines in Figure 20. If the atom with the 
 electron in the 2 p 2 orbit absorbs the line 2 p 2 Is, it is then in a position 
 to emit the lines 2 pi I s or 2 p s 1 s and the electron falls to the 
 
 2 pi or 2 p 3 orbits respectively. These two configurations possibly 
 constitute metastable forms of the mercury atom just as in the case of 
 helium, where we found that the orbits 2 S and 2 s represented metastable 
 forms of this element. Lines of the wave numbers v = 1 S 2 p\ 
 and 1 S 2 p 3 are not observed in the arc spectrum of mercury, showing 
 that an electron in either the 2 p\ or 2 p 3 orbit may reach normal only 
 by absorption of energy and hence by passing through an orbit corre- 
 sponding to a greater energy level. . 
 
 If the atom with an electron in the 2 p 2 orbit absorbs the line 2 p 2 
 
 3 d', X 3126, and then emits the line 2 P - 3 d', X 5770, the electron is 
 transferred to the 2 P orbit. It is now in a position to emit 1 S 2 P, 
 X 1849. Also transitions are readily apparent by which the electron 
 may be ejected to the 3 p 2 orbit where it is in a position to emit the line 
 1 S 3 p 2 , X 1292. Accordingly by this simple process lines of very 
 much higher frequencies than those present in the exciting source are 
 easily stimulated. This fact alone should be sufficient argument for 
 discarding Stokes' law 40 which now has as many exceptions as verifica- 
 tions, and is of little value, although often quoted. It should be noted 
 that the production of radiation by the absorption of radiation of lower 
 frequency is in accord with the principle of conservation of energy. In 
 the above example we have several frequencies transformed into one 
 of higher value, subject to the energy relation 2 f c/i^ = chv = energy, 
 where v>v t . 
 
 The entire experiment just discussed depends upon the absorption 
 of the fundamental line 1 S 2 p 2 , X 2537. When this line was cut 
 off by a thin cylinder of glass, no effect whatever could be detected. 
 The glass transmits freely the lines of series converging at 2 p 2) but since 
 with the glass, there is no radiation transmitted, through the absorption 
 
 40 This law states that the emitted radiation can not have a shorter wave-length than 
 that of the stimulus. 
 

 LINE ABSORPTION SPECTRA 103 
 
 of which the electron can reach the 2 p 2 orbit, the vapor in the inner 
 tube is unaffected. 
 
 We have already pointed out that with helium, when an electron 
 is displaced from its normal orbit it tends to assume either the 2 S or 
 2 s orbits, which are the basic energy levels for the two systems of spectral 
 series for this element. Apparently these orbits may be occupied for a 
 much greater length of time than 10" 8 seconds. 41 Hence lines in series 
 converging at either 2 S or 2 s should readily show absorption, as is 
 apparent from Figure 10. Paschen 42 has observed absorption of the 
 lines 2 S - 2 P, X 20582, and 2 s - 2 p, X 10830, in a Geissler tube 
 excited by a weak current. The stimulating current causes ionization 
 of the gas which is followed by recombination. The electron returns 
 toward normal by successive interorbital transitions, with resulting 
 radiation, ultimately reaching the orbits 2 S or 2 s, which are occupied 
 for an appreciable time. In this state the two most prominent absorp- 
 tion lines should be those observed by Paschen. The effect is of course 
 assisted by any electronic impact at the resonance potential in 
 which case an electron may be ejected directly to the 2 S or 2s 
 orbits. 
 
 A simply ionized atom should be capable of absorbing lines of the 
 enhanced spectrum. The ionized alkali earths should readily show 
 absorption for the pair 1 @ 2 $ 1)2 , and for higher terms in this series. 
 No laboratory experiments have been performed to test this fact, but 
 scattered observations point to its truth. King 43 finds that both mem- 
 bers of this doublet for calcium, X 3968 and X 3933, may appear reversed 
 in furnace spectra. These lines are respectively the H and K Fraun- 
 hofer absorption lines in the solar spectrum. The corresponding pairs 
 for strontium and barium also appear as absorption lines in the 
 sun. The pair is reversed in the spark spectra of Mg, Ca, Sr. 
 and Ba. 
 
 We may have excited ionized atoms which behave precisely like 
 the excited un-ionized atoms discussed in the foregoing paragraphs. 
 With certain types of excitation the remaining valence electron for 
 the atoms of metals of Group II may be ejected to an outer orbit such as 
 2 ^3, under which condition the atom absorbs lines of the enhanced sub- 
 ordinate series. The following partial list of reversals of enhanced 
 lines of subordinate series is typical. 44 
 
 41 See pages 73 and 93. 
 "Ann. Physik, 45, pp. 625-56 (1914). 
 Astrophys. J., 51, pp. 13-22 (1920). 
 
 44 Compiled mainly from Kayser's tables. These reversals are, however, a matter of 
 common experience. 
 
104 
 
 ORIGIN OF SPECTRA 
 TABLE XVIII 
 
 Element 
 
 Notation 
 
 X 
 
 Source 
 
 Mg 
 
 2$! - 35) 
 
 2798 
 
 Spark 
 
 
 2 <p 2 _ 3 > 
 
 2790 
 
 it 
 
 
 2 ^2 - 2 3 
 
 2928 
 
 il 
 
 Ca 
 
 2$! - 2(3 
 
 3737 
 
 u 
 
 
 2 sp 2 2 <3 
 
 3706 
 
 
 
 
 2$i 3 $> 2 
 
 8498 
 
 Sun 
 
 
 2?i- 3S>i 
 
 8542 
 
 " 
 
 
 2 $ 2 3 $) 2 
 
 8662 
 
 tt 
 
 
 2 $! 4 ) 2 
 
 3181 
 
 Spark 
 
 
 2?i - 4! 
 
 3179 
 
 u 
 
 Sr 
 
 2$! - 2(3 
 
 4305 
 
 u 
 
 
 2 $ 2 - 2 (3 
 
 4161 
 
 11 
 
 
 2 ^! 4$) 2 
 
 3475 
 
 (I 
 
 
 2 ?i -4S>i 
 
 3464 
 
 (I 
 
 Ba 
 
 2 ^i 2 (5 
 
 4525 
 
 u 
 
 
 2^-4 2 
 
 4166 
 
 (I 
 
 
 2 ''Pj 4 2)i 
 
 4130 
 
 (( 
 
 
 2 $ 2 4 $) 2 
 
 3891 
 
 u 
 
 
 2 ^5j _ 5 ^j 
 
 2634 
 
 (I 
 
 
 2 ^p 2 _ 5 $) 2 
 
 2528 
 
 u 
 
 
 Reversals of enhanced lines are of particular interest in celestial spec- 
 troscopy, where they furnish an indication of stellar temperatures as 
 indicated in the latter part of Chapter VII. 
 
 We shall consider briefly some of the rather speculative deductions 
 to be drawn from experiments with a stream of mercury vapor. Phillips 45 
 employed a long inverted quartz U-tube ; closed at each end. The leg 
 containing mercury was heated to 350 C, while the other leg into which 
 the mercury distilled was water cooled. Just above the surface of the 
 boiling mercury a beam of radiation of wave-length X 2537 was pro- 
 jected through the vapor. The entire tube was immediately filled 
 with luminous radiation. Figure 21 shows a spectrogram of the fluores- 
 cent light. The resonance line X 2537 is predominant, and in addition 
 we have a band of radiation in the extreme violet and another band, 
 which accounts for the visible luminosity, in the green. The faint lines 
 
 Proc. Roy. Soc., 89, pp. 39-44 (1913). 
 
LINE ABSORPTION SPECTRA 105 
 
 on the right are due to stray radiation from the source. Wood 46 by a 
 very ingenious method found that the luminosity began to appear 
 about 1/16000 second after the exciting stimulus was applied. At 
 very high pressure the time could be reduced to 1/40000 second. The 
 fact that the time is so much greater than 10~ 8 second suggests, and the 
 appearance of a band spectrum shows, we are dealing with a new phe- 
 nomenon. Franck and Grotrian 47 have repeated these experiments, 
 with various modifications, from which they have drawn conclusions 
 which will be reviewed in the following paragraphs. 
 
 In general band spectra are attributed to molecules. Excited atoms 
 possess an electron affinity which enables them to unite with other 
 atoms forming compound molecules. The subject of electron affinity 
 is briefly considered in Chapter VIII. We may here state that an atom 
 possessing an electron affinity may attract an electron and become a 
 negative ion. Work must be done upon the negative ion to reduce it to a 
 normal atom. Metals and the rare gases in their normal states do not 
 possess an electron affinity. We shall first consider the excited helium 
 atom for which we assume that there is one electron in orbit of quantum 
 number 1 and one electron in orbit of quantum number 2, the orbits 
 being coplanar. The total energy of this configuration, obtained by 
 means of Equations (50) and (51) is as follows: 
 
 W = W P + W a = - 4 Nhc -0.25 Nhc = - 4.25 Nhc. (71) 
 
 The helium negative ion may be assumed to contain one electron in 
 orbit of quantum number 1 and two electrons in orbit of quantum 
 number 2. Whence by means of the same equations we find: 
 
 W ' = W' v + W' q = - 4 Nhc - 0.28 Nhc = - 4.28 Nhc. (72) 
 
 The second state is accordingly stable. Work has to be done upon 
 the helium ion thus formed to remove the extra electron. This work 
 amounts to 0.03 Nhc ergs or 0.4 volts. 
 
 We have noted the extreme stability of a pair of electrons grouped 
 about a single point charge nucleus. The normal helium structure is 
 characteristic of the X-ring of all the elements. This tendency to 
 grouping in pairs appears now in the formation of negative ions, but 
 the stability of such an outer structure built about not only a nuclear 
 charge but other electrons is not very great. We have in these negative 
 ions, formed from excited atoms, a metastable compound of an atom 
 
 "Proc. Roy. Soc., 99, pp. 362-71 (1921). 
 *f Z. Physik, 4, pp. 89-99 (1921). 
 
106 ORIGIN OF SPECTRA 
 
 and an electron, with an outer structure resembling normal helium, 48 
 and an electron defect in the next to the outer shell which normally 
 is the outer shell. 
 
 If an excited helium atom which has not picked up an extra electron 
 collides with a similar atom, the electron affinity of each atom causes 
 an attraction resulting in the formation of He 2 . Lenz 49 has already 
 attributed the excitation of a band spectrum of helium in a strong 
 discharge to the presence of the helium molecule. 
 
 There is no tendency for a normal argon atom to become negatively 
 charged. However, in the Moore tube light, the pressure at the anode 
 may be double that at the cathode (measurable with an ordinary mer- 
 cury manometer) on account of the drift of negatively charged argon 
 atoms. The argon atom is excited and an electron is driven to the 
 second orbit. In this condition it attracts another electron, forming a 
 metastable configuration with a helium-like outer structure and an 
 electron defect in what was normally the outer shell, the whole being a 
 negative ion. 
 
 Franck and Grotrian suggest, that in a manner similar to the for- 
 mation of negatively charged atoms of rare gases, negatively charged 
 atoms of metals may be produced. The valence electron of a sodium 
 atom, for example, may be ejected to the 2 p 2 orbit, where the atom as a 
 whole may possess an electron affinity and may become a negative ion, 
 while there is no tendency to such a condition as long as the valence 
 electron remains in its normal orbit. 
 
 The mercury stream experiments are accordingly interpreted as 
 follows. The radiation of wave-length X 2537 is absorbed by the atom 
 with a resulting ejection of an electron to the 2 p z ring. Ordinarily 
 this electron would return to normal in 10~ 8 seconds with an emission 
 of the line X 2537. Practically no displacement of the illuminated spot 
 would be detectable. Franck and Grotrian confirmed this fact by 
 employing a low pressure in the absence of any foreign gas. At higher 
 pressures, however, the short-lived excited mercury atom may collide 
 with a normal mercury atom, forming the molecule flg2. The excited 
 atom which possesses an electron affinity is the negative component in 
 this compound. It has in the union a helium-like outer shell, completed 
 by a valence electron of the normal atom, and an electron defect in the 
 next to the outer shell. The normal atom is the positive constituent 
 like Na in NaCl. This new molecule possesses a temporary stability 
 
 48 Possibly more exact considerations would make the resemblance closer in that the 
 orbits of the outer pair would be crossed, as illustrated by Figure 11. 
 Verh. Physik. Ges., 21, p. 632 (1919). 
 
 
LINE ABSORPTION SPECTRA 107 
 
 and the duration of the after glow in the stream is a measure of its life. 
 A band spectrum results from the movement of electrons and nuclei 
 within the molecule. Dissociation arising in collision either with normal 
 mercury atoms or foreign gas, permits the electron in the excited atom 
 to return from 2 p 2 to the 1 S orbit, thus emitting X 2537, as shown by 
 Figure 21. These conclusions have been fairly definitely verified by 
 several experiments which cannot be discussed here. 
 
 The foregoing, while it apparently explains one means of forming 
 molecular compounds, is not the complete interpretation of the experi- 
 mental facts. Sodium vapor at fairly high density shows thousands 
 of fine absorption lines which Wood 50 believes are the complement of 
 the fluorescent spectrum excited by white light. Light may be ab- 
 sorbed by sodium vapor, from a nearly monochromatic source in which 
 there is no frequency corresponding to any line of the principal or other 
 series of sodium. Hence the presence of the absorbing molecules can- 
 not be attributed to the preliminary activation of the atoms by the 
 source of radiation. Strong monochromatic illumination of sodium 
 vapor by a red or green line, not present in the arc spectrum of sodium, 
 .gives re-emission of that line and a series of lines at intervals of about 
 37 A on each side of the exciting line. These spectra are almost the 
 exact counterpart of the phenomena obtained with iodine. The theory 
 that they likewise are due to a diatomic molecule is supported by this 
 similarity, but the presence of the molecules again cannot be attributed 
 to activation of the atoms by light which they are not capable of absorb- 
 ing. Likewise with mercury fluorescence it is found that the most 
 effective illumination is not light near X 2537 but of a higher frequency, 
 again in no relation to the series lines of the mercury atom. We accord- 
 ingly see that molecular compounds may be formed without excitation 
 of the atoms by light of a series converging at 1 s or 1 S. It appears 
 necessary to assume that the vapors contain molecular formations 
 whether or not they are illuminated. Wood states that the fluorescence 
 of mercury appears only in case of vapor freshly liberated from the 
 fluid metal. Fluorescence cannot be excited in a bulb of cooling (hence 
 condensing) mercury vapor, containing an excess of mercury at the 
 same temperature at which it is brilliant in case the temperature is 
 rising, accordingly where evaporation is taking place. Apparently 
 then molecular compounds such as Na 2 , Hg 2 may be evaporated from 
 the liquid surface. Now if Franck and Grotrian's explanation of the 
 structure of these compounds is correct, that is if Hg 2 consists of an 
 
 "Physical Optics," 2d Ed. 
 
108 ORIGIN OF SPECTRA 
 
 excited and a normal atom, simply boiling mercury briskly should 
 produce an emission of 1 S 2 p 2 , \ 2537. Decomposition of the 
 metastable compound Hg 2 should release an atom having an electron 
 in the 2 p% ring which on returning to normal emits this fundamental 
 line. A six hour exposure to a vessel of boiling mercury, by Dr. Meggers 
 and the authors, failed to show a trace of this line. The experiment, 
 however, is worthy of further thought. 
 
 The entire subject of the behavior of excited atoms is a new field 
 of research which promises interesting development. No doubt the 
 chemist of the future will deal familiarly with such compounds as the 
 helides, argides and so on. 51 
 
 51 Since this book has been in press a note by A. S. King, Proc. Nat. Acad. Sci., 8, 
 pp. 123-5 (1922), has appeared, in which he makes the statement that the subordinate series 
 of Na, K, Rb, and Cs have been reversed in furnace spectra obtained by heating the vapor to 
 a high temperature. This is a confirmation of the theory of absorption by excited atoms where 
 the excited atoms are produced by temperature, i.e. by the third method mentioned at the 
 beginning of the section on "Line Absorption Spectra of Excited Atoms." 
 
 A very important paper by Franck has just appeared, Zeit. Physik, 9, pp. 259-66 (1922), 
 on the subject of excited atoms. Klein and Rosseland have suggested that a slow-moving 
 electron, in collision with an excited atom, may gain kinetic energy while the atom is assuming 
 its normal state, no radiation being emitted in the process. This is the converse of excitation 
 by collision. Franck has extended this idea to coHisions between excited and unexcited atoms, 
 thereby obtaining a partial explanation of the weakening of resonance* radiation by the 
 presence of foreign gas. The theory is also used to explain the appearance of Hg \2537, 
 1 S - 2 pz, when Hg vapor is excited by A 1849, IS - 2 P. This may require a transition 
 without radiation from the 2 P state to the 2 pz state. Cario, working in Franck's laboratory, 
 has shown that thallium lines appear in mixtures of Tl and Hg vapors excited by \ 2537, which 
 is interpreted to mean that excited Hg atoms can give up their energy to unexcited Tl atoms 
 with which they collide. Other applications are to the sensitizing of photographic plates by 
 staining, to the bright fluorescence of almost all substances at low temperature, and to the 
 Maxwell velocity distribution in the emission of electrons from heated surfaces. 
 
Chapter V 
 Line Emission Spectra of Atoms 
 
 We have seen that when an electron in an atom is transferred from 
 an outer to an inner orbit, energy is released as a quantum of radiation 
 of wave number v. If W is the total energy of the atom corresponding 
 to the initial configuration and W' the energy of the final configuration, 
 the wave number of the emitted radiation has the value : 
 
 = (W - W')/kc. 
 
 The study of line emission is accordingly concerned with the various 
 modes of interorbital transitions of electrons which result in a decrease 
 in the internal atomic energy. Since, however the normal atom in the 
 gaseous state, except for elements having an electron affinity such as 
 the halogens, possesses a minimum of internal energy, it is first necessary 
 to increase this energy before any radiation can be emitted. This is 
 done by ejecting an electron to an outer orbit. Spectroscopy is mainly 
 concerned with the interorbital transitions of a valence or outer electron 
 following such an ejection. 
 
 There are at least four general processes through which an atom 
 may be left in a condition such that it is capable of emitting line spectra. 
 A valence electron in an atom may be ejected to an outer orbit (1) by 
 absorption of external kinetic energy at impact, (2) by absorption of 
 radiation as discussed in the preceding chapter, (3) by increase in tem- 
 perature of the vapor as discussed in Chapter VII. (4) The valence 
 electron of an atom in a molecular compound may be left in an outer 
 orbit or completely removed from the atom in the process of dissociation 
 of the molecule. For example, as shown earlier, the molecule Hg2 con- 
 sists of a neutral Hg atom and a Hg atom having a valence electron in 
 the 2 p z ring. If this molecule is dissociated, the excited atom subse- 
 quently should emit the radiation 1 S 2 p 2 . Hydrogen iodide upon 
 dissociation emits the hydrogen spectrum showing that in this molecule 
 the hydrogen atom possesses greater energy than in its normal mon- 
 atomic state. It is of interest to note that it requires slightly less work 
 
 109 
 
110 ORIGIN OF SPECTRA 
 
 to completely remove the valence electron from the hydrogen atom by 
 dissociation of HI than by ionization of the hydrogen atom directly. 1 
 Sodium chloride, dissociated in the bunsen flame, emits the spectrum 
 of sodium, to some extent as an immediate result of the dissociation, 
 indicating that in the molecule the sodium atom possesses a greater 
 internal energy than in its normal vapor state. Spectroscopists obtain 
 the spectra of various metals by vaporization and dissociation of their 
 salts in a carbon arc. However, it may not necessarily follow that the 
 process of dissociation leaves the atom in a positively ionized state, 
 even though the complete arc spectrum appears. For example, the 
 dissociation of CdMg may leave one of the atoms as a negative ion. 2 
 It would be necessary for this negative ion to lose two electrons before 
 it becomes capable of emitting all lines of the arc spectrum. Yet 
 CdMg in an arc would probably show the spectra of both metals. 3 In 
 this and similar cases the dissociation is merely a method for obtaining, 
 by an indirect process, vapor of the metal in the atomic state and the 
 emission phenomena properly fall under the classifications (1). (2), and 
 (3). We should accordingly distinguish between processes of dissoci- 
 ation which leave the atom in a condition to immediately emit radiation 
 and those where the dissociation serves merely for the production of the 
 metal vapor. 4 
 
 Classification (1) broadly interpreted embraces many varieties 
 of energy transfer. Radiation may result from a collision of an atom 
 with an alpha particle, with a heavy ion, possibly with a neutral atom 
 or molecule if the speed is great, but especially with a free electron. 
 Since our quantitative knowledge of emission is almost entirely limited 
 to the effect of collisions between atoms and electrons, we shall confine 
 this section to a consideration of these phenomena. The relation of 
 the processes (2) and (3) to spectral emission are treated in Chapters 
 ,VT and VII respectively and will be only casually considered for the 
 present. The fundamentally important factor in the ordinary produc- 
 tion of spectra is collision between electrons and atoms. 
 
 We have seen that a collision between an electron and an atom of 
 'the rare gases or metallic elements may be elastic, but at certain well- 
 defined velocities of the impacting electron the collision is inelastic. As 
 
 1 See Table XXXVIII. 
 
 2 A large number of such compounds is given in Gmelin- Kraut's handbook. Probably 
 other more familiar compounds illustrating this point occur in more complex molecules. 
 
 3 Probably any alkali hydride would show both the spectrum of the metal and the atomic 
 spectrum of hydrogen. In this molecule, however, the hydrogen occurs as a negative ion. 
 
 4 In general it is probably true that even hi such processes as the injection of NaCl hi 
 the arc, the salt acts mainly as a carrier for the sodium. The same sodium atom once dis- 
 sociated from the naolecule probably loses and regains its valence electron many times before 
 At leaves the arc. 
 
 
LINE EMISSION SPECTRA 111 
 
 discussed in Chapter III the energy lost by the electron and absorbed 
 by the atom at an inelastic collision corresponds to either a resonance or 
 ionization potential. If the atom is ionized by the collision, the ejected 
 electron may return to its normal orbit by a variety of interorbital 
 transitions. Each transition results in a decrease in the total energy 
 of the atom and is accompanied by the emission of one quantum of 
 radiation. The various possible steps or energy levels for several 
 typical cases have been considered in the discussion of Figures 4 to 6. 
 If the electron returns from without the atom to the normal state in a 
 single transition, the highest convergence frequency in the spectrum of 
 the neutral atom is emitted. The wave number of this radiation is 
 determined by the quantum relation hc z v = eVflW, where 7^ is the 
 jonization potential in volts. If the electron returns to the normal state 
 by several successive transitions, a corresponding number of quanta 
 of different wave numbers are emitted, of such value that the sum of the 
 quanta equals the total energy of ionization, thus : 
 
 Zfccfyfc = eV i 10 8 . (73) 
 
 With numerous atoms and electrons returning to equilibrium by various 
 paths, we have as the composite result the emission of the complete 
 spectrum of the neutral atom. This by definition is known as the 
 complete arc spectrum. 
 
 The energy absorbed by the atom during a collision of the resonance 
 type is not great enough to ionize the atom but rather is just sufficient 
 to displace a valence electron to a neighboring orbit of higher energy 
 level. Hence the atom in assuming equilibrium conditions will radiate 
 this energy as quanta of wave number v such that 
 
 ZftcS = eV r - 10 8 , (74) 
 
 where V r is the resonance potential. The resulting radiation may 
 be termed the partial arc spectrum, special cases of which are the so- 
 called single-line spectrum and the two-line spectrum, etc. 
 
 The foregoing processes which concern the neutral atom may also 
 apply to an atom which is initially simply ionized. If an ionized atom 
 collides with an electron of sufficient velocity, the collision is inelastic, 
 the atom absorbing the kinetic energy of the impacting electron. If 
 the energy absorbed is sufficient to completely eject another valence 
 or outer electron, the atom is doubly ionized, and the work required to 
 eject this electron, expressed in volts, is denoted by the symbol V* 
 or in general simply V*. Hence V t gives the work required to eject the 
 first outer electron from a normal atom, and F 4 * the work required to 
 
112 ORIGIN OF SPECTRA 
 
 eject the second electron after the first one has been removed. The 
 second electron may return to its normal state by a variety of interorbital 
 transitions. Each transition results in a decrease in the total energy 
 of the simply ionized atom and is accompanied by the emission of one 
 quantum of radiation. An example of the different energy levels in a 
 typical case (ionized magnesium) is illustrated by Figure 7. If the 
 electron returns from without the atom to the normal state in a single 
 transition, the highest convergence frequency in the spectrum of the 
 simply ionized atom is emitted. The wave. number is determined by 
 the relation hc 2 v = eV* - 10 8 . If the electron returns to the normal state 
 by several successive transitions, a corresponding number of quanta of 
 different wave numbers is emitted as follows: 
 
 = eV t * - 10 8 . (75) 
 
 Hence with numerous originally doubly ionized atoms, each with an 
 outer electron returning to the normal state of the simply ionized atom 
 by a variety of interorbital transitions, we have as the composite result* 
 the emission of the complete spectrum of the simply ionized atom. 
 This by definition is known as the complete spark or enhanced spectrum 
 (of the first type). 
 
 As with the neutral atom, electronic collisions may take place in 
 which the energy transfer is not great enough to remove the second 
 electron but rather is just sufficient to displace it to an outer orbit. 
 Hence the ionized atom in assuming equilibrium conditions may radiate 
 this energy as quanta of wave number v t such that 
 
 ZfccV t = e7 r *.10 8 , (76) 
 
 where V r * is the resonar.ee potential for the simply ionized atom. The 
 resulting radiation may be termed the partial enhanced spectrum. No 
 direct measurement! of V T * have been made, but estimates of its. magni- 
 tude for several elements may be obtained from spectroscopic consider- 
 ations, as seen later. 
 
 The numerical relationships in the foregoing paragraphs on enhanced 
 spectra require a little further explanation when applied to metals of 
 Group I of the periodic table, since for these, there is but a single valence 
 electron. Removal of the second electron accordingly must take place 
 from what is normally the next to the outer shell, as will be considered 
 later. 
 
 We note that a simply ionized atom may emit an enhanced spectrum 
 of the "first type." The above process, however, may be repeated so 
 that a doubly ionized atom should emit an enhanced spectrum of the 
 
 
112 A 
 
 Ultra- violet 
 
 Green 
 
 EJ37 Sand Band 
 
 FIG. 21. Fluorescent radiation from mercury vapor. 
 
c* * . 
 
 . 
 
LINE EMISSION SPECTRA 113 
 
 ''second type/' etc. Unfortunately practically nothing is known from 
 the spectroscopic standpoint of these higher types of spark spectra 
 and we shall omit their further consideration. 
 
 Tt is noted in Chapter III that the magnitude of the ionization 
 potential V is small for most elements, of the order 5 to 15 volts. We 
 shall see that V* also is not great, varying from 10 to 50 volts for the 
 elements concerning which any data exist. Hence 50 volt electrons 
 should be capable of exciting the enhanced spectrum of nearly every 
 element. It has been found, however, that the spectrum characteristic 
 of the neutral atom predominates in the arc, whence the terminology 
 "arc spectrum." For the excitation of the enhanced spectrum, it 
 usually has been necessary to employ a very high potential, thousands 
 of volts, across a spark discharge, whence the terminology " spark 
 spectrum." 
 
 Accordingly if spark spectra should appear at low voltage why are 
 
 they absent or at least weak in the cored carbon arc? There are two 
 
 reasons for this. First, it is difficult to maintain much of a field in a 
 
 highly ionized space. If 100 volts is applied to the terminals of the 
 
 arc, as soon as much ionization occurs, the actual voltage drop in the arc 
 
 falls to a value not greatly exceeding the ionization potential, and the 
 
 greater portion of the drop is shifted to the leads. This is simply a 
 
 i consequence of Ohm's law, since the " resistance" of the arc itself ap- 
 
 | proaches zero. Secondly and more important, the type of spectrum 
 
 j excited has little immediate relation to the applied voltage*but instead 
 
 I depends upon the speed of the impacting electron. This is a function 
 
 of the voltage drop per mean free path, and for a given applied voltage 
 
 depends upon the pressure. 
 
 Suppose, for example, we had two large, flat, parallel electrodes, 
 separated by 10 cm, such that the applied field produced a uniform 
 potential gradient throughout the 10 cm length. One of the electrodes, 
 e.g. a Wehnelt- cathode, is assumed to emit electrons. Let us suppose 
 that a potential difference of 100 volts is maintained across these ter- 
 minals, and the space is filled with mercury vapor at 357 C, that is, 
 at atmospheric pressure. We find, from the kinetic theory, for the 
 mean free path of an electron, to an approximation: 
 
 mean free path of electron = I = l/irr^n (77) 
 
 where r is the radius of the gas atom and n is the number of atoms per 
 cm 3 . For mercury r = 1.5 X 10~ 8 cm and in the present example 
 n = 1.2-10 19 . Hence I = 10~ 4 cm and the voltage drop per mean free 
 path is accordingly 0.001 volt. The lowest resonance potential of 
 
114 ORIGIN OF SPECTRA 
 
 mercury is 4.9 volts, and electrons having an energy less than this amount 
 collide with the atoms elastically. Accordingly not until each electron 
 has made 4900 collisions has it accumulated enough kinetic energy to 
 produce any disturbance of the mercury atom, and then the energy is 
 only sufficient to displace a valence electron to the 2 p z ring. (We have 
 neglected in this simple discussion the fact that the direction of motion 
 of the electron is altered after each collision.) It is evident in this 
 extreme example that very few electrons will ever attain 10.3 volts 
 velocity, sufficient to ionize mercury and produce the arc spectrum, to 
 say nothing of the higher velocity required to excite the enhanced 
 spectrum. 
 
 By fohe time the electron has attained 4.9 volts velocity it has pro- 
 gre red along the tube a distance of 5 mm. Here, to an atom, it gives 
 up its kinetic energy, which is subsequently radiated as a quantum of 
 wave number v = 1 S 2 p 2 , X 2537. The process is then repeated, 
 so that at every 5 mm along the tube is a stratum of atoms radiating 
 this ult "a- violet line. By counting the striae and measuring the applied 
 potential, or preferably by probe wire measurements of potential at 
 ' each^tria, a fairly good determination of the resonance potential may 
 Be obtained. The following illustrates such a series of readings made 
 by Grotrian. 5 
 
 Volts 15.2120.0 25.0129.6134.2 39.0 43.5 I 48.0 I 54.0 59.1 64.2169.0 
 
 Difference... 4.8 5.0 4.6 4.6 4.8 4.5 4.5 6.0 5.1 5.1 5.2 
 
 It is of interest that although the light radiated by the mercury atoms 
 lies in the ultra-violet, there is present the green fluorescence characteris- 
 tic of the molecules formed by the union of an excited and normal atom 
 as discussed on page 104. Hence the striae are readily visible although 
 no ionization is present. 
 
 The fact that by increasing the pressure of a metal vapor, all the 
 energy of electronic impact can be forced into a single type of resonance 
 collision corresponding to the lowest resonance potential, is frequently 
 made use of in securing a large number of reversals in the partial current 
 curves 6 even at voltages far exceeding the ionization potential. It is - 
 also well known that by employing sodium vapor at high pressure 
 very efficient "vacuum" arc may be obtained, all the energy of electronic 
 collision going into the production of the D-lines, the first pair of the 
 principal series. The same phenomenon is of course true physically 
 for any vapor, but physiologically sodium stands unique in the close 
 
 5 Z. Physik, 5, pp. 148-58 (1921). 
 
 6 The usual method for determining resonance potentials. See references to Chapter III. 
 

 LINE EMISSION SPECTRA 115 
 
 proximity of this line to the spectral region of maximum sensitivity of 
 
 P+,he eye. 
 The foregoing discussion clearly shows why spark lines are not 
 strongly present in the ordinary two-electrode arc. Indeed it raises 
 the question as to how any arc lines other than the first term of a princi- 
 pal series, corresponding to the lowest resonance potential, may be 
 present. We may cite five reasons in explanation of this. 
 
 (1) The partial pressure of the metal vapor in an ordinary cored 
 carbon arc may be considerably less than an atmosphere in certain 
 cases possibly only a few mm Hg. The lower the pressure the longer is 
 the mean free path and hence the greater is the chance that an electron 
 accumulates velocity sufficient to ionize. Since the resonance potentials 
 of the atmospheric gases are all high, collision with these gas moteules 
 does not materially affect the ability of the electron to ionize a metal 
 atom. 
 
 (2) The phenomenon of absorption of radiation is undoubtedly 
 a controlling factor in the operation of many arcs. This is Discussed 
 in some detail in Chapter VI. Collision of an atom and a free electron^ 
 at the resonance potential gives rise to the first line of an importan^ er ies, 
 for example I s 2 p with the alkalis. This radiation is absorbed by a 
 neighboring atom producing an ejection of an electron to the 2 p orbit. 
 Before the excited atom can resume its equilibrium state it is struck by 
 
 ! a second electron, and the valence electron is ejected to another orbit 
 : of still higher energy level or may be completely removed from the 
 : atom. The ordinary mercury vapor arc lamp is readily operated at a 
 pressure greater than one atmosphere and still it emits the complete 
 arc spectrum, although we have just shown that many thousands of 
 collisions must occur before the electron accumulates the velocity cor- 
 responding to even the resonance potential. It is safe to conclude that 
 practically no electrons at this vapor pressure have a velocity much 
 .greater than 4.9 volts. 7 However, absorption of the radiation I S 
 2 p 2 following a resonance collision leaves the atom in the excited state 
 where collision with an electron of 5.4 ( = 10.3 4.9) volts velocity is 
 sufficient to ionize. The ionizationlnay be the result of several absorp- 
 tions of radiation followed by a single electronic impact, so that in 
 general, as discussed in Chapter VI, ionization may take place in an arc 
 in which there are no electrons having a velocity greater than that 
 corresponding to the resonance potential. 
 
 7 A few electrons very close to the anode and cathode might have higher velocities for 
 reason (5). 
 
116 ORIGIN OF SPECTRA 
 
 (3) A third reason why the complete arc spectrum appears in a 
 two-electrode arc is the phenomenon of successive impact. This is the 
 same in principle as (2). In the case of mercury, for example, the atom 
 is struck by a 4.9 volt electron, and while in the excited state a second 
 electron collides with the atom and raises the valence electron to a higher 
 energy level, ultimately producing ionization. 
 
 (4) Although the mean free path of the electron may be too small 
 to permit the accumulation of the ionization velocity over its length, a 
 small proportion of the electrons will travel many mean free paths 
 without collision. At fairly low pressure and high applied voltage this 
 factor may attain considerable importance. 
 
 (5) The production of any ionization alters the form of the potential 
 gradient between the cathode and anode. With copious ionization 
 the normally negative space charge around the cathode may be neutral- 
 ized, eventually becoming positive. A major portion of the potential 
 drop across the arc may then occur within an extremely short distance 
 from the cathode. Hence the emitted electrons have an opportunity 
 for accumulating the ionizing velocity during a mean free path. Under 
 other circumstances a considerable potential drop may occur at the 
 anode with a similar result. Frequently the conditions are such that 
 the total potential drop is divided into two parts, one close to the cathode 
 and the other close to the anode, with little continuous potential vari- 
 ation through the arc itself. 
 
 From the above considerations it is evident that no very definite 
 conclusions can be drawn experimentally by observing the voltage 
 necessary to excite particular types of spectrum in a two electrode arc. 
 In general all arc lines and a few fundamental spark lines appear in the 
 arc at 100 volts. Enhanced lines are readily excited in a spark dis- 
 charge at several thousand volts. Such voltages bear no relation to the 
 minimum energy required to excite these spectra. A knowledge of 
 the actual velocity of the electrons at the instant of collision with (fcms 
 is necessary. The following method devised by the authors and 
 Dr. Meggers 8 has yielded definite and conclusive results. 
 
 Three electrodes are employed arranged as shown in Figure 22. 
 The central electrode is a heated cathode of tungsten, molybdenum, 
 lime-coated platinum, etc., depending upon the nature of the vapor. 
 Around this js mounted as closely as possible a spiral grid, arid outside 
 at a relatively large distance is placed a concentric cylindrical plate. 
 
 s Foote, Meggerfe and Mohler, PhU. Mag., 42, pp. 1002-15 (1921) ; Atrophys. J., 55, 
 145-61 (1922); Phil. Mag., 43, pp. 659-61 (1922). 
 
LINE EMISSION SPECTRA 
 
 117 
 
 The accelerating field for the electrons is applied between the cathode 
 and grid, the latter being in direct metallic contact with the plate. The 
 pressure of the vapor is so regulated that relatively few collisions of 
 electrons and atoms occur in the short space over which the accelerating 
 field is applied. Most of the electrons pass through the grid without 
 collision, thus attaining the full velocity of the impressed field. These 
 electrons then collide with atoms in the large force-free space between 
 the plate and grid, giving up their energy, which is subsequently radi- 
 
 F/ELO 
 
 Pia. 
 
 a, 22. Arrangement of electrodes for the study of critical voltages required to 
 excite different types of spectrum. The grid must be mounted very close to the 
 cathode. 
 
 ated as line spectra. By observing the minimum potentials at which 
 the different types of spectrum are excited, a direct determination may 
 be made of the amount of energy necessary for their production. The 
 values so obtained in all cases confirm the deductions from the quantum 
 theory. It is of interest to note that with this form of arc the higher 
 series terms are readily photographed. For example, the authors had 
 no trouble in observing such terms as p = 2 p IS din sodium, rarely 
 if ever detectable in an ordinary arc. 
 
 
118 ORIGIN OF SPECTRA 
 
 We shall first consider the metals of Group II of the periodic table, 
 then the alkalis and finally some observations on the rare gases. It 
 must be emphasized that the attack of the problem from our present 
 standpoint is new, practically all work being done during the past year, 
 and hence the data available are rather meager at the present time. 
 
 METALS OF GROUP II OF THE PERIODIC TABLE 
 
 These metals have two resonance potentials. We should accordingly 
 expect a four stage development in the spectra, a characteristic spectrum 
 at the lower resonance potential, a change at the higher resonance 
 potential, the complete arc spectrum at the ionizacion potential and 
 the complete spark spectrum at the potential necessary to remove the 
 second valence electron. 
 
 As discussed on page 39 the spark spectra of the alkali earths re- 
 semble the arc spectra of the alkalis, showing series of doublets as 
 follows: 
 
 Principal v = 1 @ - w$i, 2 m = 2, 3, 4, (78) 
 
 1st Subordinate v = 2 ^i, 2 - wi, 2 m = 3, 4, 5, .; (79) 
 
 2d Subordinate v = 2 &,i - m<5 m = 2, 3, 4, (80) 
 
 Bergmann v = 3 i, 2 - m$ m = 4, 5, 6, (81) 
 
 The highest convergence wave number is 1 @ and is fairly accurately 
 known for many of these elements, from computation of the observed 
 spectral frequencies. The 1 @ orbit accordingly represents the normal 
 state or energy level for the ionized atom corresponding to the state 1 S 
 for the normal atom. We shall consider as a typical example the develop- 
 ment of the spectra of magnesium . In Table XIX are listed the funda- 
 mentally important wave numbers and equivalent voltages, shown 
 graphically in the energy level diagrams of Figures 6 and 7. 
 
 Electronic impact at velocities below 2.7 volts gives rise to no emis- 
 sion whatever in magnesium vapor, the collision being elastic. Between 
 2.7 volts and 4.33 volts an inelastic impact corresponding to the first 
 resonance potential occurs, displacing a valence electron to the 2 p 2 
 orbit. The electron in returning to the 1 S orbit gives rise to the emis- 
 sion of a single line of wave number v such that hc z v = eV r '\0 8 where 
 V r = 2.7 volts. The wave-length of this line is X 4571. The first 
 spectrogram of Figure 23, by Foote, Meggers and Mohler, shows this 
 single-line spectrum of magnesium obtained with a total applied po- 
 tential of 3.2 volts, using the arrangement of electrodes illustrated in 
 Figure 22. 
 
LINE EMISSION SPECTRA 
 
 119 
 
 TABLE XJX 
 
 DEVELOPMENT OF MAGNESIUM SPECTRUM 
 
 Series 
 Notation 
 
 Wave 
 Number 
 
 Volts 
 
 Type of Collision 
 
 Type of Spectrum 
 
 1 S - 2 p. 
 
 21871 
 
 2.70 
 
 Inelastic collision, 
 
 Single-line. Electron is dis- 
 
 
 
 
 at the lower reso- 
 
 placed to 2 p 2 orbit and the 
 
 
 
 
 nance potential, 
 
 only possible return to nor- 
 
 1,1 
 
 
 
 with neutral atom. 
 
 mal is by a single transfer 
 
 
 
 
 
 to the 1 S orbit. 
 
 15 -2 P. 
 
 35051 
 
 4.33 
 
 Inelastic collision, 
 
 Two lines, 1 S - 2 P and 1 S 
 
 
 
 
 at the higher reso- 
 
 2 p 2 . Electron is dis- 
 
 
 
 
 nance potential, 
 
 placed to 2 P orbit and must 
 
 
 
 
 with neutral atom. 
 
 return directly to 1 S, since 
 
 
 
 
 
 return to 2 p violates prin- 
 
 
 
 
 
 ciple of selection. Impacts 
 
 
 
 
 
 at first resonance potential 
 
 
 
 
 
 also occur, giving rise to 
 
 
 
 
 
 1 S - 2 p 2 . 
 
 IS. 
 
 61672 
 
 7.61 
 
 Inelastic collision, 
 
 Complete arc spectrum. One 
 
 ' 
 
 
 
 with neutral atom, 
 
 valence electron is com- 
 
 
 
 
 resulting in simple 
 
 pletely removed. In re- 
 
 
 
 
 ionization. 
 
 turning to normal all inter- 
 
 
 
 
 
 orbital transitions consist- 
 
 
 
 
 
 ent with the principle of 
 
 
 
 
 
 selection may take place. 
 
 
 35761 
 
 4.4 
 
 Inelastic collision, 
 
 Single-line spectrum (d o u b- 
 
 
 35669 
 
 
 with simply ion- 
 
 let). It cannot be produced 
 
 
 
 
 ized atom : the 
 
 alone since simple ionization 
 
 
 
 
 resonance poten- 
 tial of the ionized 
 
 is first necessary, with the 
 resulting emission of the 
 
 
 
 
 atom. 
 
 complete arc spectrum. 
 
 1 <3 
 
 121267 
 
 14.97 
 
 Inelastic collision, 
 
 Complete enhanced spectrum. 
 
 
 
 
 with simply ion- 
 
 This accompanies the arc 
 
 . 
 
 
 
 ized atom result- 
 
 spectrum since the atom 
 
 
 
 
 ing in ejection of 
 
 must be first simply ionized. 
 
 
 
 
 the second val- 
 
 There is no way of main- 
 
 
 
 
 ence electron. 
 
 taining fixed, at reasonable 
 
 
 
 
 
 temperatures, an atmos- 
 
 
 
 
 
 phere of simply ionized at- 
 
 
 
 
 
 oms. Some are constantly 
 
 
 
 
 
 becoming neutral, thus emit- 
 
 
 
 
 
 ting the arc lines. 
 
 
 121267 + 
 61672 
 
 22.8 
 
 Inelastic collision, 
 with nuetral atom 
 
 Complete enhanced spectrum. 
 The arc spectrum should be 
 
 
 
 
 resulting in ejec- 
 
 present also. 
 
 
 
 
 tion of both val- 
 
 
 
 
 
 ence electrons. 
 
 
120 
 
 ORIGIN OF SPECTRA 
 
 TABLE XIX Continued 
 DEVELOPMENT OF MAGNESIUM SPECTRUM 
 
 Series 
 Notation 
 
 Wave 
 Number 
 
 Volts 
 
 Type of Collision 
 
 Type of Spectrum 
 
 Lai, 2 
 Ka 
 
 380000 
 95.8 N 
 
 46.9 
 1299 
 
 Inelastic collision, 
 with neutral atom 
 resulting in ejec- 
 tion of an elec- 
 tron from the 
 L-orbit. 
 
 Inelastic collision 
 
 L-radiation, x-rays. 
 Complete .K-radiation, x-rays. 
 
 
 
 
 with atom result- 
 ing in ejection of 
 an electron from 
 the .K-orbit. 
 
 
 It is recalled that the energy level 2 p is really triplet in character, i.e. 
 2 pi, 2 p 2 , and 2 p 3 . Lines of the wave numbers 1 S 2 pi and 1 S 
 2 p z , however, have never been photographed or observed visually for 
 any element of this family. As mentioned in Chapter I, Sommerfeld 
 has attempted to explain this fact by the use of " internal quantum 
 numbers," consideration of which is beyond the scope of this book. We 
 have never observed inelastic impact at voltages corresponding to 
 1 S 2 pi or 1 S 2 p s . In magnesium the separation of this triplet, 
 if it existed, could not be resolved by the methods employed for the 
 measurement of resonance potentials, but such is not the case for some 
 of the elements in this family, for example mercury, where the voltages 
 should be 4.5, 4.9 and 5.4. Our measurements gave 4.9 alone. Accord- 
 ingly in the present discussion we shall refer only to the 2 p 2 energy 
 level. Recently Franck and Einsporn have obtained indirect evidence 
 of the existence of these other potentials. If their work be accepted, 
 some very interesting complications arise, both in theory and experiment, 
 which are considered later. So far, the experimental evidence of all 
 spectroscopy has shown that the 2 pi and 2 p s orbits are occupied only 
 following the emission of a line of a subordinate series and a few combi- 
 nation lines, for example a transition of an electron from an md or an 
 ms orbit, and that the 2 pi and 2 p 3 orbits do not represent the initial 
 state in any transition involving the emission of radiation. 
 
 Returning to the discussion of magnesium, we find that two types 
 of electronic impact between 4.33 and 7.61 volts may occur. The atom 
 
LINE EMISSION SPECTRA 
 
 121 
 
 may absorb 2.7 volts energy from the impacting electron, causing a dis- 
 placement of a valence electron to the 2 p 2 orbit, with the subsequent 
 - emission of X 4571. The impacting electron retains the remaining 
 portion of its kinetic energy after rebound from the atom, suffering 
 only the velocity loss of 2.7 volts. Secondly, the atom may absorb 
 4.33 volts energy from the impacting electron, causing a displacement of 
 a valence electron to the 2 P orbit. On referring to Figure 6 it is noted 
 that but one energy level, 2 p. lies between the state 2 P and the normal 
 state 1 S. Transition from 2 P to 2 p involves zero change in the 
 azimuthal quantum number and by the Bohr principle of selection 
 should not take place. Hence the electron in the 2 P orbit must return 
 to normal by a single transition, resulting in the emission of v 1 S 
 2 P, X 2852. Accordingly, on account of the two types of collision 
 present, we should have between 4.33 and 7.61 volts a two-line spectrum 
 consisting of the lines X 4571 and X 2852. This is shown in the second 
 spectrogram of Figure 23, for a potential of 6.5 volts. 
 
 It is of interest to note that under the conditions of this experiment 
 we have the most favorable opportunity for the production of 2 p 2 2P 
 if this line represented a physically possible interorbital transition. 
 Only two transitions from 2 P are mathematically possible, to 2 p% 
 and to 1 S. The line 2 p 2 - 2 P would lie at X 7587. Using dicyanin- 
 stained plates having high sensitivity at this wave length, not a trace 
 of the line could be detected, the two-line spectrum appearing alone. 
 This constitutes a very interesting verification of the Bohr principle of 
 selection,. 
 
 Collision above 7.61 volts results in the complete ejection of a valence 
 electron. The electron returns to the normal 1 S orbit by successive 
 interorbital transitions, each resulting in an emission of one quantum of 
 some particular frequency v k subject to the condition laid down by 
 Equation (73). An individual atom accordingly in any single return 
 to equilibrium following ionization, may emit only a few of the arc lines, 
 in rare cases only the single convergence wave number 1 S, but with 
 numerous atoms approaching equilibrium by the various different com- 
 binations of transitions possible, we have as the macroscopic result the 
 emission of the complete arc spectrum. This is shown in the third 
 spectrogram of Figure 23, obtained at 10 volts. 
 
 If an electron of 4.4 volts velbcity, or greater, collides with an ionized 
 magnesium atom, the single remaining valence electron may be ejected 
 from the normal 1 @ state to the 2 $ state, as shown in Figure 7, the 
 energy corresponding to 4.4 volts being abstracted from the impacting 
 electron which rebounds from the atom with the equivalent velocity 
 
122 ORIGIN OF SPECTRA 
 
 loss. The atom in assuming its equilibrium state as a positive ion 
 accordingly emits the pair 1 @ - 2 $i, 2 , X 2796 - 2802. This is the 
 "single-line" spectrum of ionized magnesium, a doublet, analogous to 
 the single- doublet spectra of the alkalis, considered later. It requires 
 for its excitation the preliminary ionization of the atom for which a 7.61 
 volt collision is necessary. Hence it will appear only at potentials 
 greater than 7.61 volts although the pair itself requires but 4.4 volts 
 for its excitation. Two successive collisions are necessary, the first 
 resulting in ionization of the normal atom, and the second correspond- 
 ing to a resonance potential of the atom-ion. The pair appears clearly 
 in the 10 volt spectrogram of Figure 23. 
 
 If an electron of 14.97 volts velocity, or greater, collides with an 
 ionized magnesium atom, the single remaining valence electron may be 
 completely ejected, leaving the atom doubly ionized. The electron 
 returns to the normal 1 @ orbit of the simply ionized atom by successive 
 interorbital transitions, each resulting in an emission of one quantum of 
 some particular frequency fc (subject to the condition laid down by 
 Equation (75) where V* = 14.97 volts J For many atoms, the com- 
 posite result is the emission of all the enhanced or spark lines, the com- 
 plete doublet spectrum of magnesium. This is shown by the last three 
 spectrograms of Figure 23. Over thirty well known enhanced lines 
 belonging to series are readily visible in the original negatives of these 
 illustrations. The wave-lengths of some of the more prominent lines 
 are indicated in the figure. 
 
 At 22.8 volts, corresponding to 1 @ + 1 S, there is a possibility of 
 doubly ionizing magnesium in a single electronic collision. With any 
 mechanical, symmetrical model of a heavy atom, it is rather difficult 
 to see how this could occur, and as yet no one has shown that an increase 
 in radiation takes place at this velocity. However, the numerical 
 value is of importance in thermochemical relations as it gives the total 
 work of double ionization regardless of how the process is effected. 
 
 At 46.9 volts and J.299 volts, respectively, the L and K x- radiations 
 appear (cf . Chapter IX)* Apparently no change in the visible radiation 
 occurs as the voltage 46.9 is exceeded. One should expect to find the 
 spectrum of doubly ionized magnesium in this voltage range. Possibly 
 a difficulty in producing such spectra is the small probability of the 
 three successive collisions necessary, where the energies absorbed from 
 the impacting electrons have wide variation. In this case we require 
 7.61, 14.97 and a value slightly exceeding 46.9 volts, the excess arising 
 in the fact that removal of two outer electrons produces some effect on 
 the work required to eject an L-electron. 
 
LINE EMISSION SPECTRA 
 
 123 
 
 The foregoing discussion outlines the fundamental stages in the 
 excitation of the spectra of magnesium by electronic impact. We have 
 yet to consider certain auxiliary processes which involve absorption of 
 radiation followed by electronic impact or processes which involve two 
 successive electronic collisions, as mentioned on page 115, items (2) 
 and (3). 
 
 If the current density is high, fundamental lines of the subordinate 
 series may be excited below the ionization potential, in addition to the 
 two-line spectrum. A valence electron of the normal atom is ejected 
 to the 2 p 2 orbit by direct impact or more probably by absorption of 
 radiation of wave number 1 S 2 p% emitted by a neighboring atom 
 which is previously excited. Before the first atom can assume equilib- 
 rium, with the resulting radiation 1 S 2 p%, it collides with an electron 
 and the valence electron is displaced to a higher energy level, for ex- 
 ample 1 s, 2 s, 3 d, etc. From these energy levels the electron may fall 
 to 2 pi, 2 p 2 or 2 p 3 , giving rise to subordinate series triplets. Thus we 
 have observed at 7 volts in addition to 1 S 2 P and 1 S 2 p 2 the 
 following lines of subordinate series of magnesium. 
 
 Notation 
 
 \ 
 
 2pi 
 
 - 2s 
 
 3336 
 
 2p, 
 
 - 3d 
 
 3838 
 
 2p 2 
 
 -3d 
 
 3832 
 
 2p 3 
 
 - 3d 
 
 3829 
 
 2j>, 
 
 - Is 
 
 5183 
 
 2p 2 
 
 - Is 
 
 5173 
 
 2p 3 
 
 - Is 
 
 5168 
 
 For a similar reason we find lines of the subordinate series of the 
 enhanced spectrum below 14.97 volts, the potential required to remove 
 the second electron and produce double ionization. In the original 
 negative for the 10 volt spectrogram 9 of Figure 23 the following enhanced 
 lines of subordinate series are prominent in addition to the single- 
 doublet spectrum 1 @ 2 $1,2. 
 
 Notation 
 
 X 
 
 2?!- 3 
 
 2 % - 3 2) 
 2 ?i 2 @ 
 2 $ 2 - 2 @ 
 
 2798 
 2790 
 2936 
 
 2928 
 
 ! 
 
 9 See Phil. Mag., 42, 1006 (1921), Table I, for a complete analysis of these spectrograms. 
 
124 ORIGIN OF SPECTRA 
 
 The simply ionized atom absorbs radiation of wave number 1 @ 2 $i, 2 
 and before it can assume equilibrium and emit this pair, it collides with 
 an electron. The remaining valence electron is displaced to an outer 
 orbit such as 2 @ or 3 2), in which states the ionized atom is capable of 
 emitting the above listed lines. 
 
 This development of the spectrum of magnesium is typical of all 
 the metals of this group of the periodic table. Franck and Hertz, 10 
 working with mercury vapor, were the first to obtain a single-line spec- 
 trum. Nearly every one who has made photographs at low voltage has 
 since observed X 2537 as a single line, the vapor frequently occurring 
 as an impurity in spectra of other vapors, when not produced inten- 
 tionally. We have observed the single-line and two-line spectrum of 
 zinc as an impurity in magnesium. 11 McLennan and Henderson 12 show 
 photographs of the single-line spectra of mercury, cadmium and zinc. 
 They also in 1915 observed that the complete arc spectrum appeared 
 slightly above the ionization potentials, the values of which were un- 
 known at this date. McLennan and Ireton 13 show photographs of 
 the two-line spectra of zinc and cadmium. No investigations of the 
 enhanced spectra in the low voltage arc for metals of Group TI, aside 
 from magnesium, have been published, a problem upon which Dr. 
 Meggers and the authors are engaged at the present time. However, 
 the critical frequencies are fairly accurately known from spectroscopic 
 data, except for mercury and radium. We are accordingly able to 
 summarize completely in Table XX the successive stages of develop- 
 ment in the spectra of these elements, excited by electronic impact. 
 This table gives all the spectra arising in disturbances of the valence 
 electrons, which the atom, in the absence of a magnetic or electric field, 
 is capable of emitting. 
 
 RELATION BETWEEN 1 @ AND 1 S 
 
 There appears to be a definite relation of some physical significance 
 between the limiting frequencies 1 @ and 1 S. In Table XXI are given 
 the values of the ratio 1 @ /I S, using the data of Table XX. 
 
 The physical significance of this ratio can be roughly obtained in 
 the following manner. Referring to Table III, the magnesium atom is 
 seen to consist of three shells of electrons in the arrangement 2, 8, 2. 
 By means of an equation similar to (51) we shall compute the total 
 
 "Verb. Physik. Ges., 16, p. 512 (1914). 
 
 11 Foote, Meggers and Mohler, Phil. Mag., 42, p. 1014 (1921) 
 
 Proc. Roy. Soc., 91, pp. 485-91 (1915). 
 
 Phil. Mag., 36, pp. 461-71 (1918). 
 
LINE EMISSION SPECTRA 
 
 125 
 
 
 .S.-5 S o 
 
 ' - 
 
 C<l rH 
 
 00 <N 
 
 i" 00 
 
 rtH (N 
 
 "fi o 
 
 *O o> 
 
 fc CP 
 
 ^ 00 
 
 40 
 
 S3 
 
 
 O co i 
 
 1& 
 
 ll'!| 
 
 rH Oi OO5 
 CO IO CO C^' 
 
 00 "* 
 
 id id 
 
 Q 
 
 rH O5 Tf^ C^J IO(M t^lO 
 
 COCO rHOi IOOO rHrH 
 
 t^ CO -^ rH 
 
 C iO IOIO 
 
 COCO <N (N 
 
 00 CO 
 
 rH CO 
 
 Tt< CO 
 
 
 (M_ CO 
 CO(N 
 
 <N CO 
 (M C^ 
 
 g 
 
 Jill 
 
 sir 
 
 CO O 
 
 ^ CO 
 
 1^1' 
 
 ^ 
 
 9- 8 
 
 1111 
 
 s 
 
 8 
 
 OJU 
 
 ^ t. &d 
 
 '3 0) ^(M 
 
 'I ^ S I 
 
 
 fafi 
 
 c 
 
 113 
 
 fill 
 
 00 rH O5 
 
 00 O l> 
 
 H co 
 
 rH O g Tg 
 
 00 C<l IO XO 
 
 s s 
 
 Q "" 
 
 M 
 
 O 
 
 _ 
 
 02 
 
 O 
 
126 
 
 ORIGIN OF SPECTRA 
 
 energy of the outer ring (1) TF 2 with both valence electrons and (2) 
 Wi with one valence electron. 
 
 w r = - 
 
 (82) 
 
 (83) 
 
 (84) 
 
 The value Wz represents the work required to remove both valence 
 electrons and is accordingly proportional to 1 @ + 1 <S. The value Wi 
 represents the work required to remove the second valence electron 
 after the first has been ejected and is accordingly proportional to 1 @. 
 Hence : 
 
 2(2 - 0.25) 2 
 
 W i 
 
 = 1.531, 
 
 and 
 
 (85) 
 
 This value agrees approximately with that given in Table XXI. Similar 
 computations for the other elements lead to the same numerical relation. 
 The value 1 @ for mercury in Table XX was obtained in this manner 
 from the known magnitude of 1 S, since the series relations in the en- 
 hanced spectrum are unknown. 
 
 TABLE XXI 
 RATIO 1 @/l S FOR METALS OF GROUP II 
 
 Element 
 
 re/is 
 
 Mg 
 
 1.97 
 
 Ca 
 
 1.94 
 
 Zn 
 
 1.95 
 
 Sr 
 
 1.94 
 
 Cd 
 
 1.93 
 
 Ba 
 
 1.92 
 
 
 Mean 1.94 
 
LINE EMISSION SPECTRA 127 
 
 METALS OF GROUP I OF THE PERIODIC TABLE 
 The metals of Group I as shown in Table X all have a single resonance 
 potential. We accordingly find a three-stage development in the 
 spectra. A single-line or more precisely a single-doublet spectrum, 
 1 s 2 pi, 2 , appears at the resonance potential. The complete arc 
 spectrum is excited at the ionization potential and at a still higher 
 potential the enhanced spectrum appears. 
 
 There is no reason in the Bohr theory why resonance potentials of 
 higher magnitudes, corresponding to 1 s 3 pi, 2 , 1 s 4 pi, 2 , etc., 
 should not exist, a statement applying equally well to the metals of 
 Group II. Thus we might expect that the valence electron could be 
 displaced from the normal 1 s orbit directly to any mp orbit as a result 
 of inelastic collision with the proper energy exchange. In the complete 
 arc spectrum the intensity of 1 s 2 p is many times greater than that 
 of 1 s 3 p. In fact in every series, the intensity of the lines, referred 
 to absolute value from which plate- or eye-sensitivity is eliminated, 
 decreases rapidly from the first term to zero at the convergence. Now 
 it seems possible that just as the probability of the transfer of the valence 
 electron from an mp orbit to the 1 s orbit evidently decreases rapidly 
 as m increases, so the probability of the displacement of the valence 
 electron to an mp orbit as a result of electronic collision with a normal 
 atom may decrease as m increases, even though all the impacting 
 electrons have a velocity corresponding to 1^ s mp. If this were so, 
 these higher resonance potentials might exist and not be detectable by 
 the ordinary methods of measurement. For example if one hundred 
 collisions resulting in a displacement of the valence electron to 2 p 
 occurred while one collision resulted in a displacement to the 3 p orbit, the 
 effect of the latter would be nearly indistinguishable by the electrical 
 methods employed in the investigation of inelastic impact. On the 
 other hand one collision of the 3 P type in a hundred or more of the 2 p 
 type should produce an observable spectroscopic effect. 
 
 Referring to Figure 5, electronic displacements to the 3 p orbit 
 enable the vapor to emit 1 s 3 p, the second pair of the principal 
 series, besides the first pair and infra-red lines representing the indirect 
 transition from .3 p to 2 p, and the first pair of each subordinate series. 
 The various lines which may be emitted following a displacement to 
 J* p i are summarized in Table XVII . At the inelastic impact correspond- 
 ing to l_s_ 3 p we should accordingly observe the emission of the 
 following more important pairs: Is 2 p, Is 3 p, 2 p 2 s and 
 2 p - 3 d. 
 
 
128 
 
 ORIGIN OF SPECTRA 
 
 Foote and Meggers 14 attempted to investigate this for caesium. 
 Unfortunately for this element the latter two pairs lie in the far infra- 
 red and could not be observed. The wave number Is 2 pi corre- 
 sponds to 1.4 volts; 1 s 3 pi to 2.7 volts; 1 s 4 pi to 3.2 volts; 1 s 
 5 pi to 3.4 volts; and 1 s to 3.9 volts. The ratio of absolute intensities 
 of the lines (1 s 2 pi) -r- (1 s 3 pi) i.e. X 8521/X4555 were measured 
 for a series of accelerating potentials as follows : 
 
 Volts 
 
 7 
 
 4 
 
 3.8 
 
 3.4 
 
 3.2 
 
 2.8 
 
 
 
 
 
 
 
 
 X 8521/X4555 
 
 350 
 
 2100 
 
 8300 
 
 10500 
 
 > 10000 
 
 == 00 
 
 Accordingly at voltages less than 3.9, the ionization potential, and 
 greater than 2.7, corresponding to 1 s 3 p, there appears to be no 
 emission of 1 s 3 pi, X 4555, which cannot be attributed to ionization. 
 At 3.4 volts for example the intensity of 1 s 3 p\ is but 1/10000 that 
 of 1 s 2 pi, although all the electrons have a velocity sufficient to 
 eject the valence electron to the 3 pi orbit. 
 
 The electrons emitted by a heated cathode (equipotential surface) 
 have a velocity distribution given by Maxwell's law. It may be readily 
 shown that on account of this temperature distribution, the fractional 
 number F of emitted electrons having a velocity greater by F than 
 the applied potential V is: 
 
 erfx + -L e~* t 
 VTT 
 
 where x 2 = 11600 V /T , 
 
 (86) 
 
 where T is the absolute temperature of the cathode. At a dull red 
 heat about 30 electrons per 10,000 have a velocity 0.5 volt greater than 
 V. One in 10,000 should be sufficient to account for the intensity of 
 X 4555 at 3.4 volts. Similar conclusions may be drawn from observa- 
 tions on other lines. For example the line 2 pi 5 d, X 6974, was found 
 by absolute intensity measurement to be of such low intensity below 
 the ionization potential that its excitation may be explained by the 
 small number of high velocity electrons present. No line, other than 
 the pair 1 s 2 p, shows a rapid increase in intensity when the velocity 
 of the electrons reaches that corresponding to its particular energy level. 
 Hence we conclude that the valence electron may be ejected only to the 
 2 p orbit, following electronic impact with the normal atom, thus con- 
 firming the data obtained by direct measurement of critical potentials. 
 
 " Bur. Standards Sci. Paper No. 386 (1920). 
 
128 A 
 
ll 
 
 3 * 
 8,1 
 
 o ^ 
 
 s * 
 
 CB 
 
 O5 ^ 
 
 S 
 
 ^ 
 
LINE EMISSION SPECTRA 129 
 
 As the electronic velocity is increased above that corresponding 
 to the resonance potential, we have the emission of 1 s 2 p. As soon, 
 however, as the ionization potential is reached all arc lines are emitted. 
 If an atom emits any line of the principal series beyond 1 s 2 p, it can- 
 not at the same time emit 1 s 2 p, as seen from Figure 5. Hence 
 electrons, which just below the ionization potential give rise to 1 s 2 p, 
 just above ionization produce other principal series lines at the sacrifice 
 of 1 s 2 p. There should be accordingly, for the same current, a 
 decrease in the intensity of 1 s 2 p, as the ionization potential is 
 passed, a fact confirmed by direct experiment. 
 
 The intensity of each line above the ionization potential was ob- 
 served to be approximately proportional to the number of electrons 
 leaving the cathode. This follows from the quantum theory. The 
 number of electronic collisions and hence, roughly, the number of quanta 
 of any particular frequency is proportional to the number of electrons or 
 approximately proportional to the total current, a fact substantiated 
 earlier by Jolly and other investigators. 
 
 This work on caesium should be repeated, using a 3-electrode instead 
 of 2-electrode discharge tube, and should be extended to other metal s r 
 especially mercury. The foregoing is by no means conclusive, for 
 quantitative spectrophotographic measurements at and slightly above the 
 threshold value of the plate are exceedingly difficult if not impossible. 15 
 
 Foote and Meggers 16 show photographs of the single-doublet spectrum 
 of caesium, X 8521 and X 8943 at the resonance potential, and the com- 
 plete arc spectrum slightly above the ionization potential. The single- 
 doublet emission spectra of the alkalis are precisely the absorption lines 
 shown in Figure 15, the pair 1 s 2 pi and 1 s 2 p 2 . The authors 
 and Dr. Meggers, 17 using the design of Figure 22, have obtained 
 photographs illustrating the successive stage development in the spectra 
 of sodium and potassium, the latter being reproduced here as Figure 24. 
 
 With potassium, from 1.60 to 4.32 volts, we have the single pair X 
 7664 and X 7699, as seen in the first spectrogram. From 4.32 to about 
 20 volts the arc spectrum consisting of the series of doublets represented 
 by Equations (34) to (37) are excited, as seen in the second and third 
 spectrograms. Above about 20 volts the enhanced lines are prominent, 
 
 15 Dr. C. E. Kenneth Mees, Director, Eastman Kodak Research Laboratory, where 
 every conceivable means and instrument for spectrophotographic analysis are at hand, 
 together with a staff trained in the technique of plate sensitometry, hi 1920 stated that it 
 was a fixed policy of their laboratory not to rely on spectrophotographic photometry for such 
 types of problem, if other methods are possible. It is certainly doubtful if any laboratory not 
 specially equipped for such work can hope to secure unquestionable results. 
 
 is Loc. cit. 
 
 " Foote, Meggers and Mohler, Astrophys. J., 55, pp. 145-61 (1922). 
 
130 ORIGIN OF SPECTRA 
 
 appearing in the last two spectrograms. Several hundred lines are 
 readily visible on the original negatives. 
 
 The third spectrogram shows the pair 1 s 3 d, which as mentioned 
 on page 36 is an exception to the principle of selection, since the change 
 in azimuthal quantum number is two units. Here the presence of the 
 line cannot be attributed to an incipient Stark effect, since there is no 
 applied field in the space between the grid and plate of Figure 22. The 
 corresponding pair in sodium is similarly excited. These exceptional 
 lines appear at high current density, and the physical basis for their 
 excitation is still an open question. 18 
 
 With sodium, from 2.09 to 5.12 volts we have the single-pair, the 
 D-lines. From 5.12 to about 35 volts the complete arc spectrum appears, 
 while above 35 volts the many-line enhanced spectrum is excited. 
 
 The enhanced spectra of the alkalis should resemble the arc spectra 
 of the rare gases. In the richness and complexity of the lines the re- 
 semblance fulfils all expectations. As yet, however, no series relations 
 have been determined. It is nevertheless possible to roughly estimate, 
 theoretically, the potentials required to excite these enhanced lines. 
 Referring to Table III, for sodium, we have the K-ring with 2 electrons, 
 the L-ring with 8 electrons and the outer ring with the single valence 
 electron. Suppose the valence electron is removed by a 5.1 volt elec- 
 tronic impact and then an electron is removed from the L-orbit, thus 
 leaving the atom doubly ionized. The atom is now ready to emit any 
 line of the enhanced spectrum. Suppose that the highest convergence 
 frequency in the enhanced spectrum is emitted. Would this involve 
 the return of an electron from without the atom to the L-ring from 
 which it was originally ejected? There is some reason for believing that 
 the electron should assume an orbit outside the shell of seven, forming 
 a metastable sodium ion. That is, two kinds of simply ionized sodium 
 atoms may exist with electrons distributed in shells as follows : 
 
 1st 
 
 2d 
 
 3d Shell 
 
 2 
 
 8 
 
 
 2 
 
 7 
 
 1 
 
 The first type is in a state preliminary to the emission of the arc spec- 
 trum; the second type is in the normal state for the absorption of principal 
 
 18 Possibly it has something to do with the interaction of atomic fields of neighboring 
 atoms and ions. This suggestion was made by the authors, Phil. Mag., 43, pp. 659-61 (1922), 
 and later was affirmed by Bohr, Phil. Mag., 43, pp. 1112-16 (1922), in discussion of the paper. 
 
LINE EMISSION SPECTRA 131 
 
 series enhanced lines, a state corresponding to 1 @ of the ionized alkali 
 earths. In the second arrangement, the single outside electron revolves 
 in a quantized orbit of unit azimuthal quantum number, about the 
 nucleus and the nine remaining electrons. 
 
 Proceeding by a method identical with that used in the derivation 
 of the Ritz equation, page 32, we shall compute the energy required to 
 eject the outer electron in the configuration!^: 7:1. ~~ 
 
 Let p = number of electrons in inner ring, radius 
 
 g= " " " " 2d " radius a 2 ^ 
 
 atomic no. = Z = p + q + k where k =_2_for spark spectra and 1 for 
 
 arc spectra. 
 
 e 
 where c i = T (P a ^ + 2<*2 4 ). -f JJ (88) 
 
 4 > 
 
 Performing the quantum integration as in Equations (28) and (29) 
 we obtain: 
 
 W= _NM* 
 
 (n a + n r + a) 2 
 
 (2 TT^ mWkci 
 
 where a = v '^T. - - (90) 
 
 n a *h 4 
 
 For the normal state n a + n r = 1^ and expressing our values in volts, 
 we find from Equation (89) : 
 
 Normal state V = 7J^r^ 2 ' (91) 
 
 Eliminating ai and a 2 from Equation (88) by use of Equations (47) to 
 (49) we obtain from Equation (90) when n a + n r = 1 
 
 _fcr P . leg 
 
 On account of the assumptions involved in the derivation of Equation 
 (92), coplanar orbits, etc., it should not be expected that it would yield 
 exact numerical magnitudes. But by applying Equations (91) and 
 (92), first to arc spectra and then to sgark__sgectra ? the ratios a* /a 
 and V*/V may possess some physical significance. Substituting the 
 value of V, the simple ionization potential, in Equation (91) and 
 solving.,fpr a where^j=_l, we may compute a* from the ratio a* /a ob- 
 tained through Equation (92), and then by Equation (91) compute V* 
 
132 
 
 ORIGIN OF SPECTRA 
 
 where k = 2. We thus obtain the value of the work, expressed in volts, 
 necessary to remove the second electron from its quantized orbit in the 
 simply ionized sgdiiini atom. The equations are equaHjT applicable 
 to the other alkalis. We accordingly compute the following table: 
 
 Element 
 
 a*/a 
 
 V* 
 
 Na 
 
 1.50 
 
 14 
 
 K 
 
 1.50 
 
 11 
 
 Rb 
 
 1.66 
 
 10 
 
 Cs 
 
 1.68 
 
 9 
 
 These voltages should correspond approximately to the highest con- 
 vergence frequencies of the spark spectra. 
 
 In the case of sodium, for example, the complete spark spectrum 
 requires for its excitation the removal of one L-electron corresponding 
 to the work La = 35 volts, as shown in Chapter IX, followed by a 14 
 volt collision through which the outer electron is removed. The total 
 work required to remove both electrons is equivalent to the sum of these 
 voltages or 49 volts. The process may be effected in the reverse order; 
 removal of the valence electron requiring 5 volts followed by removal of 
 the L-electron at 44 volts, the sum necessarily being the same. The 
 enhanced spectrum should accordingly begin to appear in an arc at 
 about 35 volts. Now by three successive impacts resulting in (1) 
 ejection of valence electron, (2) transition of L-electron to new quantized 
 orbit, (3) ejection of the electron from this new orbit, the enhanced 
 spectrum might appear at a somewhat lower voltage. However, since 
 three successive impacts are in general improbable, we may conclude 
 that the enhanced spectrum of sodium accompanies its L-radiation, 
 at the minimum voltage corresponding to La = 35. This conclusion is 
 substantiated by the work of Dr. Meggers and the authors. 
 
 In a similar manner, the enhanced spectrum of potassium should 
 accompany its M -radiation appearing at the minimum voltage Ma. 
 As shown in Chapter IX, Ma = 20 to 23 volts. 19 We see in Figure 24 
 that the enhanced lines have put in their appearance at 25 volts, con- 
 firming the above deductions. 
 
 Likewise, the enhanced spectra of rubidium and caesium should 
 accompany their N and x-radiation respectively. No data exist 
 relative to either these x-rays or the excitation potentials for the en- 
 hanced spectra. 
 
 19 Mai, 2 = 20. When the limits are complex, probably the lower value is effective. 
 
PLINE EMISSION SPECTRA 133 
 
 We may contrast the behavior of the alkalis and the alkali earths. 
 Simple ionization of the latter leaves the atom in a normal state for the 
 absorption of enhanced lines, in a state where the remaining; valence 
 electron occupies the 1 @ orbit. Simple ionization of the alkali, however, 
 does not do this. As a consequence the entire enhanced spectrum of an 
 alkali earth appears at the potential V* corresponding; to 1 @, whereas 
 it requires a potential somewhat greater than F* to excite the enhanced 
 spectrum of an alkali. For example, in sodium, although V* = 14 
 volts, the enhanced lines do not appear below La = 35 volts. Similarly 
 with potassium: although F* = 11 volts, it requires 20 volt electronic 
 impact to produce the enhanced lines. 
 
 Table XXII summarizes the development in the spectra of metals 
 of Group I, excited by electronic discharge. 
 
 THE RARE GASES 
 
 The spectra of the rare gases, except ionized helium, are character- 
 ized by exceedingly complicated combination systems of series lines. 
 Most of the fundamentally important lines should lie far in the ultra- 
 violet, in many cases beyond the range of the vacuum spectrograph. 
 
 Helium. As seen from Table XIV helium has an ionization potential 
 
 {> about 25.5 volts and two resonance potentials at 20.4 and 21.2 volts. 
 
 If we could reason by analogy to the alkali earths, we should expect a 
 
 single line spectrum. X 603, at 20.4_vplts and a two-line spectrum, X 603 
 
 I and X 580 at 2J.2 volts. However, as discussed in the section on "The 
 
 Normal Helium Atom," Chapter III, only the line 585 is known, and 
 
 the true significance of and nomenclature for this line is possibly a 
 
 matter of doubt. We are accordingly unable to draw any conclusion 
 
 in regard to the excitation of helium lines below the ionization potential. 20 
 
 The work of double ionization of Bohr's normal coplanar helium 
 
 atom should be 83 volts, as shown by Equation J$5). We have seen that 
 
 this configuration is incorrect, since it gives 28.8 instead of 25.5 for the 
 
 ionization potential. We may, however, readily determine the work 
 
 required to remove the second electron after the first has been ejected. 
 
 J This value, computed from Equation (20) by putting Z = 2, is 54.2 
 
 volts. Hence the correct value for the work of double ionization is 
 
 7 54.2 + 25.5 or 79.7 volts. 21 
 
 2 Franck and Knipping's work, as discussed on page 73, Indicates the presence of 
 15 2P and IS 3P below ionization. See also important foot note 39, page 77, added since 
 book was in page proof. 
 
 21 Possibly 79.5 is a closer value. 
 
134 
 
 ORIGIN OF SPECTRA 
 
 I 
 
 1! 
 
 o 
 
 - 
 - 
 CQ 
 
 
 V 
 
 
 g 
 
 
 1 T^ r-H O I O5 
 1 i-H T-H i-H 1 
 
 1 
 
 gfiw- 
 
 
 & 
 
 ex 
 02 
 
 |8i 
 
 |lll 
 .a*s -g> 
 
 (N 10 g c- S 
 
 CO CO CM 2 
 
 1 
 
 S 
 
 
 ! 
 
 .1 MS 
 
 
 O 
 
 
 <N *e * 
 
 
 a >-g'-3 
 
 l*Jj 
 
 ^ ^~*f-< 
 
 S ;? ;? * 
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 ^K^^I^^^OO 
 
 
 o 
 
 
 
 s o 
 
 ^ 
 
 3 
 
 E 
 
 fill 
 
 l>.(MC<IG5COTt<OOCi 
 
 COrHCOCOTH^OOO Q 
 
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 fir 
 
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 c 
 
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 S 
 
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 p^ O^ CO OO O^ P^ iO C^ 
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 6 
 
 f S5 
 
 TfTFCOCOCOCOCOI> 
 
 
 P 
 
 
 
 a g-a 
 
 1111 
 
 TJH O I-H O 00 CO *O 
 
 OOi-HCOCOlOt > -'^t | T-H 
 
 
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 THCCJT-5c6i-HCOi-HlO 
 
 
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 ^ 
 
 E 
 
 Sw^ 
 
 
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 SCO ^O ^O O5 O^ 00 O^ 
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 T-HT-HT icOi-HCMT ICO 
 
 j. 
 
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 00 
 
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 i-H 
 
 1-HT-HT-HCOT-HCOT-HTtl 
 
 
 -I-S 
 
 ^ ^ i^J bC DQ ^ 
 
 
 
 3r^iMOPH<1O<1 
 

 LINE EMISSION SPECTRA 
 
 135 
 
 Accordingly, the arc lines represented by Figure 10 should appear 
 at a potential of 25.5 volts. Spark lines should be excited at 54.2 volts 
 in case the impacting electron collides with a simply ionizexi atom. A 
 79.7 volt electron is capable of doubly ionizing the normal atom so that 
 an increase in intensity of the spark lines may take place at this voltage. 
 
 We have seen from Figure 2 that the wave-lengths and even the fine 
 structure of the spark lines are accurately given by Equation (22)- r ^ 
 The mean wave-length of each spark line is fairly closely representea 
 by the simpler Equation (9') in which the higher order terms of Equa- 
 tion (22) are omitted: 
 
 < ft( > 
 
 Table XXIII gives the computed wave-lengths for the first and second 
 terms and convergence of each of the four series where n = 1, 2, 3, 4 
 respectively. In a general way the first series corresponds to the 
 
 TABLE XXIII 
 IMPORTANT ENHANCED LINES OF HELIUM 
 
 Line 
 
 *MH) 
 
 'MHO 
 
 'MH) 
 
 <MM) 
 
 m 
 
 \(vac) 
 
 m 
 
 \(vac) 
 
 m 
 
 X(oir) 
 
 m 
 
 X(oir) />- 
 
 First 
 
 2 
 3 
 
 00 
 
 304 A 
 256 
 
 228 
 
 3 
 4 
 
 00 
 
 1640 A 
 1215 
 911 
 
 4 
 5 
 
 00 
 
 4686 A 
 3203 
 2050 
 
 5 
 6 
 
 00 
 
 10124 A 
 6560 
 3644 
 
 Second 
 
 Convergence 
 
 
 Corresponding 
 series in hydrogen 
 
 Lyman 
 
 Balmer 
 
 Paschen 
 
 Brackett* 
 
 * Of. Nature, 109, p. 209 (1922). 
 
 principal doublet enhanced series of the alkali earths and the second 
 series to the subordinate doublet series of these metals, while the direct 
 observations on the excitation potential for the enhanced lines of helium 
 are confined to the line X 4686 of the third series. We may be certain, 
 however, if the latter appears, the lines of the more important series are 
 also present in even greater intensity. 
 
 Compton and Lilly, 22 using a two electrode discharge tube, observed 
 the emission of the arc lines of helium, Figure 10, at an applied potential 
 of 25 to 35 volts. The spark line X 4686, in an intense arc, was observed 
 
 M Astrophys. J., 52, pp. 1-7 (1920). 
 
136 ORIGIN OF SPECTRA 
 
 at a minimum potential of 55 volts, and the brightness of the line in- 
 creased considerably at 80 volts. At low gas pressure and current 
 density X 4686 was not perceptibly excited below 80 volts. Under 
 these conditions two successive collisions, each resulting in the expulsion 
 of a single electron, were much less probable than a single 80 volt collision 
 resulting in the ejection of two electrons. 
 
 We may accordingly conclude that, as predicted by theory, the arc 
 spectrum of helium appears at 25.5 volts, the ionization potential, and 
 that the spark lines are excited at 54.2, by successive impact, and at 79.7 
 by single impact, the latter values corresponding respectively to the 
 work required to eject the second electron after the first is removed, and 
 to the work required to eject both electrons. 
 
 Neon. The intricate spectrum of neon has been recently correlated 
 in series by Paschen. 23 It is characterized by sequences of the form 
 1 s x mp v , which are analogous to the principal series of the metals, 
 and sequences of the form 2 p x md y and 2 p x ms y , which are analo- 
 gous to the subordinate series of the metals. As shown in Table XIV 
 there are two resonance potentials and three ionization potentials. The 
 latter all correspond to the removal of a single electron as none is great 
 enough to represent successive or double ionization. Apparently there 
 are three slightly different energy levels in which the outer shell of 
 eight electrons are distributed. The work required to remove a second 
 electron from the neon atom after the first has been ejected cannot be 
 computed nor has it been observed experimentally. 
 
 Horton and Davies 24 have observed visually the stage development t 
 in the neon spectrum at the three ionization potentials. Their con- 
 clusions are summarized as follows. 
 
 First ionization 16.7 volts. No visible radiation. Probably all the radiation 
 
 lies in the extreme ultra-violet. 
 
 Second ionization 20.0 volts. Principal series lines 1 s x mp v begin, to appear. 
 
 Third ionization 22.8 volts. Subordinate series lines 2 p x ms u and 2 p x 
 
 md v begin to appear. 
 
 Apparently the phenomena concerned with the production of the 
 arc lines of neon are nearly as complicated as the spectrum itself. The 
 series relations in the arc spectrum may be intimately connected with 
 those in the L series of the x-radiation. 25 Higher types of spectra which 
 are probably enhanced lines may be obtained in a spark discharge but 
 
 I 
 
 23 Ann. Physik, 60, p. 405 (1919); 63, p. 201 (1920). This work is simply summarized 
 by Fowler, "Series in Line Spectra," Chapter XXI. 
 
 ** Phil. Mag., 41, pp. 921-40 (1921). 
 
 25 Grotrian, Z. Physik, 8, p. 116 (1921) , pointed out that a constant frequency difference 
 between arc series is apparently equal to the extrapolated L-doublet separations. 
 
LINE EMISSION SPECTRA 137 
 
 no attempts have been made to relate these to the velocity loss at elec- 
 tronic impact. 
 
 FRANCK AND EINSPORN'S OBSERVATIONS ON MERCURY 
 
 In order to discuss the recent paper of Franck and Einsporn 26 with 
 sufficient clarity, it appeared advisable to consider it following the 
 foregoing sections, rather than to have introduced it earlier in the treat- 
 ment of the metals of Group II. These investigators obtained evidence 
 that there are a large number of resonance potentials in mercury vapor 
 and that lines which have never been observed should be present in 
 considerable intensity. 
 
 The method 27 employed is a common one in the determination of 
 critical potentials (see general references to Chapter III) . The electrons 
 from a hot wire fall through a definite potential and collide with mercury 
 atoms. The radiation, emitted by an atom in returning to or toward 
 the normal state following the disturbance produced by an inelastic 
 impact, is measured by its photo-electric effect upon an auxiliary electrode. 
 The photo-electric current leaving this electrode is plotted as a function 
 of the accelerating voltage of the impacting electrons. As the velocity, 
 or equivalent voltage, of the latter is gradually increased, an increase 
 in the radiation, and hence in the observed photo-electric current, 
 takes place at each critical voltage representing an inelastic impact. 
 Ordinarily one observes an increase at 4.9 and 6.7 volts corresponding 
 to the well-known resonance potentials, an increase at 10.3 corresponding 
 to ionization, and further increases at combinations of these values such 
 as 4.9 + 4.9 = 9.8; 4.9 + 6.7 = 11.6, etc. These latter represent 
 successive collisions of the impacting electrons. 
 
 Franck and Einsporn's curves, which were obtained with the greatest 
 precision, show these, and many more, rapid increases, as illustrated by 
 Figure 25. In Table 24 is their interpretation of the observed critical 
 voltages. Column 2 gives the observed voltages obtained from Figure 
 25 and similar curves; column 6 the series notation of the radiation 
 supposedly producing the effects observed; and the last column gives the 
 values computed from the wave numbers by Equation (63). Point 
 No. 3 at 5.32 volts corresponds closely to measurements of McLennan 
 and Edwards, 28 who found a group of absorption bands in mercury 
 
 2 6 Z. Physik, 2, pp. 18-29 (1920). 
 
 27 This method, which permits of many modifications, was devised by Davis and Goucher. 
 Phys. R. 10, p. 101 (1917), and has proved to be one of the most important means for the 
 study of electron impact. 
 
 2 8 Phil. Mag., 30, pp. 695-700 (1915). 
 
138 
 
 ORIGIN OF SPECTRA 
 
 vapor between X 2313 and X 2338. These have been since observed 
 as emission bands by Grotrian. 29 Probably they have no relation to 
 the arc spectrum of the atom. 
 
 Point 13 corresponds to a displacement of the valence electron to the 
 3 p 2 orbit and point 14 to a displacement to either 3 P or 3 d'. Points 
 
 i-Kurvel _ 
 7 Kurvenll 
 
 FIG. 25. Photo-electric current versus accelerating voltage. Franck and Einsporn's 
 observations with mercury vapor. 
 
 16 and 17 may be due to displacements to higher energy levels or may be 
 the result of two successive collisions, each displacing an electron to a 2 p 
 orbit. Besides these ejections to the higher mpz and mP orbits we note 
 displacements to 2 p s in points 1, 15 and possibly 16, and to 2 p\ in 
 point 4. Point 5 corresponds to the removal of an electron from the 2 p 3 
 orbit, an effect of cumulative ionization (Chapter VI). 
 
 2 Z. Physik, 5, pp. 148-58 (1921). 
 
LINE EMISSION SPECTRA 
 
 139 
 
 TABLE XXIV 
 CRITICAL VOLTAGES IN MERCURY VAPOR; FRANCK AND EINSPORN 
 
 No. 
 1 
 
 Observed 
 Volts 
 
 Intensity of 
 Radiation 
 
 X 
 
 V 
 
 Notation 
 
 Computed 
 Volts 
 
 4.68 
 
 Strong. 
 
 2656 
 
 37643 
 
 IS -2p, 
 
 4.66 
 
 2 
 
 4.9 
 
 Very strong, especially 
 at high pressure. 
 
 2537 
 
 39413 
 
 1 S - 2 7)2 
 
 4.86 
 
 3 
 
 5.32 
 
 Weak. 
 
 2313 
 to 2338 
 
 
 ? 
 
 5.3 
 
 4 
 
 5.47 
 
 Weak; at medium pres- 
 sure strong. 
 
 2271 
 
 44041 
 
 !S-2pi 
 
 5.43 
 
 5 
 
 5.76 
 
 Strong. 
 
 2150 
 
 46534 
 
 2p 3 
 
 5.73 
 
 6 
 
 6.04 
 
 Weak. 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 7 
 
 6.30 
 
 Weak. 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 8 
 
 6.73 
 
 Medium strong. 
 
 1849 
 
 54066 
 
 IS -2P 
 
 6.67 
 
 . 
 9 
 
 7.12 
 
 Strong at high pres- 
 sure; weak at low 
 pressure. 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 10 
 
 7.46 
 
 Medium strong. 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 11 
 
 7.73 
 
 Medium strong. 
 
 1604 
 
 62347 
 
 IS -Is 
 
 7.69 
 
 12 
 
 8.35 
 
 Weak. 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 13 
 
 8.64 
 
 Weak. 
 
 1436 
 
 69658 
 
 1 S - 3 p z 
 
 S.58 
 
 14 
 
 8.86 
 
 Medium strong. 
 
 1403 
 1400 
 
 71291 
 71393 
 
 IS -3P 
 
 IS -3d' 
 
 8.79 
 8.81 
 
 15 
 
 9.37 
 
 Weak.' 
 
 2656 
 + 2656 
 
 37643 
 
 lS-2p s 
 
 4.66 + 4.66 
 = 9.32 
 
 16 
 
 9.60 
 
 Weak. 
 
 1308 
 / 2556 
 
 \+2537 
 
 76463 
 37643 
 39413 
 
 1 S - 4 p 2 
 lS-2p, 
 lS-2p z 
 
 9.44 
 4.66 + 4.86 
 = 9.52 
 
 17 
 
 9.79 
 
 Medium strong. 
 
 / 2537 
 \+2537 
 1269 
 
 39413 
 78810 
 
 1 S - 2 pz 
 1 S - 2 pz 
 IS -4P 
 
 4.86 + 4.86 
 = 9.72 
 9.73 
 
 18 
 
 10.38 
 
 Strong at low pressure; 
 weak at high pressure. 
 
 1188 
 
 84178 
 
 IS 
 
 10.39 
 
140 ORIGIN OF SPECTRA 
 
 There is nothing contradictory to the quantum theory in the presence 
 of inelastic impacts corresponding to 1 S 2 pi and 1 S 2 p 3 or to 
 the other higher mp and mP terms. Displacement by electronic impact 
 to 2 pi or 2 pz does not violate the principle of selection even when 
 applied to so restricted a theory as that involved by Sommerf eld's 
 internal quantum numbers, 30 since no radiation is absorbed or emitted. 
 However, these inelastic collisions were observed through the effect of 
 the resulting radiation. Moreover, if an electron is displaced to 2 p 3 , 
 the next orbit to 1 S, the only radiation which can be emitted directly 
 would appear to be 1 S 2 p 3 . Figure 25 shows that the increase in 
 photo-electric current, which is proportional to the intensity 4of radiation, 
 is just as reat as 1 S 2 p 3 (4.68 volts) as at 1 S 2 p 2 (4.9 volts). 
 Hence this unknown line X 2656 should have been as bright as the well- 
 known line X 2537. It is scarcely possible that if such a line existed 
 it would not have been observed in the arc spectrum of mercury, which 
 has been investigated with almost all possible electron velocities in this 
 neighborhood. A similar statement applies to the emission of 1 S 
 2 pi, X 2271. Possibly the inelastic impacts corresponding to these lines 
 exist and a secondary process such as interatomic collision produces a 
 transfer from 2 pi or 2 p 3 to 2 p 2 , so that the resulting radiation is 1 S 
 2 p 2 . Or ejection of a valence electron to 2 pi and 2 p 3 may give rise to a 
 metastable form of the atom which, as discussed on page 106, possesses 
 an electron affinity. Molecules may be then formed and the increase 
 in the photo-electric current may be due to the decomposition of these 
 metastable compounds of excited and normal atoms. 
 
 The subject is by no means closed. If further work more clearly 
 interprets and verifies the present observations, it will not seriously 
 conflict with the principles developed in this book. In the discussion 
 of resonance potentials where we have made the statement "only two 
 resonance potentials exist" we may eventually modify this to read 
 "only two important or pronounced resonance potentials exist," admit- 
 ting the possibility of a relatively small number of displacements to 
 higher energy levels. Possibly some one will be able to demonstrate 
 that lines involving higher series terms are emitted as a result of elec- 
 tronic impact below the ionization potential, all other effects of cumula- 
 tive ionization being subordinated. At the present time, however, 
 cumulative ionization and the few high velocity electrons always present 
 on account of velocity distribution are easily sufficient to explain all 
 experiments where higher series terms have been observed spectroscopi- 
 cally below the ionization potential. 
 
 30 Sommerfeld, " Atombau," 3d Ed., Chapter VI, Section 5. 
 
 
LINE EMISSION SPECTRA 141 
 
 QUANTITATIVE SPECTROSCOPIC ANALYSIS IN ITS RELATION TO THE 
 
 ORIGIN OF SPECTRA 
 
 The possibility of making quantitative analyses by spectroscopic 
 means has been agitated for a century. Some success has been attained 
 in the past, but many of the excellent ideas proposed by such pioneers 
 in this field as Lockyer, 31 Hartley 32 and more recently by de Gramont 33 
 have not received the attention they merit. For several years Dr. 
 W. F. Meggers and his colleagues have been engaged in a systematic 
 investigation of the possibilities of the method and have clearly demon- 
 strated that quantitative analyses can be made, at least when the 
 material sought occurs in small percentages, of the order of one per cent 
 and less. 34 
 
 Several experimental facts have been disclosed in this work which 
 have some bearing upon the subject matter of this book. These will 
 be considered in detail in a future paper by Dr. Meggers, who has placed 
 the preliminary draft of his manuscript at our disposal. The empirically 
 developed subject of spectroscopic analysis has to deal with two general 
 phenomena: (1) the " long lines" of Lockyer, and (2) the "raies ultimes" 
 of de Gramont or " persistent" lines of Hartley. As to the application 
 of these phenomena to precise analysis, the original papers of Meggers 
 
 j must be consulted. 
 
 Long Lines. If the entire spark or arc discharge is focused on the 
 
 !; slit of a spectroscope so that the poles appear in the spectrum, certain 
 
 ! lines of an impurity, or element occurring in a small proportion, appear 
 long, extending from pole to pole, while the emission of other spectral 
 lines is confined to a short distance in the immediate neighborhood of 
 the poles. With increasing percentage of impurity the short lines 
 
 i increase in length. 
 
 Raies Ultimes. As the percentage of the impurity is decreased, 
 more and more of its spectral lines disappear. Certain lines, however, 
 persist even when the impurity, magnesium for example, is present in 
 the extremely minute extent of one part in 10 10 . The persistent lines, 
 termed by de Gramont, "raies ultimes," were recognized as not being 
 necessarily the strong or intense lines of the ordinary spectrum. Further- 
 more the type of persistent line depends upon the method of excitation. 
 In general the sensitive lines for any element are both "long lines" 
 and "raies ultimes." Discrepancies arise here and there which are 
 
 Phil. Trans. 163, pp. 253, 639 (1873). 
 
 32 Phil. Trans. 175, p. 325 (1884). 
 
 33 Ann. chim. phys. 17, pp. 437-77 (1909). Compt. rend., 171, p. 1106 (1920). 
 
 34 Meggers, Kiess and Stimson, Bur. Standards Sci. Paper No. 444. 
 
142 
 
 ORIGIN OF SPECTRA 
 
 probably attributable to the fact that different observers have investi- 
 gated different spectral regions and certain lines have been thought to 
 have been the long lines when the actual long lines may lie in a spectral 
 region not yet investigated carefully. 
 
 Table XXV summarizes Dr. Megger's correlation of the raies ultimes 
 made from empirical spectroscopic observations. It may be found, 
 especially with elements of other than Groups I and II of the periodic 
 table, that as the spectral range investigated is extended, even more 
 sensitive lines will be discovered replacing some of those here listed. 
 
 TABLE XXV 
 RATES ULTIMES OF THE ELEMENTS 
 
 Element 
 
 Wave-length 
 Angstrom Units 
 
 Intensity 
 
 Notation 
 
 Arc 
 
 Spark 
 
 Li . . 
 
 6707.85 
 6708.00 
 4602.19 
 5889.96 
 5895.93 
 3302.35 
 7664.94 
 7669.01 
 4044.15 
 4201.82 
 4215.56 
 4555.3 
 4593.2 
 3247.53 
 3280.66 
 2427.97 
 2852.13 
 2795.53 
 4226.72 
 3933.67 
 4607.34 
 4077.75 
 5535.53 
 4554.04 
 
 3075.88 
 2138.5 
 3261.05 
 2288.03 
 2144.39 
 
 20 
 
 10 
 50 
 35 
 30 
 40 
 30 
 30 
 30 
 20 
 20 
 10 
 100 
 100 
 10 
 100 
 20 
 100 
 50 
 50 
 20 
 10 
 10 
 8 
 4 
 
 20 
 10 
 4 
 
 20 
 
 8 
 20 
 15 
 20 
 30 
 20 
 20 
 20 
 10 
 10 
 5 
 30 
 30 
 20 
 20 
 50 
 10 
 100 
 20 
 40 
 10 
 20 
 5 
 4 
 6 
 10 
 8 
 
 Is - 2 pi 
 Is - 2p 2 
 2p - 4d 
 l-2p, 
 
 1 s 2 p 2 
 Is - 3pi 
 Is - 2 Pl 
 Is - 2p 2 
 Is - 3 pi 
 
 1 8 - 3 pi 
 
 1 s - 3 p 2 
 1 s - 3 pi 
 Is - 3p 2 
 Is - 2 pi . 
 Is - 2 pi 
 1 s - 2 pi 
 IS - 2P 
 1 @ - 2 9i 
 IS- 2P 
 1@ - 2?i 
 18- 2P 
 
 1@ - 2?! 
 
 IS - 2P 
 
 i3>-2fi 
 
 1 S - 2 p z 
 1S-2P 
 IS -2p z 
 1S-2P 
 
 i @ - 2 y$i 
 
 Na 
 
 K 
 
 Rb 
 
 Cs 
 
 Cu 
 
 Ag 
 
 Au 
 
 Mg.. 
 
 Ca 
 
 Sr 
 
 Ba 
 
 Zn 
 
 d 
 
 
LINE EMISSION SPECTRA 
 
 TABLE XXV Continued 
 RAIES ULTIMES OF THE ELEMENTS 
 
 143 
 
 Element 
 
 Wave-length 
 Angstrom Units 
 
 Intensity 
 
 Notation 
 
 Arc 
 
 Spark 
 
 Hg 
 
 2536.52 
 3630.75 
 3710.29 
 3961.54 
 4172.05 
 4511.37 
 5350.49 
 2478.6 
 2881.59 
 3361.22 
 3391.98 
 3039.08 
 
 2863.32 
 3262.31 
 
 4057.84 
 4379.24 
 4058.97 
 3311.13 
 
 2535.63 
 2553.32 
 
 2349.84 
 2780.24 
 
 10 
 15 
 30 
 100 
 30 
 100 
 100 
 10 
 30 
 10 
 10 
 50 
 
 20 
 100 
 
 100 
 
 30 
 50 
 10 
 
 10 
 10 
 
 10 
 50 
 100 
 20 
 20 
 20 
 30 
 10 
 15 
 30 
 20 
 20 
 
 15 
 30 
 
 50 
 30 
 10 
 3 
 
 5 
 5 
 
 10 
 10 
 
 1 S - 2 p, 
 
 2 pi - Is 
 2 pi -Is 
 
 2 Pl - Is 
 2 Pi - Is 
 
 Sc 
 
 Yt 
 
 Al 
 
 Ga 
 
 In 
 
 Tl 
 
 C 
 
 Si 
 
 Ti 
 
 Zr 
 
 Ge. .. 
 
 Sn 
 
 Pb 
 
 V. . . 
 
 Cb 
 
 Ta . 
 
 P 
 
 As 
 
 
144 
 
 ORIGIN OF SPECTRA 
 
 TABLE XXV Continued 
 RAIES ULTIMES OF THE ELEMENTS 
 
 Element 
 
 Wave-length 
 Angstrom Units 
 
 Intensity 
 
 Notation 
 
 Arc 
 
 Spark 
 
 Sb 
 
 2528.54 
 3067.69 
 
 3578.68 
 3593.48 
 4254.34 
 
 3798.25 
 3864.11 
 
 4008.77 
 2385.81 
 
 2576.15 
 4030.80 
 
 2382.04 
 2749.33 
 3734.86 
 
 2388.93 
 2416.15 
 3498.95 
 3434.90 
 3609.55 
 3220.79 
 3922.96 
 
 10 
 100 
 
 30 
 30 
 50 
 
 50 
 50 
 
 10 
 3 
 
 4 
 
 100 
 
 6 
 4 
 5 
 
 2 
 2 
 50 
 100 
 100 
 15 
 10 
 
 20 
 30 
 
 20 
 20 
 50 
 
 20 
 20 
 
 10 
 20 
 
 30 
 20 
 
 10 
 20 
 10 
 
 10 
 15 
 8 
 10 
 50 
 -5 
 15 
 
 | 
 
 Bi 
 
 Cr 
 
 Mo 
 
 W < .. ; 
 
 Te 
 
 Mn 
 
 Fe At 
 
 Co :/:/. 
 
 Ni 
 
 Ru 
 
 Rh 
 
 Pd... 
 
 Ir .... 
 
 Pt 
 
 
 The important fact which Meggers points out is that these raies 
 ultimes are almost always prominent absorption lines, and are in most 
 
144 A 
 
 Ti 
 
 -336 / Tt 
 ^.3373 71 
 
 \3363 
 
 FIG. 26. "Raies ultimes" for several elements. 
 
Pb-Al 
 
 It 14 1 i i 
 
 FIG. 27. An example of "long" and "short" lines. 
 
 
 
LINE EMISSION SPECTRA 145 
 
 cases the first lines of series converging at 1 S or Is, where the spectrum 
 of the element concerned has been correlated in series. 
 
 That is, they are the same lines which determine the value of the 
 resonance potential, or which appear in the so-called single-line spectrum 
 of the element excited below the ionization potential. We accordingly 
 have another method for locating these fundamentally important lines 
 of elements for which the series relations have not been as yet established. 
 
 If the spectra are excited in the arc the raie ultime is usually the 
 first line of a fundamentally important arc series; if in a condensed 
 spark, usually the first line of a fundamentally important spark series. 
 This fact is indicated by the intensity relations given in Table XXV. 
 
 Figure 26 clearly illustrates these conclusions. The material in- 
 vestigated was carbon, which contained small amounts of a large number 
 of impurities for several of which the series relations are known. The 
 outer spectrogram in each group was obtained with a spark discharge. 
 The magnesium lines appearing are the pair X 2795 2802, 1 <5 2 $ 
 belonging to the spark spectrum and the single line X 2852, 1 S 2 P, 
 of the arc spectrum, the former being present in the greater intensity. 
 The second spectrogram of each group was obtained in an arc discharge. 
 Here again the spark pair 1 @ 2 ^ is present, but with less intensity 
 than the arc line I S 2 P. The inner two spectrograms are the 
 ordinary arc and spark spectra of magnesium. Certain lines which 
 are extremely intense in these spectra are readily seen to be absent when 
 the amount of the metal is decreased, as in the two outer spectrograms, 
 so that the phenomenon is not at all a matter of relative intensity with 
 the ordinarily brighter lines persisting when the dilution increases. 
 Similar results may be noted with calcium. The spark pair 1 @ 2 $ 
 and the single line 1 S 2 P are prominent. Another calcium pair is 
 also present, belonging to a subordinate series in the spark spectrum. 
 This is due to the fact that more calcium is present than is necessary 
 to produce the raies ultimes alone. At percentages of Ca> 0.001 per 
 cent, this second pair is always found, while for lower percentages only 
 the raies ultimes are present, one of the empirically determined and 
 useful facts of spectroscopic analysis. 
 
 In addition to these lines we note the appearance of the first pair of 
 the principal series of both copper and silver. By analogy one would 
 conclude that the sensitive lines shown for the other impurities should 
 also belong to fundamentally important series of a similar type, but 
 unfortunately these are unknown. 
 
 Figure 27 shows some long and short lines in the spark spectra of two 
 
 
146 ORIGIN OF SPECTRA 
 
 different alloys. For example, the three aluminum lines X 3587, 3602 
 and 3613 in the upper spectrogram appear at the electrodes only, while 
 the lines X 3944, 3962 are long lines extending throughout the space 
 between the electrodes. The latter constitute the first pair of the 2d 
 Subordinate series while the classification of the former is unknown. In 
 the lower spectrogram one may readily note the difference in appearance 
 of the lead lines X 4019, 4168 and the lines X 4245, 4387, the latter being 
 " short" lines, as is evidenced by the very much higher intensity at the 
 poles. 
 
 This figure is given simply to indicate the general appearance of 
 long and short lines. Unfortunately photographs, suitable for reproduc- 
 tion, are not available to the authors to clearly illustrate the present 
 discussion of the physical behavior of long lines. Most of the work in 
 this field has been done either with elements for which the series rela- 
 tions are unknown or has embraced a too limited portion of the spectrum. 
 
 A careful study of Table XXV shows that some fundamentally 
 important series lines do not appear to be raies ultimes, for example 
 the line 1 S 2 p 2 , X 4571 of magnesium. Why this should be true is 
 not apparent. In fact the true physical significance of all the foregoing 
 phenomena is not evident, and will involve further study. 
 
 We probably have in the arc or spark a distribution of potential 
 in which most of the gradient is confined to the anode and cathode, with 
 very little drop in the arc itself. Consequently the electrons, except 
 near the electrodes, may not accumulate velocities exceeding the reso- 
 nance potentials of the impurities. Accordingly lines of the arc and 
 spark spectra other than those of the so-called fundamental type can 
 not be excited throughout the central portion of the arc. Furthermore, 
 the excitation of these fundamentally important lines may give rise to 
 resonance radiation which through absorption and re-emission becomes 
 uniformly distributed throughout the volume of vapor, thus accentuating 
 the presence of the "long lines." 
 
 We are able to offer only a suggestion in regard to the origin of the 
 raies ultimes. Suppose Zn occurs as an impurity in Mg to the extent of 
 1 Zn atom for every 100,000 Mg atoms. The arc spectrum will show 
 all arc lines of Mg and the Zn arc lines 1 S 2 p 2 and 1 S 2 P, the 
 raies ultimes of Zn. We may assume that since the electrons emitted 
 by the cathode can not be discriminatory, the probability of collision 
 with a metal atom is proportional to its concentration. 
 
 Hence in general an arc line of Zn will be 1/100,000 as intense 35 as th< 
 
 35 Neglecting modifying factors such as differences in ionization potential, cross 
 of atom, etc. 
 
LINE EMISSION SPECTRA 
 
 147 
 
 corresponding line in Mg, and would certainly not be observed. But 
 in the case of resonance lines (lines absorbed and re-emitted by the 
 surrounding vapor) the above reasoning does not hold. The absorption 
 factor increases with the concentration. Hence only for extremely 
 rare vapors is the intensity of emission proportional to the concentra- 
 tion, and with increasing partial pressure of the absorbing atoms a stage 
 is soon reached where the increase in intensity becomes relatively small. 
 The problem of the arc discharge is so complicated that a mathematical 
 treatment of the subject is out of the question, but in the much simpler 
 case of flame spectra (Chapter VII) the emission of resonance lines under 
 thermal excitation is treated in some detail. The theory is applied 
 only to dilute vapors, but the equations used indicate the manner in 
 which the absorption factor would enter with increased concentration. 
 These considerations apply equally well to either electrical or thermal 
 excitation. 
 
 The quantitative results for extremely dilute vapors in flames indi- 
 cate that in an arc the thermal excitation alone would suffice to explain 
 the appearance of the raies ultimes of minute traces of an element. 
 This fact together with the above mentioned absorption factor gives 
 at least a qualitative explanation for the appearance of resonance lines 
 of an impurity, with an intensity comparable to that of the arc lines 
 of a concentrated vapor. The fact that some of the raies ultimes listed 
 in Table XXV are subordinate series lines is not necessarily in con- 
 tradiction to the above theory. Resonance lines of normal atoms are 
 indeed principal series lines, but if the resonance potential is very low, 
 
 ly of the atoms in an arc will be in the 2 p state. These excited 
 atoms will absorb and re-emit subordinate series lines. For such atoms, 
 lines of subordinate series will possess the characteristics of " raies 
 ultimes" and "long lines. 7 ' 
 
Chapter VI 
 Cumulative lonization 
 
 Cumulative ionization denotes the process whereby atoms may be 
 ionized by successive stages of excitation. (1) A valence electron may 
 be ejected to an outer orbit such as 2 p z by electronic collision and the 
 excited atom thus formed may collide with a second electron having a 
 velocity sufficient to completely eject the valence electron. This 
 process is known as ionization by successive impact. (2) A valence 
 electron may be ejected to an outer orbit by absorption of radiation, 
 and the excited atom thus formed may collide with an electron having a 
 velocity sufficient to complete the process of ionization. Compton 
 designates this as photo-impact ionization. (3) The valence electron 
 may be ejected to an outer orbit by absorption of radiation, and the 
 process of line absorption continued until the atom is ionized. This 
 may be called ionization by successive photo-electric action. These pro- 
 cesses may be of course jointly involved with several absorptions of 
 radiation followed by an electronic impact. 
 
 K. T. Compton 1 has made a mathematical analysis of the processes 
 (1) and (2) . He has derived an expression, in terms of measurable quan- 
 tities, which gives the fractional number of gas atoms at any instant in 
 the excited state, and hence in a condition for ionization by electronic 
 impact below the ionization potential; (1) as a result of electronic 
 collision and (2) as a result of absorption of resonance radiation from 
 neighboring atoms which have been previously excited by electronic 
 impact. Necessarily rather questionable assumptions must be made 
 in order to simplify the analysis, but the results are probably somewhere 
 near the correct order of magnitude, which is sufficient for the present. 
 The following outlines Compton's method in the treatment of the 
 problem. 
 
 Figure 28 represents a cylindrical, two-electrode discharge tube, 
 filled with vapor, in which A is the anode and C the hot wire cathode, 
 mounted concentrically. If the accelerating field V is less than the 
 
 i Phys. B., 20 (1922). 
 
 148 
 
CUMULATIVE IONIZATION 
 
 149 
 
 ionization potential T r but greater than the resonance potential V r , 
 inelastic collisions will occur resulting in excitation of the atoms and 
 subsequent emission of radiation. For a given applied potential differ- 
 ence V, an individual electron will attain a velocity V r at a certain 
 distance from the cathode. However, since an impact with an atom 
 may not occur at precisely the instant the electron attains this velocity, 
 and for another reason explained later, we shall have for all the emitted 
 electrons a region of effective collision, a small volume inclosed by two 
 concentric cylindrical surfaces, represented by the shaded portion of the 
 diagram. 
 
 FIG. 28. Cross section of discharge tube. 
 
 EXCITATION BY ELECTRONIC IMPACT 
 
 Let the n electrons emitted per second by the cathode collide effectu- 
 ally in the shaded space of Figure 28. Excited atoms are accordingly 
 produced which remain in the excited state for an average time interval 
 T second. If P denotes the fractional number of atoms which at any 
 instant, for any reason whatever, are in the excited condition, then 
 n(lP) atoms are excited per second by electronic impact, and the aggre- 
 gate time of excitation of all the atoms is n (I P) T. This divided 
 by the total number of atoms in the shaded volume gives the fractional 
 
 
150 ORIGIN OF SPECTRA 
 
 number of atoms which at any instant are in the excited state as the 
 direct result of electronic impact. Calling this fraction P t , we have 
 
 n(l P)r nr 
 
 Pt = NT = ^' approximately 
 
 where p is the gas pressure in mm Hg, N is the number of atoms per 
 cm 3 at a pressure of 1 mm Hg and v is the volume of the shaded cylindri- 
 cal shell within which the effective impacts occur. If / is the length of 
 this volume and d its width, evidently 
 
 v = 2 7r(6 + c)/5. (94) 
 
 From the distribution of potential in a concentric arrangement 
 such as here considered we find 
 
 V ~ V r i a 
 
 b + c = at~ v ln *, (95) 
 
 where a and c are the respective radii of the anode and cathode. The 
 calculation of d is more difficult, for it depends on the average distance 
 which the electrons move beyond the point at which they have acquired 
 the velocity V T before making an effective impact, and also on the 
 distribution of velocities of electrons which causes them to gain the 
 critical velocity at different distances from the cathode. Compton 
 derives the formula 
 
 5= A/I -+^(6 + c)Zn-, (96) 
 
 in which Y 8 p eV c ' 
 
 I = mean free path of an electron at a pressure of 1 mm Hg 
 
 aT = average kinetic energy of an atom at the cathode temperature T. 
 
 We accordingly obtain from Equations (93) , (94) and (95) 
 
 2 ir(b + c)f5Np ' 
 
 where d may be computed from Equation (96). This gives the frac- 
 tional number of atoms which at any instant are in the excited state as 
 the direct result of impact. 
 
 EXCITATION BY ABSORPTION OF RADIATION 
 
 Impacts in the shaded layer produce radiation which is absorbed 
 and re-emitted by atom after atom before escaping from the vapor so 
 that, as a result of the activation of a single atom by direct impact, 
 many other atoms are successively activated through absorption of the 
 emitted radiation. Thus at any instant the fractional number P r of 
 atoms in the excited state as a result of absorption of radiation should 
 be greater than P i if much absorption occurs. 
 
CUMULATIVE IONIZATION 151 
 
 The quanta of radiation are passed on from atom to atom, diffusing 
 through the vapor in all directions in a manner analogous to the diffusion 
 of a foreign gas, and accordingly the same mathematical procedure 
 may be employed in the treatment of the two problems. A beam of light 
 passing through an absorbing or scattering medium decreases in intensity 
 according to the law 
 
 I = I e-* x , (98) 
 
 where k is the absorption coefficient. A stream of particles passing 
 through a gas is reduced by collisions or scattering according to the law 
 
 n = n Q e- x/l , (99) 
 
 where I is the mean free path. 
 
 We may define p as the reciprocal of the absorption coefficient fc, 
 i.e. as the distance in which the intensity of a beam of monochromatic 
 radiation through a vapor at 1 mm pressure decreases to 1/6 of its initial 
 value. By analogy to Equation (99), this is the mean free path of a 
 quantum in a gas at 1 mm pressure, and the mean free path at p mm 
 pressure is accordingly p/p. Although in our particular problem some 
 of the atoms are excited and hence are incapable of absorbing or scatter- 
 ing resonance radiation, the fractional number in this condition is too 
 small to alter materially the value of the mean free path p/p strictly 
 applicable to normal atoms. Accordingly the average speed c of the 
 radiation is equal to the distance p/p divided by the time r in which an 
 atom on the average remains in the excited condition. We may there- 
 fore apply the diffusion equation: 
 
 where N' is the number of excited atoms per cm 3 at any point at any 
 instant in the vapor of pressure p, R is the net rate at which atoms are 
 excited by direct electron collision and t\ is the outward normal to the 
 closed surface over which the surface integral and within which the 
 volume integral are taken. For details as to the application of Equation 
 (100) in the solution of our problem, the original paper must be consulted. 
 Compton shows that with reasonable assumptions and for V not very 
 much greater than V T the following expression is derivable. 
 
 Since there are Np atoms, N 7 of which at any instant are in the excited 
 state, we obtain 
 
 -T1 a. 
 
 Np 2 irfNp 2 
 
152 ORIGIN OF SPECTRA 
 
 NUMEKICAL MAGNITUDES 
 
 The relative importance of P r and P ( is obtained on dividing 
 Equation (102) by Equation (97) as follows. 
 
 P r _ 3p(6 + c)g V-V r , a 
 Pi" ~^~ ~V~ ln c' 
 
 As mentioned on page 89 Wood found that the intensity of the 
 resonance radiation of mercury X 2537 was reduced to \ its value in 
 traversing a distance of 0.5 cm through mercury vapor at a pressure 
 0.001 mm Hg. This datum in the above defined units makes p = 0.0007. 
 Reasonable constants for the dimensions of the discharge tube are: 
 a = 0.5 cm; c = 0.025 cm; / = 1 cm. For mercury V r = 4.9 volts. Let 
 the total applied potential exceed this by one volt, i.e. V = 5.9. 
 
 On carrying through the computations involved in Equation (96) 
 it is found that 5 is roughly constant, averaging about 8 = .04 for a wide 
 range of pressure and temperature of the cathode. We thus obtain 
 from (103) ^ 
 
 ^ = 40,000 p 2 
 * i 
 
 = 40,000 at 1 mm pressure 
 
 = 4,000,000 at 10 mm pressure. 
 
 Now the probability of an electron colliding with an excited atom 
 and of ionizing below the ionization potential is proportional to P r + 
 P. It is therefore evident that ionization by photo-impact is relatively 
 of far greater importance than ionization by successive impact es- 
 pecially at the higher vapor pressures. 
 
 We shall now consider Equation (102) to determine whether ioniza- 
 tion by photo-impact is, in itself, an important factor in arc phenomena. 
 One serious difficulty here is our inadequate knowledge of the quantity r 
 an estimate of which was stated in Chapter IV to be 10~ 8 seconds. 
 Using this value and the data given above we accordingly obtain from 
 (102) 
 
 P r = 
 
 The number of electrons n leaving the cathode in the absence of any 
 ionization is limited by the space charge and may be computed from the 
 Langmuir formula n = 1.8-10 14 V* = 2.5-10 15 in which the constants 
 of the particular apparatus have been substituted. This relation is 
 strictly true only in vacuo, and actually, the current will be somewhat 
 
CUMULATIVE IONIZATION 153 
 
 less since the presence of the gas around the cathode reduces the rate of 
 escape of electrons. We finally obtain for P T in this favorable case: 
 
 P T = 2.5-10~ 4 p, 
 
 or at a pressure of 2 mm Hg, P r = 5-lQ- 4 . If r = 6-10- 7 (cf. Stark 2 
 for work with helium) this value should be increased by a factor of 60. 
 
 ARCS BELOW THE IONIZATION POTENTIAL 
 
 It is a well-known observation that arcs in vapors may be struck 
 when the applied potential is only slightly greater than the resonance 
 potential. We shall show that the computed value of P r is sufficient to 
 explain this phenomenon. If P r represents the fractional number of 
 excited atoms at any instant and n the number of electrons emitted 
 per -second by the cathode in the absence of ionization, the number of 
 electronic collisions per second in the shaded space of Figure 28, which 
 occur with excited atoms, is nP r . If V > (V t V r ), these collisions 
 result in the production of nP T ions per second. 
 
 The ionization of an atom increases the current in two ways, first by 
 releasing an electron and second by creating a slowly moving positive 
 ion and thus neutralizing a part of the negative space charge which 
 limits the thermionic emission. The positive ion remains in the field 
 4 V3680 M times as long as an electron, where M is the atomic weight 
 of the atom-ion. One ion accordingly neutralizes the effect on the space 
 charge of 4 V3680 M electrons. This permits the emission of more 
 electrons from the cathode, some of which in turn collide with excited 
 atoms, produce more ions and release more electrons. Compton shows 
 that under these conditions the total number n' of electrons leaving the 
 cathode per second is 
 
 n' = J 1 , (104) 
 
 1 - 4 \/3680 M P r 
 
 where P r as before is the fractional number of atoms which at any 
 instant are excited by the radiation produced by an emission of n elec- 
 trons per second, that is, in the absence of any cumulative ionization. 
 As P r is increased, the ratio n'/n increases more and more rapidly, 
 becoming infinite at P r = 1/4 A/3680 M were the emission not limited 
 physically by the value corresponding to the saturation thermionic 
 current at the temperature of the cathode. With mercury such a 
 condition is reached when P r = 2.91 10" 4 , whereas our computed value 
 
 2 Ann. Physik, 49, p. 731 (1916). 
 
154 ORIGIN OF SPECTRA 
 
 of P T at 2 mm pressure was nearly double this. The value P r = 5- 10" 4 
 was computed, however, with very favorable assumptions. If P r is 
 only 2.9 -10- 4 we find by Equation (104) that n'/n = 1000. Observed 
 values range roughly from 2 to 100. The observed rapid increase in 
 current just before the arc strikes is accordingly amply explained by 
 cumulative ionization of the photo-impact type. 
 
 This rapid increase in ionization and resulting production of ions 
 thus neutralizes the space charge, and as the electron emission is limited 
 by its saturation value, finally develops a positive space charge. When 
 the space charge becomes positive, the potential drop is concentrated 
 at the cathode so that the electrons attain their critical speed within a 
 short distance from the cathode. This concentration of the region of 
 effective impacts tends further to increase the probability of cumulative 
 ionization. At the same time the temperature of the cathode is raised 
 by the bombardment of the positive ions 3 which again increases n and 
 P r . We now have a condition of instability: the arc strikes, and the 
 complete arc spectrum of the vapor may be produced below the ioniza 
 tion potential, at a potential V = V t V r . 
 
 On account of the concentration of the potential gradient near the 
 cathode as soon as a large number of ions are formed, electrons more 
 nearly attain the full velocity of the impressed field before the first 
 collisions with atoms occur. Somewhat the same distribution of po- 
 tential is produced as that obtained in a more controllable manner by 
 the use of an auxiliary electrode, as shown in Figure 22. Hence as the 
 applied voltage is increased to V* corresponding to 1 for the alkali 
 earths, enhanced lines may appear. The favorable condition for excita- 
 tion of enhanced lines in a two electrode arc is high current density. 
 The high current involves a large number of ions which neutralize the 
 negative space charge and increase the potential gradient at the cathode. 
 This well-known method for exciting enhanced lines has led to some 
 misapprehension as to their origin. Many investigators have con- 
 sidered the purely incidental effect of high current to be the prime factor 
 in the physical process of the excitation. 
 
 IONIZATION BY SUCCESSIVE PHOTO-ELECTRIC ACTION 
 
 The mathematical analysis of this process is so involved that the 
 results are not readily interpreted. However, there is no doubt from 
 the experimental standpoint that the phenomenon is of importance. 
 We may have several absorptions of radiation followed by an electronic 
 
 3 The beginner usually burns up the cathode and an ammeter at this stage. 
 
CUMULATIVE IONIZATION 155 
 
 impact which completes the ionization process, or without any electronic 
 impact whatever most of the arc lines may be produced, under proper 
 experimental conditions, showing that the valence electron may be 
 driven to a remote outer orbit if not completely ejected. 
 
 A notable example of the latter process is the experiment of Fucht- 
 bauer 4 who observed the emission of the mercury arc lines as a result 
 solely of the absorption of radiation. This was considered in detail in 
 Chapter IV, the last half of which is intimately concerned with the 
 experimental verifications of this theory of successive photo-electric 
 action. In the case of sodium, for example, the atom absorbs a quantum 
 of D-radiation resulting in the ejection of a valence electron to the 2 p 
 orbit. Before the time interval r elapses, a second quantum may be 
 absorbed. This may have a frequency corresponding to any term in 
 any series converging at 2 p. For example it may be the first term of the 
 first subordinate series 2 p 3 d, in which case the valence electron is 
 ejected to the 3 d orbit, et cetera. At any stage in this process of absorp- 
 tion, in an arc, an electronic impact may occur, assisting in the process 
 of the ejection of the valence electron. 
 
 FURTHER CONCLUSIONS 
 
 We have noted above that an arc may be struck below the ionization 
 potential if the applied voltage V> (V t V r ). With mercury V t 
 V T = 10.3 4.9 = 5.4 volts. The phenomenon of absorption, how- 
 ever, under suitable experimental conditions, reduces this minimum 
 voltage to V r or 4.9 volts. The 4.9 volt impacts, indirectly through 
 the absorption of the resulting radiation, maintain a large number of 
 atoms with the valence electron in the 2 p 2 orbit. A 4.9 volt impact 
 with such an excited atom is capable of ejecting an electron to the 3 s 
 or 4 d orbits. The radiation subsequently resulting from this ejection 
 will maintain a proportion of excited atoms with electrons in these higher 
 energy levels. A collision of 4.9 volts with such atoms is more than 
 sufficient to ionize. Accordingly arcs may be struck at the lowest 
 resonance potential of the vapor. 
 
 A final observation is the well-known fact that arcs once struck will 
 continue to operate even when the applied voltage is less than the 
 resonance potential. The most important factor here, in addition to the 
 points brought out in the foregoing discussion, is the photo-electric effect 
 of the resonance radiation on the cathode. Van der Bijl 5 mentions that 
 
 4 Physik. Z., 21, pp. 635-8 (1920). 
 s Phys. R., 10, p. 546 (1917). 
 
156 ORIGIN OF SPECTRA 
 
 X 2537 of mercury should liberate photo-electrons from a calcium-coated 
 cathode with an initial velocity of 1.5 volts, so that an arc in mercury 
 once started, might be maintained at 4.9 1.5 = 3.4 volts. Radiation 
 of wave-length as short as X 1188 is present in the arc so that some 
 photo-electrons of still higher velocity are liberated. Still further, a 
 few high velocity electrons are emitted in accordance with the Max- 
 wellian distribution of velocities, as shown by Equation (86). And 
 finally the ions created, in falling into the cathode, may liberate electrons 
 of considerable speed. All of these factors must be considered in inter- 
 preting the action of certain rectifiers which may be operated at astonish- 
 ingly low voltages. In this case we have in addition the favorable fact 
 that the maximum voltage is greater than the measured root mean 
 square voltage. However, a discussion of rectifiers is beyond the scope 
 of this book. 
 
 The conclusion to be drawn from the foregoing considerations is that 
 the phenomenon of absorption of radiation plays an important role in 
 arc characteristics and emission of radiation. Cumulative ionization 
 of the photo-impact type becomes a controlling factor with high elec- 
 tronic emission and vapor pressure. It is possible that ionization by 
 successive impact is of some importance at very low pressure, but in 
 general, compared to the effect of absorption of radiation, its action is 
 insignificant. 
 
 This latter statement of course applies only to simple ionization. 
 Successive or multiple ionization is readily produced by successive impact 
 as shown in the appearance of the enhanced spectrum of magnesium at 
 14.97 volts (cf. discussion of Figure 23). The probability of multiple 
 ionization by successive impact depends upon the time of recombination 
 for the ion formed at the first impact. This time interval, which 
 corresponds to r, may be relatively very large, depending upon the 
 probability of a collision between an ion and an electron of small kinetic 
 energy. It should be accordingly a function of the design of any particu- 
 lar apparatus. Child 6 has made extensive experiments with a mercury 
 arc excited by a sixty cycle current. By examining the intensity of 
 the arc lines at various phases of the cycle he found that the minimum 
 intensity lagged behind the time of zero current and voltage by an 
 interval of 1/1800 second. Experiments of other observers also indicate 
 that we are here dealing with a time interval of an entirety different order 
 of magnitude than 10" 8 seconds, the value of r for a neutral atom. 
 
 Phys. R., 9, pp. 1-14 (1917). 
 
Chapter VII 
 Thermal Excitation 
 
 THERMODYNAMIC CONSIDERATIONS 
 
 The absolute entropy of a mol of perfect gas is given by the following 
 formula: 
 
 S = | R InT - R Inp + f R InM + Si, (105) 
 
 where M is the molecular weight, R = 1.985 cal. deg' 1 , p throughout 
 this chapter except where otherwise noted, the pressure expressed in 
 atmospheres, T the absolute temperature, and S\ = 3.2 cal. deg~ l . 
 Evidence for the value of S\ and its constancy with various mona- 
 tomic gases has been discussed by Tolman 1 and others. 
 
 It has been recognized for some time in mathematical treatments 
 of thermionic emission, thermoelectricity, contact potential, etc., that 
 electrons may be considered as a gas, the laws of which they obey in 
 detail, one example being the Maxwellian distribution of velocities. 
 The pressure of this gas in any laboratory experiment is exceedingly 
 small, of the maximum order of magnitude 10" 8 atmospheres, so that 
 considering an electronic atmosphere as a perfect gas should be open to 
 no objection. 
 
 From data on the thermionic emission of tungsten, tantalum and 
 molybdenum, and measurements of the cooling of the filament, due to 
 the latent heat of vaporization of the electrons, Tolman 2 shows that 
 the entropy of electron gas is given by Equation (105) where S\ has 
 the same value as for a perfect monatomic gas. The value of M for 
 electrons is of course expressed on the scale M = 1.008 for the hydro- 
 gen atom, whence M e = 5.46- 10~ 4 . 
 
 
 1 J. Am. Chem. Soc., 42, pp. 1185-93 (1920). 
 
 2 J. Am. Chem. Soc., 43, pp. 1592-1601 (1921). 
 
 157 
 
158 ORIGIN OF SPECTRA 
 
 Accordingly if it is possible to determine the absolute entropy of 
 both gases and electrons by Equation (105), we may predict from 
 thermodynamic considerations the extent to which a reaction such as 
 ionization may proceed at any desired temperature. Tolman's 3 deriva- 
 tion of the react ion-isochore is given in the following paragraphs. 
 
 Consider a reversible reaction of the type 
 
 Ca = Ca+ + E- - J, (106) 
 
 where Ca, Ca + and E~ are respectively gram mols of neutral calcium 
 atoms, simply charged positive calcium ions, and electrons, and J is the 
 work, expressed in calories, required to ionize one mol of calcium atoms. 
 If / is the value of the faraday. V t the ionization potential in volts, and 
 j = 4.183, the mechanical equivalent for converting joules to calories, 
 we have 
 
 ,. 23070 v> 
 
 This is simply a more direct method of deriving Equation (69) . 
 
 The heat AH of the reaction at constant pressure and at temperature 
 Tis: 
 
 (108) 
 
 The quantity J is accordingly the increase in heat content of the system 
 at the absolute zero and f RT the value of Ac P T where c p is the specific 
 heat of a perfect gas at constant pressure. 
 
 The change in entropy of the system when the reaction occurs at 
 constant temperature, obtained directly from Equation (105), is: 
 
 AS = | RlnT + f RlnM e + Si, (109) 
 
 in which we have neglected the slight difference between the molecular 
 weights of the ionized and the neutral atom. 
 
 We have the following fundamental, definitory equation of ther- 
 modynamics 4 connecting free energy with heat content and entropy: 
 
 AF = AH - TAS. (110) 
 
 Introducing the values of AH and AS from Equations (108) and (109) 
 we obtain 
 
 AF = J - | RTlnT + (f R - %RlnM e - Si) T. (Ill) 
 
 3 J. Am. Chem. Soc., 43, pp. 1630-2 (1921). 
 
 4 This is a generally accepted definition among physical chemists. 
 

 THERMAL EXCITATION 159 
 
 The equilibrium constant K P by definition takes the following form 
 for a reaction of the type given by Equation (106) 
 
 ..''/: K r = ,, : ' (112) 
 
 where p + , p~, and p denote respectively the partial pressures in the 
 equilibrium state of the ions, the electrons and the neutral atoms. 
 
 Now for any reaction there is a perfectly definite relation expressed 
 by Equation (113), between the change in free energy and the equilib- 
 rium constant. The derivation of this relation, which is familiar to 
 chemists, consists simply in the manipulation of thermodynamic equa- 
 tions, and can be found in text books on physical chemistry. 
 
 AF = - RTlnK p . (113) 
 
 Substituting the value of AF from Equation (111) we obtain: 
 
 (114) 
 
 On changing to common logarithms, expressing J in terms of V i} and 
 substituting the other numerical magnitudes mentioned above, we find, 
 
 7i+ . n ^0^0 V 
 
 log K p = log E-j- = - 25LL< + 2.5 log T - 6.69. (115) 
 
 This is the reaction-isochore by which we may compute the degree of 
 ionization of any monatomic vapor as a function of the temperature. 
 If x represents the fractional number of the atoms which are ionized, 
 we may write 
 
 T -' + 2.5 % T 7 - 6.69, (116) 
 
 rhere P is the total pressure, i.e. P p + + P" + P 
 
 SIMPLE IONIZATION 
 
 Sana 5 has employed this equation to compute the degree of ionization 
 various elements at high temperatures. As a particular example we 
 give in Table XXVI his computations for calcium for which the ioniza- 
 tion potential is 6.1 volts. The degree of ionization is expressed in 
 percentage, pressure in atmospheres, and temperature in degrees abso- 
 lute. 
 
 * Proc. Roy. Soc., 99, pp. 135-53 (1921). 
 
160 
 
 ORIGIN OF SPECTRA 
 
 TABLE XXVI 
 THERMAL IONIZATION OF CALCIUM EXPRESSED IN PERCENTAGE 
 
 Pressure 
 
 
 
 
 
 
 
 j 
 
 ^~ -_^ 
 
 10 
 
 1 
 
 10- 1 
 
 lO- 2 
 
 lO- 3 
 
 io-< 
 
 io- 
 
 10~ 8 
 
 Temperature 
 
 
 
 
 
 
 
 
 
 2000 
 
 
 
 
 
 5-10- 4 
 
 1.4-10- 3 
 
 
 
 2500 
 
 
 
 
 
 2-10- 2 
 
 7-10- 2 
 
 
 
 3000 
 
 
 
 
 
 3-10- 1 
 
 1 
 
 9 
 
 
 4000 
 
 
 
 
 2.8 
 
 9 
 
 26 
 
 93 
 
 
 5000 
 
 
 2 
 
 6 
 
 20 
 
 55 
 
 90 
 
 
 
 6000 
 
 2 
 
 8 
 
 26 
 
 64 
 
 93 
 
 99 
 
 
 
 7000 
 
 7 
 
 23 
 
 68 
 
 91 
 
 99 
 
 
 7500 
 
 11 
 
 34 
 
 75 
 
 96 
 
 
 
 8000 
 
 16 
 
 46 
 
 84 
 
 98 
 
 
 9000 
 
 29 
 
 70 
 
 95 
 
 
 10000 
 
 46 
 
 85 
 
 98 
 
 
 11000 
 
 63 
 
 93 
 
 
 12000 
 
 76 
 
 96 
 
 Complete lonization 
 
 13000 
 
 84 
 
 98 
 
 
 14000 
 
 90 
 
 
 As is evident from Equation (116), the percentage ionization increases 
 with (1) increasing temperature, (2) decreasing pressure, and (3) decreas- 
 ing ionization potential. Calcium has a medium low ionization po- 
 tential. It is therefore interesting to contrast the figures of Table 
 XXVI with those of Table XXVII for atomic hydrogen which has an 
 ionization potential of 13.5 volts. At the temperatures given, the 
 dissociation H 2 > 2 H can be readily shown to be complete, so that we 
 do not need to consider the molecule. 
 
THERMAL EXCITATION 
 
 161 
 
 TABLE XXVII 
 THERMAL IONIZATION OF HYDROGEN EXPRESSED IN PERCENTAGE 
 
 Pressure 
 Temperature 
 
 1 
 
 10- 1 
 
 1C- 2 
 
 ID' 3 
 
 10- 4 
 
 io- 5 
 
 7000 
 
 
 
 
 1 
 
 4 
 
 12 
 
 8000 
 
 
 
 2 
 
 5 
 
 18 
 
 50 
 
 9000 
 
 
 2 
 
 6 
 
 20 
 
 63 
 
 90 
 
 10000 
 
 2 
 
 6 
 
 17 
 
 49 
 
 87 
 
 99 
 
 12000 
 
 9 
 
 28 
 
 68 
 
 94 
 
 
 
 14000 
 
 27 
 
 65 
 
 93 
 
 
 
 16000 
 
 55 
 
 90 
 
 
 
 18000 
 
 80 
 
 97 
 
 
 20000 
 
 92 
 
 Complete lonization 
 
 22000 
 
 97 
 
 
 It is thus seen that very much greater temperatures are required 
 to produce the same degree of thermal ionization in hydrogen than in 
 calcium vapor on account of the higher ionization potential of the former. 
 Caesium, which has the lowest ionization potential of all the elements so 
 far measured, should be completely ionized at about 4000 and 1Q- 4 
 atmospheres, while about 20,000 at the same pressure should be neces- 
 sary for helium, which has the highest known ionization potential. 
 
 DOUBLE IONIZATION 
 
 The analysis for the simple ionization of atoms by thermal excitation 
 lay be extended so that the fractional number of atoms which are 
 mbly ionized may be computed. Using calcium as an example, we 
 ive the reactions: 
 
 Ca = Ca+ + E-- VJ/j > 
 Ca+ = Ca++ + E-- V?ffj\ 
 
 (117) 
 
162 ORIGIN OF SPECTRA 
 
 Here F* corresponds to the work required to remove the second electron 
 from the atom after the first has been ejected. As discussed in the latter 
 part of Chapter V, this is determined by the wave number 1 @ for metals 
 of Group II (cf. Table XX). Its value is 54.2 volts for helium. The 
 spectroscopic relations are unknown for metals of Group I, but probably 
 the voltages should correspond to x-ray limits rather than to highest 
 convergence frequencies of the enhanced spectra, as shown in column 7 
 of Table XXII. Nothing is known of the values of V t * for other ele- 
 ments. 
 
 If x and y represent the fractional number of Ca atoms which are, 
 respectively, simply and doubly ionized, it may be shown that 
 
 x (x + 2 y) P 50507, ,* ogy , R o 
 
 ** = 6 ' 59 ' 
 
 If we confine our attention to the temperature and pressure ranges 
 where the proportion of neutral Ca atoms is very small, we may put, 
 approximately, x + y ! Equation (119), which then alone need be 
 considered, takes the form: 
 
 Since V* is always considerably greater than V t it will necessarily 
 require a much higher temperature to produce the same degree of double 
 ionization as of simple ionization. For example with helium at 10" 4 
 atmospheres but 77% of the atoms will be doubly ionized at 30,000 
 while simple ionization is practically complete at 20,000. Table 
 XXVIII gives the temperatures at which several elements will be simply 
 and doubly ionized to the extent of 50%. By means of the above 
 equations one will readily find that if 50% of the atoms are just simply 
 ionized, practically none will be doubly ionized (0.1% and less) and the 
 remaining 50% will be normal. Similarly if 50% are doubly ionized, 
 the other 50% will be simply ionized with practically no neutral atoms 
 present. The temperatures here given are comparatively high. If 
 lower pressures had been selected, the temperatures would have been 
 very much lower, as indicated in the table by the large temperature 
 change from a pressure of 1 to 0.01 atmosphere. 
 
THERMAL EXCITATION 
 
 163 
 
 TABLE XXVIII 
 SIMPLE AND DOUBLE THERMAL IONIZATION 
 
 Element 
 
 50% simply ionized 
 Practically 50% normal 
 
 50% doublv ionized 
 Practically 50% 
 simply ionized 
 
 98% doubly ionized 
 
 
 Li.. . . 
 
 P = 1 
 
 P = 0.01 
 
 P = 1 
 
 P = 0.01 
 
 P = 1 
 
 P = 0.01 
 
 7800 abs 
 7500 
 6600 
 10300 
 6300 
 10100 
 6000 
 11000 
 16000 
 10200 
 8600 
 12000 
 8100 
 11600 
 7500 
 13000 
 
 5300 abs 
 5100 
 4400 
 7100 
 4300 
 7000 
 4100 
 7800 
 11500 
 7100 
 5900 
 8400 
 5500 
 8100 
 5200 
 9200 
 
 18000 
 15000 
 21000 
 14000 
 20000 
 13000 
 23000 
 
 13000 
 10700 
 15300 
 10000 
 14700 
 9200 
 16500 
 
 26500 
 22000 
 30500 
 21000 
 29500 
 20500 
 33000 
 
 17000 
 14000 
 20000 
 13500 
 19000 
 12500 
 22000 
 
 Na ...... 
 K 
 
 Cu 
 Rb 
 Ae. . 
 
 Cs 
 Au 
 H 
 Mg 
 Ca 
 
 Zn 
 
 Sr 
 
 Cd 
 Ba 
 
 Hg 
 
 
 THERMAL EXCITATION WITHOUT IONIZATION 
 
 The fact that we have been able to derive from thermodynamic con- 
 siderations certain quantitative data in regard to thermal ionization, 
 which, as will be apparent later, seem to interpret satisfactorily phe- 
 nomena heretofore very puzzling, does not of course argue that heat in 
 itself drives an electron out of the vapor atom. All that the thermo- 
 dynamic treatment has done is simply to give a statistical survey of 
 the actual state at any temperature without the introduction of any 
 postulates as to how the ionization is produced physically. Since at any 
 high temperature free electrons are admittedly present in the vapor, it is 
 likely that the ionization is accomplished in part by collision with these 
 electrons, the speed of which, and hence the number capable of ionizing, 
 increases rapidly, with the temperature. Also cumulative ionization 
 involving absorption of radiation must play an important role at high 
 pressure, as discussed in Chapter VI. Howbeit, it is of interest to con- 
 
164 ORIGIN OF SPECTRA 
 
 sider in the above statistical manner this indirect effect of tem- 
 perature on the excitation of atoms without ionization. For example, 
 let No,' represent a sodium atom in which the valence electron is in the 
 2 p instead of the normal 1 s orbit. For a mol of the vapor we have the 
 reversible reaction: 
 
 Na = Na' _ j n (121) 
 
 where J r = fV r /j, the quantity V r being the resonance potential ex- 
 pressed in volts. Since both the normal and the excited atoms are 
 assumed to act as perfect gases, there is no change in volume or pressure 
 and no external work is done. Accordingly 6 instead of Equations (108) 
 and (109) we have: 
 
 Atf = J r , (122) 
 
 AS = 0. (123) 
 
 Substituting these values in Equation (110) we obtain: 
 
 AF = J r (124) 
 
 and from (113) it follows that 
 
 J r = - RTlnK p = - RTln^ , (125) 
 
 where p f and p denote respectively the partial pressures of the excited 
 and normal atoms. If we confine our attention to such a temperature 
 range that p' is small compared to p we may consider p to be approxi- 
 mately the total pressure and p'/p the fractional number of excited 
 atoms, whence, 
 
 PL = e-w, (126) 
 
 p 
 or 
 
 N' = Ne- J S RT , (127) 
 
 where N is the total number of atoms, of which N f are excited, the 
 latter having an increase in energy of J r calories per mol of excited 
 atoms. 7 
 
 As an example we shall apply Equation (126) to sodium. Since V r 
 = 2.1 volts we find 
 
 pf 24400 
 
 = e T for sodium. 
 p 
 
 Table XXIX gives the fractional number of atoms, computed from 
 this formula, which have an electron in the 2 p orbit. 
 
 e This method of derivation was suggested by Tolman. 
 
 7 An expression equivalent to this results directly from probability considerations. See 
 any treatise on quantum theory, for example, Tolman, Optical Soc. Am. and R". S. I., May 
 
 (1922). 
 
 
THERMAL EXCITATION 165 
 
 TABLE XXIX 
 
 THERMAL EXCITATION OF SODIUM 
 
 
 Fractional number of 
 
 Temperature 
 
 atoms with electron 
 
 
 in 2 p orbit 
 
 800 abs 
 
 5-10- 14 
 
 1000 
 
 2-10- 11 
 
 1500 
 
 i-io- 7 
 
 2000 
 
 5-10- 6 
 
 3000 
 
 3-10- 4 
 
 A similar table might be computed for an orbit of greater energy level 
 illustrated by Figure 5, for example for 2 s , or 3 d, in which case we 
 should find a higher temperature necessary to maintain the same con- 
 centration of excited atoms. 
 
 FLAME SPECTRA 
 
 If a metal is vaporized in a bunsen flame, an emission spectrum is 
 produced. Usually this consists of the first pair 1 s 2 p of the princi- 
 pal series for the alkalis and 1 S 2 p 2 and sometimes 1 S 2 P f or 
 the metals of Group II. Observations on the alkalis are a matter of 
 common experience. The slightest trace of sodium vapor in the bunsen 
 gives rise to the D-lines. Using a very simple device of McLennan 
 and Thomson 8 in which a small furnace surrounding the bunsen main- 
 tains the heat necessary to vaporize the metal at a slow and constant 
 rate, the flame spectra of the elements of Group II are readily observed, 
 as indicated by F in the last column of Table XVI. 
 
 In general we may conclude that the fundamentally important 
 lines, from the standpoint of atomic theory, are those which appear in 
 the low temperature flame. These same lines determine the values of 
 the resonance potentials, as discussed in Chapter III. They appear in 
 the arc below ionization, as shown in Figures 23 and 24. They are 
 prominent absorption lines of the normal vapor and are readily reversed, 
 as shown in Figures 14 and 15. They are the "long" lines and the 
 "raies ultimes" as discussed in the latter part of Chapter V. They are 
 the result of the ejection of an electron to an orbit of next higher energy 
 level than the normal state of the unexcited atom. 
 
 Proc. Roy. Soc., 92, pp. 584-90 (1916). 
 
 
166 ORIGIN OF SPECTRA 
 
 These lines by no means appear in the flame because they normally 
 are the most intense lines of the arc spectrum and hence by contrast 
 only seem to be excited alone. In fact usually they are not the bright 
 lines of the arc ; especially is this true of the metals of Group II. Further- 
 more one may photograph a low temperature sodium flame until the 
 plate is " burned up" at the D-line and only a slight trace of other lines 
 can be detected. We may conclude that in general the ratio of intensi- 
 ties of these fundamental lines to other lines is extraordinarily high in 
 the flame. We have in the bunsen another method of producing single- 
 line or two-line spectra. 
 
 When a salt is injected in the flame we obtain again the simple single- 
 line spectrum of the metal, as shown in Figure 28 A, prepared by Meggers. 
 Under certain conditions, however, other lines appear faintly, for example 
 lines of the subordinate series. This is readily explained by the fact 
 that dissociation of the salt, such as NaCl, by the flame, gives rise to 
 Na + and Cl~. If the sodium ion captures an electron, it is thereby 
 able to emit any line of the arc spectrum. Zahn 9 estimates that each 
 sodium atom in a bunsen flame fed with NaCl emits on the average 
 2000 quanta of D-radiation per second. It is readily believable with 
 the minute partial pressures of sodium or chlorine in a flame (order of 
 magnitude 10" 6 mm Hg and less) that the probability of a sodium atom 
 capturing a chlorine atom and forming NaCl to be again dissociated is 
 comparatively small. In other words the number of times a reaction 
 of the form 
 
 occurs, which may involve a subsequent reaction 
 
 Na + + E- = Na, 
 
 and the emission of all arc lines is small compared to the number of 
 times the reversible reaction 
 
 Na'-+Na 
 
 takes place with the emission of the D-lines. Hence while the dis- 
 sociation of NaCl does give rise to all arc lines, the formation of Na', 
 having the short life T 10~ 8 seconds (page 93) is so much more 
 frequent that the intensity of these fundamental lines is extraordinarily 
 high relative to the other arc lines. The main service of the salt is 
 accordingly in furnishing a carrier for the metal and the immediate 
 spectroscopic consequence of the dissociation is incidental. 
 
 Verb. Physik. Ges., 15, pp. 1203-14 (1913). 
 
THERMAL EXCITATION 
 
 167 
 
 Again emphasizing that temperature in itself may not be the cause 
 of the excitation of a neutral atom but rather is the source of some other 
 direct cause, such as high electronic velocities, let us apply the foregoing 
 statistical reasoning to the emission of light from a bunsen. 
 
 Zahn observed that when 6.9-10 13 sodium atoms per sec. were fed 
 into a bunsen having a flame propagation of 510 cm/sec., a rate of emis- 
 sion of D-radiation resulted, amounting to 10 2 ergs/sec, cm 2 , as shown 
 by photometric measurements. He states that the bright flame was 
 3 cm long but does not give its radius. We shall assume the flame to be 
 a cylinder 1 cm in diameter. Using the above figure for the rate of 
 emission, we accordingly find that the total emission of the flame is 10 14 
 quanta/sec., which is Zahn's experimental value expressed in other units. 
 
 The volume of the flame is 2 cm 3 . Hence 
 
 number of Na atoms /cm? = 
 
 6.9 -IP 13 
 2-510 
 
 7 10 10 at any instant. 
 
 Let us consider the temperature 10 of the flame as 2000 abs. Referring 
 to Table XXIX we find that the fractional number of atoms in the 
 2 p state at 2000 is 5-10~ 6 . 
 Whence 
 
 No. excited atoms/ cm? = 5 - 1Q- 6 - 7 10 10 = 3.5 -10 5 
 and 
 
 total no. excited atoms (2 cm?) = 7 1C 5 at any instant. 
 
 The average duration of life of an excited atom, as discussed in 
 Chapters IV and VI, is r = 10~ 8 seconds. Accordingly the number of 
 excited atoms formed per second is 7-10 5 -f- 10~ 8 = 7-10 13 = 10 14 . This 
 is equivalent to the number which pass into the normal state each 
 second so that a total of 10 14 quanta per second of D-radiation are 
 produced within the flame. Let us see how many of these escape. 
 
 At atmospheric pressure the number of atoms per cm 3 is 2.7 -10 19 . 
 Accordingly the partial pressure (p mm) of the sodium atoms is 
 
 7-10 10 -760 
 P = 2.7- 10" = mm g ' 
 
 Let us assume that at any instant the quanta of radiation are uni- 
 formly distributed throughout the cylindrical volume. The quanta 
 which escape will be those which pass through this volume to the outside 
 boundaries without colliding with an atom. We shall assume that all 
 
 recognize the academic question here involved, but these computations are suffi- 
 itly inexact to permit the assignment of " temperature" to a state not in statistical equilib- 
 
168 ORIGIN OF SPECTRA 
 
 directions of propagation of the quanta are equally probable. Pro- 
 ceeding in a manner somewhat similar to that discussed in Chapter VI, 
 Dr. K. T. Compton very kindly derived the following expression for the 
 authors, giving approximately the fractional number of the quanta 
 which escape. 
 
 Fraction = 
 
 In this formula X is the. mean free path of a quantum at the pressure p, 
 as defined in Chapter VI, a is the radius of the cylindrical flame, and 
 h its height. 
 
 In the discussion following Equation (99) we show that the mean 
 free path of a quantum is p/p where p is an absorption constant and p 
 is the pressure in mm Hg. Using Wood's value of p determined for 
 mercury, we obtain for the mean free path X = (0.0007/p) cm. The 
 value of p is probably of the same order oi magnitude for the sodium and 
 mercury resonance lines. Hence with the present data we have X = 
 7-10~ 4 -T- 2-10~ 6 = 300 cm for the mean free path of the quantum of 
 D-radiation in this particular bunsen flame. The values of h and a 
 are 3 cm and 0.5 cm respectively. Since X is large compared to h or a, 
 the above formula reduces to 
 
 Fractional number escaping = 1 - ^- 
 
 A O A 
 
 On substituting the values for these constants we find that 299/300 
 of the quanta produced in the flame are actually emitted. In con- 
 tradistinction to arc phenomena discussed in the chapter on cumulative 
 ionization, absorption is of very slight importance in flame spectra on 
 account of the low partial pressure of the metal vapor. Accordingly we 
 conclude that the bunsen flame of the type described should emit 10 14 
 quanta/sec. The observed value was also 10 14 quanta/sec, in complete 
 agreement with theory. 
 
 Zahn has also made observations on the lithium flame. His data 
 show that under specified conditions the total emission of the flame 
 amounted to 10 15 quanta/sec, for the red lithium line. The value com- 
 puted theoretically in the manner illustrated above is 10 16 quanta/sec., in 
 satisfactory agreeement considering the assumptions involved. 
 
 If the temperature of a flame is increased by the addition of oxygen, 
 other lines are readily excited. Many lines of the principal and sub- 
 ordinate series of sodium, if not the complete arc spectrum, appear in the 
 
THERMAL EXCITATION 169 
 
 oxy-acetylene burner fed with sodium or its salts, and the same phenome- 
 non occurs with other elements. As the temperature is increased, the 
 valence electrons are driven to successively higher energy levels, ulti- 
 mately giving rise to the state of ionization. We may therefore correlate 
 spectral lines with temperature, whether or not this be the direct cause 
 for their production. 
 
 SPECTRAL LINES CORRELATED WITH TEMPERATURE 
 
 If a metal vapor is gradually heated in a furnace we observe first the 
 emission of a fundamental line of the type 1 s 2 p or 1 S 2 p%. 
 This is also true when the vapor of a metallic salt is heated. We have 
 found that the D-lines produced when NaCl is raised to 1000 C in 
 vacuo are quite brilliant. Higher stages of temperature excitation 
 progress through furnace spectra, which have been investigated by 
 King 11 from 2000 to 3000 abs, spectra in the carbon arc at 3900, 
 chromospheric spectra at possibly 6000, photospheric spectra at possi- 
 bly 7000, spark spectra, to stellar spectra at temperatures ranging up 
 to 30,000. Of course the correlation of arc and spark spectra with 
 temperature is complicated by the superposed electrical excitation. 
 As discussed in Chapter V, spark lines may be excited at very low 
 temperatures, with a proper arrangement for producing high electronic 
 velocities by electrical means. Hence our present classification must 
 be considered as very qualitative. 
 
 Accordingly as the temperature of calcium vapor, for example, is 
 increased, we should first have no emission, but rather absorption of 
 fundamental lines belonging to the series IS mp 2 and 1 S mP. 
 On further increase in temperature the line 1 S 2 p 2 , X 6573, should 
 appear in emission and when the temperature is sufficient to maintain 
 a fair proportion of electrons in the 2 p 2 orbit, lines of the subordinate 
 series should show absorption. Gradually the line 1 S 2 P, X 4227, 
 puts in its appearance as an emission line, and finally all arc lines are 
 excited when the thermal ionization becomes pronounced. If the 
 temperature is further increased until a fair proportion of the atoms 
 are simply ionized, the arc absorption and emission spectra fade, and 
 fundamental lines of the enhanced spectra such as 1 2 Si,2, 
 X 3968 and X 3933 appear both in absorption and emission. Later other 
 enhanced lines are excited, and if the process of heating is continued all 
 the atoms will be doubly ionized. When this state is reached, steps 
 
 11 Long series of papers in Astrophys. J. and Mt. Wilson Contrib. 
 
170 
 
 ORIGIN OF SPECTRA 
 
 begin toward triple ionization; the arc lines vanish and the ordinary 
 enhanced lines should eventually fade, giving place to enhanced spectra 
 of the ''second type." There is no sharp division line between the 
 various spectra. At any one temperature we may have spark lines 
 from ionized atoms and arc lines from neutral atoms. If, however, the 
 temperature is great enough to produce much double ionization it 
 may be readily shown as pointed out earlier, that most of the atoms 
 should be either simply or doubly ionized, with practically none in the 
 neutral state. Hence if we have present the enhanced spectrum of the 
 second type, all arc lines are absent. In other words but two types of 
 spectra may be present simultaneously. Unfortunately as yet we have 
 no knowledge of the higher types of enhanced lines, so that this deduc- 
 tion from theory cannot be verified. 
 
 If we select a fundamental arc line such as 1 S 2 P and a funda- 
 mental spark line such as 1 @ 2 ^ and observe the ratio of intensity 
 of the latter to the former, we should expect this ratio to increase with 
 the temperature. This is verified qualitatively by King's results with 
 furnace spectra and other data from the spectroscopic tables, as shown 
 in Table XXX. 
 
 TABLE XXX 
 RATIO OF INTENSITY OF 1 @ 2$ TO IS 2 P 
 
 Element 
 
 Flame 
 
 Furnace Abs. 
 
 Arc 
 3900 "* 
 
 Chromo- 
 sphere 
 6000 
 
 Photo- 
 sphere 
 7000 
 
 2000 
 
 2300 
 
 2600 
 
 Ca 
 
 
 
 
 
 .06 
 .03 
 .1 
 
 .05 
 .05 
 .1 
 
 .06 
 .06 
 .09 
 
 .8 
 .7 
 .8 
 
 4 
 20 
 20 
 
 40 
 
 7 
 4 
 
 Sr 
 
 Ba 
 
 
 SOLAR SPECTRA 
 
 As illustrated by Table XXVI the degree of ionization of an element 
 depends greatly upon the pressure as well as the temperature. Thus 
 the pressure differences existing in the sun may produce a wide variation 
 in the type of spectrum excited. Also the quantity of the element 
 present is of importance. Other things being equal we should expect 
 lines from elements present in relatively large amounts to be the more 
 prominent. If the element does not exist in the sun its spectrum will 
 
THERMAL EXCITATION 171 
 
 be absent. However, the failure to detect arc lines of caesium for 
 example is insufficient proof that the element is not present even in 
 considerable quantity. 
 
 In the following we shall review some of the recent developments 
 only in the roughest qualitative manner. For more detailed informa- 
 tion, all necessarily qualitative however, the papers of Saha, 1 - 2 Russell, 13 
 Milne 14 and others should be consulted. 
 
 The solar spectrum should be characterized by lines of elements in a 
 state corresponding to that at about 6000 to 7000, and 4000 for a sun- 
 spot. A considerable portion of the alkalis should be simply ionized, 
 especially at the higher levels, where the pressure is less. Although 
 much ionization is present, enhanced lines should not appear, for as 
 discussed in Chapter V, the alkalis, with their single valence electron 
 removed, are not in a condition to emit or absorb enhanced lines. This 
 requires a further expenditure of energy of such magnitude that at least 
 for sodium, potassium and lithium, for which the values are known, 
 temperatures of 7000 are insufficient. One may fairly definitely state 
 that enhanced lines of Na and K are absent in the sun. The arc spectra 
 of Li, Na, K and a trace of Rb are present, arising in the small percentage 
 of un-ionized atoms at solar temperatures. The failure to detect Cs 
 may be due to the fact that the element is absent or that it may be 
 nearly completely ionized and incapable of showing arc lines. The arc 
 lines of the alkalis are strengthened in the sun-spots on account of the 
 lower temperature and resulting lesser degree of ionization. 
 
 Table XXVI shows at 6000 a considerable proportion of ionized 
 calcium vapor and the same is true for magnesium, barium and stron- 
 tium. We find in the solar spectrum both arc and spark lines of these 
 elements although for barium many of the arc lines are absent or very 
 faint. The arc lines of Ca and Sr are strengthened in the sun-spofcs. 
 As zinc has a high ionization potential, spark lines are probably absent, 
 and the arc lines are weaker in the sun-spots. 
 
 The ionization potential of helium is so high that practically no 
 atoms are ionized. Hence we may now understand the experimental 
 fact that all enhanced lines of helium are absent. 
 
 Hydrogen also is not ionized except possibly at the very highest 
 levels of the chromosphere, and then scarcely appreciably. We should 
 expect to find all the lines of the Lyman series were it not for the absorp- 
 tion of the earth's atmosphere. A small proportion of the atoms have 
 
 " Phil. Mag., 40, pp. 472-88 (1920); 40, pp. 809-24 (1920). 
 is Astrophys. J., 55, pp. 119-44 (1922); 55, pp. 354-9 (1922). 
 " Observatory, 44, pp. 261-9 (1921). 
 
172 ORIGIN OF SPECTRA 
 
 electrons in the second orbit, sufficient to account for the reversal of 
 Balmer lines such as H a . 
 
 At great heights above the reversing layer, where the temperature 
 is still high but the pressure is extremely low, simple ionization of ele- 
 ments having a fairly low ionization potential will be practically com- 
 plete, as illustrated by Table XXVI. Accordingly while enhanced lines 
 may be emitted, the arc spectrum of many of the elements should be 
 absent in the high level chromosphere. Mitchell found from observa- 
 tion of the flash spectrum that the H and K enhanced lines of Ca ex- 
 tended to 14,000 km while the g arc line terminated at 5000 km. The 
 ionization potential of Sr is lower than that of Ca and complete ioniza- 
 tion will be produced at higher pressures or lower levels. The flash 
 spectrum shows that the arc lines of Sr disappear before those of Ca. 
 At pressures below 10" 3 atmosphere, Na is completely ionized; in the 
 chromosphere the D-lines reach only to 1200 km. The ionization 
 potential of magnesium is the highest of the alkali earths and the arc 
 lines are found at 7000 km. 
 
 Russell points out that the behavior of Sc, Ti, V, Fe, Mn, Cr, Co 
 and Ni in the spot spectrum is intermediate to that of Ca and Zn and 
 states, "It may be surmised that the ionization potentials for these 
 metals lie between 6 and 9 volts, as Saha has suggested without specify- 
 ing his reasons." 
 
 STELLAR SPECTRA 
 
 The temperatures of stars are usually measured by observing the 
 spectral distribution of their radiant energy, just as has been done with 
 our sun, and comparing this with the black-body distribution computed 
 by Planck's law. The temperature of a black body for which the rela- 
 tive spectral distribution most nearly fits a particular stellar distribution 
 curve is considered as the temperature of the star. Wilsing and 
 Scheiner 15 and others have made such observations through the visible 
 spectrum for a large number of stars, and Coblentz, 16 using a spectroradio- 
 metric method, has been able to extend the data from the ultra-violet 
 to the far infra-red. It is evident from what has been discussed in the 
 present chapter that a systematic correlation of the stellar spectra also 
 permits the assignment of temperatures. This will be considered more 
 fully in the following paragraphs, but to anticipate, we may state that 
 such computations agree fairly well with the temperatures determined 
 
 is Wilsing, Scheiner and Munch, Pub. Astrophys. Obs. Potsdam, Vol. 24, No. 74, 1920. 
 " Bur. Standards Sci. Paper No. 438. 
 
THERMAL EXCITATION 
 
 173 
 
 from the black-body distribution without reference to spectral lines. 
 This is illustrated by Table XXXI, in which the data of Saha were ob- 
 tained by the degree of ionization method. In general the P stars are 
 the hottest with a continuous decrease in temperature in the order P, 
 0, B, A, F, G, K, M, N to R. 
 
 TABLE XXXI 
 RANGE OF STELLAR TEMPERATURES 
 
 Stellar 
 Class 
 
 Typical Star 
 
 Wilsing & 
 Scheiner 
 and others 
 
 Coblentz 
 
 Saha 
 
 Remarks 
 
 Pb 
 
 Great Orion Nebula 
 
 15000 
 
 _ 
 
 __ 
 
 
 PC . 
 
 I. C. 4997 
 
 30000 
 
 
 
 Gaseous nebulae 
 
 Oa.... 
 
 B. D. +35, 4013.. 
 
 23000 
 
 
 23000 
 
 with bright lines 
 
 Ob 
 Bo 
 
 B. D. +35, 4001.. 
 c Orionis .... 
 
 20000 
 
 13000 
 
 22000 
 18000 
 
 Hereafter, all lines 
 are dark 
 
 B5 A 
 
 q Tauri. . . 
 
 14000 
 
 
 14000 
 
 
 Ao 
 ASF 
 
 a Canis Majoris .... 
 ft Trianguli ... 
 
 11000 
 9000 
 
 8000 
 
 12000 
 
 
 Fo 
 
 a. Carinae 
 
 7500 
 
 
 9000 
 
 
 F5A... 
 Go 
 
 a Canis Minor 
 a Aurigae 
 
 7200 
 7100 
 
 6000 
 6000 
 
 7000 
 
 The sun is a. dwarf 
 
 G5K 
 
 a. Reticuli 
 
 4500 
 
 
 
 star of this class 
 
 Ko 
 
 a Bootis 
 
 3700 
 
 4000 
 
 
 
 K5M 
 
 a Tauri 
 
 3500 
 
 3500 
 
 
 
 Ma 
 
 a Orionis 
 
 3000 
 
 3000 
 
 5000 
 
 
 Md. . . 
 
 Ceti 
 
 2950 
 
 
 4000 
 
 
 m 
 
 W 
 
 
 2300 
 
 
 
 
 , 
 
 Table XXXII, taken from Sana's paper, is a compilation of the 
 intensity of several typical lines appearing in stellar spectra. Lines 
 which are barely visible are assigned the numeral 1. The symbol 
 
174 
 
 ORIGIN OF SPECTRA 
 
 HH H 
 
 - 
 
 M CQ 
 
 n 
 
 IS 1 
 
 o 
 
 O 
 
 M 
 
 ^iSb 
 
 | | 
 
 1 1 1 1 
 
 b bC 
 
 I I 
 
THERMAL EXCITATION 175 
 
 denotes a line the intensity of which cannot be obtained from the Har- 
 vard Annals. An interrogation point (?) denotes that the intensity is 
 not stated in numbers in the Harvard Annals but is compiled from 
 scattered descriptions. The symbol M + denotes that the line is due to 
 the simply ionized atom of the element M. This table shows that the 
 lines of an element begin to appear at a certain stage, rise step by step 
 to a maximum and disappear at the other end of the scale. Thus 
 hydrogen X 4860, a line of the neutral atom, begins to appear in the 
 low temperature Ma stars, reaches a maximum in the hotter A group 
 and fades out as the temperature increases, finally vanishing at Oc 
 where the temperature is sufficient to ionize hydrogen completely. 
 In low temperature stars the arc spectrum of calcium is prominent. As 
 we progress to stars of higher temperature, spark lines appear, arising in 
 ionized atoms. Further increase in temperature increases the propor- 
 tion of doubly ionized atoms and initiates the process of triple ionization. 
 The arc lines vanish because neutral atoms are no longer present. Fi- 
 nally the spark lines fade out, giving place to enhanced lines of the 
 second type, the identification of which is yet to be made. A similar 
 development may be carried through for lines of other elements. 
 
 From a consideration of the degree of ionization of the elements, a 
 
 table may be prepared showing the characteristic spectra which may be 
 
 expected as the temperature increases. Saha has pointed out several 
 
 striking phenomena in this manner, which are briefly summarized in 
 
 f Table XXXIII. It is evident from this table that a star which shows 
 
 j lines of ionized helium, for example, must have a very high temperature. 
 
 The new field which Saha has opened appears to offer great possibilities 
 
 in the realm of astrophysics. At present however the subject is in only 
 
 the earliest stage of development, and as Russell states, it will require 
 
 , years of work to correlate systematically the numerous variables involved. 
 
176 
 
 ORIGIN OF SPECTRA 
 
 TABLE XXXIII 
 
 IMPORTANT STEPS IN THERMAL IONIZATION 
 
 Phenomena 
 
 Stellar 
 Class 
 
 Tempera- 
 ture 
 
 Remarks 
 
 Appearance of the K line 
 
 Me 
 
 4,000 K 
 
 Beginning of the ionization 
 of Ca 
 
 Disappearance of the g line 
 
 B8A 
 
 13,000 
 
 Ca completely ionized 
 
 Appearance of Mg + 4481 
 
 Go 
 
 7,000 
 
 Mg considerably ionized 
 
 Disappearance of the K line 
 Mg~*~ 4481 disappears 
 
 Oc 
 Oa 
 
 20,000 
 23,000 
 
 Ca + completely ionized 
 Mg"*~ completely ionized 
 
 Appearance of 4686 
 
 B2 A 
 
 17,000 
 
 He considerably ionized 
 
 Disappearance of 4471 
 
 Oa 
 
 24,000 
 
 He completely ionized 
 
 
 
 (10- 1 atm.) 
 
 
 Appearance of Balmer lines. 
 Appearance of He lines 
 
 Mb 
 Ao 
 
 4,500 
 12,000 
 
 Appearance of the 2-quan- 
 tum orbits of H 
 
 Appearance of 2-quantum 
 
 
 
 
 orbits of He 
 
 Maximum absorption of hydro- 
 gen lines 
 
 Ao 
 
 12,000 
 
 Maximum concentration of 
 2-quantum orbits of H 
 
 Maximum absorption of helium 
 lines 
 
 B2A 
 
 17,000 
 
 Maximum concentration of 
 2-quantum orbits of He 
 
 Disappearance of 4295 
 
 B8A 
 
 14,000 
 
 Sr + completely ionized 
 
 Disappearance of Balmer hydro- 
 gen lines 
 
 Ob 
 
 (10- 1 atm.) 
 22,000 
 
 H completely ionized 
 
 Disappearance of 4686 
 
 Pe 
 
 25,000- 
 
 He"*~ completely ionized 
 
 
 
 30,000 
 
 
176 A 
 
 Joel turn 
 
 Strontium 
 
 FIG 28A. Bunsen flame spectra. Swan spectrum, CO, 4314, 4737, 5165 A. 
 vapor, H 2 O, 3064 A. Li, 6708; Na, 5890, 5896; Ca, 4227; Sr, 4607 A. 
 in yellow and red due to CaO and SrO. 
 
 Water 
 Bands 
 
 A4800 
 
 FIG. 29. Emission spectrum of iodine. 
 
Chapter VIII 
 Thermochemical Relations 
 
 ELECTRON AFFINITY OF ATOMS 
 
 We have mentioned in the latter part of Chapter IV that excited 
 atoms may possess an electron affinity, tending to pick up an electron 
 and become negative ions. This is also true of many diatomic molecules 
 in the normal state, and on page 76 we showed that the Bohr hydrogen 
 molecule leads to a value of 1.6 volts for its electron affinity. That is, 
 work equivalent to 1.6 volts must be done on the negative molecular 
 ion to reduce it to the normal molecular state. 
 
 Certain normal atoms, particularly the halogens ; are known to 
 possess an attraction for electrons. An atom of a halogen gas has an 
 outer shell containing seven electrons. We have seen that there 
 is a general tendency for electrons to be grouped in pairs or octets, as 
 such a grouping represents a high degree of stability. The halogen 
 atom tends to pick up an extra electron, completing its outer shell of 
 eight. As a negative ion it resembles the stable rare gases in structure. 
 It is this tendency, for example, for the normal chlorine atom to complete 
 its outer shell, which enables it to attract the valence electron of sodium 
 and form the compound NaCl. If a chlorine atom captures an electron 
 and thus becomes a negative ion, work must be done on the ion to reduce 
 it to the neutral condition. This work may be expressed in volts per 
 atom or in calories per gram atom, the latter referring to the work 
 which must be done to reduce 1 gram atom of the gas (i.e. 6.06 X 10 23 
 negative atom-ions) to neutral atoms. 
 
 Franck 1 in a very suggestive paper has recently opened a new field 
 connecting electron affinity with spectroscopic phenomena. The 
 system neutral halogen atom and a stationary electron just outside the 
 atom represents the initial quantized state on the Bohr conception. The 
 final state is that of the atom-ion with its outer shell of eight electrons. 
 If the electron falls directly from the initial state of energy TF 4 to the 
 
 'Z. Physik, 5, pp. 428-32 (1921). 
 
 177 
 
178 ORIGIN OF SPECTRA 
 
 final state of energy W f the system loses an amount of energy W t W f . 
 This is assumed to be radiated as a single quantum of wave number V Q 
 so that W t W f = IICVQ. Since W t W f represents the work which 
 must be done upon the atom-ion to reduce it to a normal atom, the 
 radiated light of wave number V Q is -a direct measure of the electron 
 affinity E. The question as to whether intermediate quantized states 
 may exist between the initial and final configuration may be of little 
 importance. If intermediate states do exist they may not differ materi- 
 ally from the initial state since the field in the neighborhood of a neutral 
 atom must decrease with a high power of the distance. Hence we 
 should have a spectral series, the first line of which is nearly as short a 
 wave-length as its convergence. The entire series should lie in an 
 extremely narrow spectral region which for the present may be con- 
 sidered a single line. 
 
 This line of wave number v is emitted only in case an electron of 
 zero velocity is captured. However, the atom may attach to itself 
 an electron which initially is speeding toward it with a velocity v. Possi- 
 bly the range of initial velocities may not be large. An electron of 
 velocity greater than that corresponding to the electron affinity might 
 penetrate the atom and escape. If, however, for a small range of the 
 velocity v the atom captures the electron, the energy of the system will 
 be altered from W t + mv 2 , initial, to "FT/, final, and the resulting radia- 
 tion will be given by the equation : 
 
 hcv = W t - W f + 4- mv* = hcr + J mv*. (128) 
 
 Since the term ^ mv* may assume any value equal to or greater than 
 zero, with possibly certain restrictions above mentioned, the emitted 
 radiation is a continuous spectrum with a sharp limit on the long wave- 
 length side corresponding to v = 0, and with gradually decreasing 
 intensity toward the short wave-length side representing a decreasing 
 probability of the capture of high velocity electrons by the atoms. 
 
 Figure 29 shows a spectrogram, made by Steubing, 2 of the emission 
 spectrum of iodine. We find a region of bright continuous emission 
 sharply defined on the long wave-length side at X 4800 15. Higher 
 resolution showed that this was perfectly continuous and did not possess 
 structure characteristic of ordinary band spectra. The continuous 
 radiation was shown to be emitted by the atom rather than by the 
 molecule. This was indicated by certain tests in a magnetic field and 
 by the fact that it increased in intensity when the vapor was heated to a 
 
 ' Ann. Physik, 64, pp. 673-92 (1921). 
 
THERMOCHEMICAL RELATIONS 
 
 179 
 
 point where, at the pressure employed, the greater part of the iodine 
 must have been dissociated. 
 
 Using for V Q the wave number corresponding to the observed limit 
 X 4800, one computes for the electron affinity of iodine a value 2.57 volts 
 per atom or 59.2 kg. cal. per gram atom. This is in only fair agreement 
 with determinations by less precise means. Unfortunately in this new 
 field satisfactory spectroscopic data are not as yet available for other 
 elements. 
 
 In Table XXXIV is a summary of determinations of electron affinity 
 of several elements by the spectroscopic method just described and by 
 two other methods discussed in the following sections. 
 
 TABLE XXXIV 
 ELECTRON AFFINITY 
 
 Method 
 
 Spectroscopic 
 
 Grating Energy 
 
 lonization 
 
 Element 
 
 volts /atom 
 
 kg. cal. /g atom 
 
 volts /atom 
 
 kg.cal./gatom 
 
 volts /atom 
 
 kg.cal./gatom 
 
 ci-. 
 
 2.57 
 
 59.2 
 
 5.0 
 3.8 
 3.5 
 2.0 
 
 116 
 
 87 
 81 
 45 
 
 4.8 
 3.1 
 
 2.8 
 
 110 
 71 
 64 
 
 Br~ 
 
 I- 
 
 s-- 
 
 
 GRATING ENERGY, IONIZATION POTENTIAL AND ELECTRON AFFINITY 
 
 On the assumption that in addition to the ordinary Coulomb force 
 of repulsion or attraction between the charges on the ions forming the 
 crystal structure of certain salts, there exists between two ions a repul- 
 sive force, 3 the potential of which is inversely proportional to the nth 
 power of the distance apart, Born 4 has computed the grating energy 
 of various crystals. This is the amount of work U necessary to convert 
 1 mol of the crystal into free positive and negative ions, and its com- 
 putation is purely an electrostatic problem. The value of the exponent 
 n depends upon the form of the lattice space, as determined by x-ray 
 analysis, and upon other physical constants. For most of the alkali 
 halides n = 9. To discuss the assumptions here involved or to enter 
 into a consideration of the details of the problem is beyond the scope of 
 
 3 This force represents, as an approximation, the electrostatic fields due to the outer 
 electrons of the atoms. 
 
 Verb. Physik. Ges., 21, pp. 13-24 (1919); 21, pp. 679-85 (1919). 
 
180 ORIGIN OF SPECTRA 
 
 this book. Suffice to say that determinations of grating energies have 
 yielded results of the greatest importance in many fields of physics 
 and chemistry. We shall indicate here in the most elementary manner 
 how spectroscopy is involved, through electron affinity and ionization 
 potential, in grating energies. 
 
 Let us consider a salt of the form RX where R is an alkali and X a 
 halogen atom. All heat and work units are expressed in kg. cal. 
 Let 
 
 [ ] denote solid phase or crystalline state. 
 ( ) denote gaseous phase. 
 D = heat of dissociation of |- gram mol (1 gram atom) halogen gas 
 
 into monatomic gas. 
 S heat of sublimation at absolute zero of 1 gram mol metal or 
 
 salt. 
 Q = heat of formation of the salt from the elements in the ordinary 
 
 state. 
 
 J = Work in kg. cal. necessary to ionize 1 gram mol salt or metal. 
 E = Electron affinity of 1 gram atom halogen gas, expressed in 
 
 kg. cal. 
 E~ = 1 gm. mol of electron gas. 
 
 RX 
 (RX) U J R 
 
 l i ;. i 
 
 J RX (R)(Xr- -E x - -(XMRHe) 
 
 FIG. 30. Dissociation of the salt RX. 
 
 We shall consider the process in which the initial state contains 
 ionized vapor atoms or the metal and negatively charged vapor atoms 
 of the halogen gas, and in which the final state represents the solid 
 crystal. The difference in total energies for these two states referred 
 to a gram mol of the crystal is the grating energy U which Born com- 
 putes from purely electrostatic and geometric considerations of the space 
 grating. Physically the transition between the two states may be 
 made according to the two schemes shown in Figure 30. We shall 
 start with (R)+ (X)~ and go to the right. Traveling against the arrow, 
 
THERMOCHEMICAL RELATIONS 181 
 
 work must be done; with the arrow, the reaction gives out energy. 
 The first step requires an expenditure of the work E X) resulting in a 
 gram atom of neutral halogen atoms, positively charged metal atoms 
 and electrons. The electrons are allowed to combine with the ionized 
 metal atoms, giving up the energy J R , the ionization potential in heat 
 units, and producing a gram atom of monatomic halogen gas and a 
 gram atom of the metal gas. In the next step we allow the metal gas 
 to condense, giving up the heat of sublimation S R , and the halogen 
 atoms to combine into diatomic molecules, giving up the energy of dis- 
 sociation D x . The product is 1 mol solid metal and mol molecular 
 halogen gas. These now combine into the solid crystal, giving up the 
 heat of formation. Of course the reaction need not proceed in exactly 
 this order. The step involving Q RX is introduced because this is the 
 quantity the chemist measures in determining heats of formation. 
 
 Another method of transition between the initial and final states 
 is shown on the left of the figure. This probably more nearly represents 
 the true physical process. The positive metal ion and the negative 
 halogen ion react, forming the gas (RX) and give up the heat represented 
 by the ionization potential 5 of this molecular gas. The gas is then 
 condensed to the crystal state, during which process it gives up its heat 
 of sublimation. 
 
 From the above considerations we may write at once the following 
 thermochemical relations 
 
 U = J RX + S RX (129) 
 
 and U = - E x + J R + D x + S R + Q RX . (130) 
 
 Hence knowing the grating energy U and the heat of sublimation 
 of the salt, it is possible to compute the ionization potential of the salt 
 from Equation (129). Equation (130) gives a value of the electron 
 affinity, which as discussed above determines the long wave-length 
 limit of the continuous spectrum of the halogen. Eliminating U from 
 the two equations, we obtain an expression for the ionization potential 
 of the salt involving important physical and chemical constants. Un- 
 fortunately for the salts RX neither the ionization potentials nor the 
 heats of sublimation are known. It is doubtful if the former may be 
 determined at all by the ordinary methods of measurement. The 
 heated vapor appears to dissociate very readily with temperature alone, 
 
 6 Theoretically other types of ionization may exist as discussed later. In the example 
 under consideration, however, ionization of RX in the vapor state without doubt produces 
 dissociation as here assumed. For the present, if there be any question, we may consider 
 this to be a definition of J^. 
 
182 
 
 ORIGIN OF SPECTRA 
 
 completely masking any ionization by electronic impact. The chemical 
 data involved in Equation (130) are not known with a high degree of 
 accuracy, but it is of interest to compute the electron affinity of several 
 halogens, using what meager data exist. Equation (130) may be solved 
 directly for E x and the experimentally determined values substituted 
 for the various constants or we may obtain the same result by consider- 
 ing in Table XXXV each separate step in the reaction illustrated by 
 Figure 30. For the relation between volts/molecule and kg. calories/ 
 mol, refer to Equation (70). We shall first consider the salts KC1, 
 KBr and KI, all data being expressed in kg. calories/mol or gram atom. 
 
 TABLE XXXV 
 ELECTRON AFFINITY OF HALOGENS FROM GRATING ENERGIES 
 
 Reaction 
 
 Cl 
 
 Br 
 
 I 
 
 Remarks 
 
 [KX] = (K) + + (X)~ 
 
 - 163 
 
 - 155 
 
 - 144 
 
 Bern's grating energies. 
 
 [K] + * (X 2 ) = [KX] 
 
 + 106 
 
 + 99 
 
 + 87 
 
 Heat of formation: cf. Fajans, 
 Verb. d. Phys. Ges., 21, p. 716, 
 1919. 
 
 (X} = | (X,) 
 / * 
 
 + 53 
 
 + 23 
 
 + 18 
 
 Heat of dissociation: cf. Fajans, 
 idem. 
 
 (K) = [K] 
 
 + 21 
 
 + 21 
 
 + 21 
 
 Heat of sublimation, from vapor 
 pressure curve. 
 
 (K)+ + E- = (K) 
 
 + 99 
 
 + 99 
 
 + 99 
 
 Ionization potential, Table X, 
 
 V = IS. 
 
 m + E- = (xr 
 
 + 116 
 
 + 87 
 
 + 81 
 
 Electron affinity, kg. cal./gram, 
 atom. 
 
 
 5.0 
 
 3.8 
 
 3.5 
 
 Expressed in volts/atom. 
 
 
 2440 
 
 3350 
 
 3490 
 
 Expressed in Angstroms. 
 
 Of these three halogens we see that chlorine possesses the highest 
 electron affinity. A similar set of results may be obtained from a 
 consideration of other alkali halogen compounds. Equation (130) 
 may be employed directly in the following manner, using chlorine as an 
 example 
 
 Q 
 
 KCI 
 
 - 163 + 99 + 53 + 21 + 106 = 116 kg. cal./gram atom. 
 
 
THERMOCHEMICAL RELATIONS 
 
 183 
 
 It is noted that the value obtained from the grating energy for the 
 electron affinity of iodine is not in close agreement with that found by 
 Franck by the direct optical method. Part of this discrepancy may be 
 due to the inaccurate chemical data involved, but Born 6 is inclined to 
 attribute it to the computation of the grating energy. Little is known 
 of the existence of the repulsive force between the atoms in the crystal, 
 and it is likely that the resulting potential energy cannot be represented 
 by a single term of the form br~ n , an additional correction term being 
 necessary. 
 
 The grating theory has been applied to other types of compounds. 
 For example Born and Bormann 7 have used it to compute the electron 
 affinity of the sulphur atom. The sulphur atom has an outer shell 
 containing six electrons. In order to form the stable configuration of 
 eight, it possesses a tendency to attract two electrons . It may therefore 
 capture the two valence electrons of a zinc atom, forming the compound 
 ZnS. The zinc atom in this union is doubly ionized, while the sulphur 
 ion possesses a negative charge of two units. Table XXXVI represents 
 the successive stages in the decomposition of this compound. 
 
 TABLE XXXVI 
 ELECTRON AFFINITY OF SULPHUR FROM GRATING ENERGY OF ZnS 
 
 Reaction 
 
 Heat 
 
 Remarks 
 
 [ZnS] = (Zn)-^ +OS) 
 
 -753 
 
 Grating energy of crystal, computed by Born and 
 Bormann and later corrected by Born. 
 
 (Zn) =[Zn] 
 
 + 28 
 
 Heat of sublimation obtained from vapor pressure 
 data and other data; cf. Born. 
 
 iOSi) = [S\ 
 
 + 14 
 
 Heat of sublimation to diatomic vapor (Pollitzer) . 
 
 (S) = iGSi) 
 
 + 52 
 
 Heat of dissociation (Budde). 
 
 [Zn] + [S] = [ZnS] 
 
 + 41 
 
 Heat of formation from metallic Zn and rhombic 
 S (Mixter). 
 
 (Zn)++ + 2 E- = (Zn} 
 
 + 663 
 
 From ionization potential Table XI and work re- 
 quired to remove 2d electron, Table XX, i.e. 
 
 (1S + KS). 
 
 (S} + 2 E- = (S)~ 
 
 + 45 
 2.0 
 
 kg. cal./gram atom = Eg = electron affinity for 
 two electrons, 
 expressed in volts /atom. 
 
 Born and Gerlach, Z. Physik, 5, pp. 433-41 (1921). 
 Z. Physik, 1, pp. 250-55 (1920). 
 
184 ORIGIN OF SPECTRA 
 
 The electron affinity of the sulphur atom for two electrons is accord- 
 ingly 2.0 volts/atom or 45 kg. cal./gram atom, a value which will be used 
 in the following section. 
 
 lONIZATION OF VAPORS OF COMPOUNDS 
 
 Ths simple ionization of a compound molecule, R^Xi, may result in 
 the following end products: 
 
 (a) a positive molecular ion (RX) + and an electron. 
 
 (b) a positive atom ion (R) + , a neutral atom X, and an electron. 
 
 (c) a positive atom ion (R) +, and a negative atom ion (X)~. 
 
 In the association of these products of decomposition and the formation 
 of the original molecule, radiation should be produced, but practically 
 nothing either of a theoretical or experimental nature has been contrib- 
 uted to this phase of spectroscopy. A material ionizing according to 
 (a) may possess an ordinary series line spectrum, an example of which 
 may be CO. This molecule gives a definite line emission spectrum, but 
 one which has not been correlated in series. Materials ionizing accord- 
 ing to (b) or (c) , besides emitting any radiation characteristic of associa- 
 tion, should show the line spectrum of the component R. The former 
 type of radiation has not been identified as yet, but the latter is very 
 commonly observed. For example, the oxy-gas flame fed with NaCl 
 shows the arc lines of sodium. The molecule is dissociated in the flame 
 and the positively charged sodium atom picks up a free electron instead 
 of the negative chlorine atom. Union of the electron and sodium ion 
 gives rise to the arc spectrum of sodium. The sodium flame emission 
 is known to be suppressed by an excess of chlorine. This is due to the 
 fact that with a large number of chlorine ions present, the chance of a 
 collision between the positive sodium ion and the negative chlorine ion 
 is increased and the number of free electrons is reduced because of the 
 electron affinity of the chlorine atom and its tendency to capture a free 
 electron. Hence relatively more combinations of the type Na + + Cl~ 
 take place than of the type Na + + E~, with the resulting decrease in 
 intensity of emission of sodium lines. Hydrogen chloride in a spark 
 discharge shows the spectrum of hydrogen which is produced in the 
 above described manner. 
 
 The ionization of a molecule of the type R r X x is still more compli- 
 
THERMOCHEMICAL RELATIONS 185 
 
 cated and nothing whatever is known of the spectroscopic relations. 
 In the case of ZnCU, for example, the following may result : 
 
 (a) (ZnClz) + and an electron 
 
 (b) (ZnCl)+ and (Cl)~ or (Cl) and an electron. 
 
 (c) (Zn)++ and 2 (Cl)~ etc. 
 
 The second type of ionization appears very likely in low voltage dis- 
 charge. The two negative chlorine ions are probably joined to opposite 
 sides of the doubly charged zinc atom, and one of these may be ejected 
 by a single electronic impact. Even though such compounds as ZnCl 
 are incapable of stable existence, there is no apparent reason why they 
 may not exist momentarily as a product of decomposition, and especially 
 so as positive ions. In fact the existence of ZnCl + is recognized in 
 electrolytic dissociation. 
 
 Lohmeyer 8 has studied the emission spectra of the mercury halides 
 HgCl and HgCl 2 . Each shows a characteristic complicated band struc- 
 ture, and it is possible that these will be interpreted after a careful con- 
 sideration of the thermochemical relations involved. 
 
 In certain cases enough chemical data are known to enable the 
 prediction of the ionization potential for molecules of the type RX, 
 assuming they are ionized by dissociation. As an example we shall 
 consider HC1, HBr, and HI. For HC1 we have 
 
 +D H = (H), 
 +D cl = (CZ), 
 (H) + J H = (H)+ 
 (CQ + E- - E cl = (CQ-, 
 
 QHCI + D H + D cl + J H - E cl = (#)+ + (CO- (131) 
 
 The last five terms on the left give the work required to ionize by 
 dissociation one mol of hydrogen chloride. Hence the ionization 
 potential J HC i of HC1 vapor may be computed from the following 
 equation 
 
 JHCI = QHCI + D H + D cl + J H - E cl . (132) 
 
 A similar relation holds for HBr and HI. Table XXXVII summarizes 
 the thermochemical data involved and shows the close agreement 
 between the computed and observed ionization potentials. We have 
 
 Z. wiss. Phot., 4, p. 367 (1906). 
 
186 
 
 ORIGIN OF SPECTRA 
 
 used here the electron affinities determined from the grating energies, 
 Table XXXIV. Hence the computed values may be in error by several 
 tenth volts from this source alone. The value 13.7 volts for HC1 was 
 obtained by the authors while the other determinations are by Knip- 
 ping. 9 
 
 TABLE XXXVII 
 
 COMPUIED AND OBSERVED lONIZATION POTENTIALS OF 
 
 HC1, HBr, AND HI 
 
 
 HC1 
 
 HBr 
 
 HI 
 
 Remarks 
 
 Q HX .. 
 
 22 
 
 12 
 
 1 
 
 From Landolt-Bornstein. 
 
 D H 
 
 42^ 
 
 42 
 
 42 
 
 Heat of dissociation ^ gram mol Hj 
 
 
 
 
 
 (Langmuir). 
 
 D x 
 
 57 
 
 23 
 
 18 
 
 Cl Pier; Br Bodenstein ; I Starck and 
 Bodenstein. 
 
 JH 
 
 312 
 
 312 
 
 312 
 
 Bohr 13.54 volts confirmed by authors: 
 cf. Table XV. 
 
 -Ex 
 
 -116 
 
 -87 
 
 -81 
 
 From Bora's grating theory; cf. Table 
 XXXIV. 
 
 JHX 
 
 317 
 
 302 
 
 292 
 
 Expressed in kg. cal./mol. 
 
 
 13.7 
 
 13.1 
 
 12.7 
 
 Expressed in volts/molecule. 
 
 
 i 13.7 
 \ 14.4 
 
 13.8 
 
 13.4 
 
 Observed values. 
 
 It is evident that one may use the observed values of the ionization 
 potentials to compute the electron affinity of the three halogen gases. 
 We accordingly obtain 4.8, 3.1, and 2.8 volts for Cl, Br and I atoms 
 respectively. The value for iodine is closer to Franck's determination 
 by the optical method than is Born's value obtained from grating energy. 
 However, this may be accidental, as the experimental values of the 
 ionization potential may be in error by 0.5 volt. 
 
 Born and Bormann 10 have computed the ionization potential of 
 hydrogen sulphide from thermochemical considerations on the assump- 
 tion that the molecule is dissociated into two positive hydrogen atoms 
 and a doubly charged negative sulphur ion. While computations of 
 this kind are necessary in considering energy relations, it does not follow 
 
 Z. Physik, 7, pp. 328-40 (1921). 
 10 Z. Physik, 1, pp. 250-55 (1920). 
 
THERMOCHEMICAL RELATIONS 187 
 
 that this value of the ionization potential would be observed directly. 
 In a low voltage arc it is possible that only one of the hydrogen atoms is 
 readily ejected by a single impact. This would permit the temporary 
 existence of the negative ion (HS)~. If such an ion collided with another 
 electron the second hydrogen atom could be ejected, producing (S) 
 and (H) + . The computed ionization potential 31.8 volts should be 
 accordingly the sum of these two observed ionization potentials. The 
 thermochemical relations for complete dissociation are as follows: 
 
 Q M = (#2) + [SI, 
 
 2(H)+2J H = 2 (fl)+ + 2 E-, 
 [S] + S s = (S), 
 
 Q HtS + 2 D H + 2 J H + S s - E s = 2 (H)+ + (S), (132) 
 /. JB* = Qms + 2D H + 2J H + S S -E S (133) 
 
 = 5 + 84 + 624 + 66 -45 
 = 734 kg. cal./mol = 31.8 volts/molecule. 
 
 The authors have observed the ionization potential of ZnCU as 12.9 
 volts. This can be shown from a consideration of the thermochemical 
 relations to be far less than the value necessary for complete dissociation 
 into (Zn) ++ + 2 (Cl)~. Complete ionization of this compound, as 
 noted earlier, is more likely a two stage process with the intermediary 
 production of (ZnCl)~. Table XXXVIII gives a summary of recent 
 determinations of critical potentials in compound vapors. 
 
 It is of interest that with zinc ethyl we were unable to obtain the 
 spectrum of zinc, indicating that double ionization with this material 
 in our apparatus was improbable. 
 
 CKITICAL POTENTIALS AND RADIATION FKOM ELEMENTS IN THE POLY- 
 
 ATOMIC STATE 
 
 We have pointed out in Chapter III that the quantum relation 
 hc 2 v = eV- 10 8 where V is a critical potential, cannot be safely employed 
 for the computation of characteristic wave numbers for elements which 
 are polyatomic in the vapor state. Of course, if by increasing the 
 temperature of the vapor a sufficient proportion of the molecules are 
 dissociated into atoms, the critical potentials are then identified with 
 the atom and the quantum relation may hold. There still may be 
 exceptions to this, however, with atoms possessing an electron affinity. 
 
188 
 
 ORIGIN OF SPECTRA 
 
 TABLE XXXVIII 
 RESONANCE AND IONIZATION POTENTIALS OF MOLECULAR COMPOUNDS 
 
 Molecule 
 
 Critical I 
 
 'otential 
 
 Investigator and Remarks 
 
 
 Resonance 
 
 lonization 
 
 
 HC1 
 
 
 13.7 
 
 Foote and Mohler. 
 
 HBr 
 
 
 14.4 
 13.8 
 
 Knipping. 
 Knipping. 
 
 HI 
 
 
 13.4 
 
 Knipping 
 
 HCN 
 
 , 
 
 15.5 
 
 Knipping. 
 
 ZnCl 2 
 
 
 12.9 
 
 Foote and Mohler 
 
 CO 
 H 2 
 
 ? 
 7.6? 
 
 10.1 
 14.3 
 
 15.0 
 13 ? 
 
 Foote and Mohler (two ionization po- 
 tentials and inelastic impacts at 
 6.4, 12.3, 14.0, 19.7, 22.3, 25.2, 27.7 
 and 30.9 volts). 
 
 Found and Stead, and Gossling. 
 Foote and Mohler. 
 
 HgCl 2 
 
 
 12.1 
 
 Foote and Mohler. 
 
 Zn(C 2 H 5 ) 2 .. 
 C 4 H 10 O 
 C 6 H 6 
 
 7 
 6.6 
 6.0 
 
 12 
 13.6 
 
 9.6 
 
 Foote and Mohler. 
 Boucher* 
 Boucher. 
 
 C 7 H 8 
 CsHio 
 CHCI 3 . 
 
 6.2 
 6.5 
 6.5 
 
 8.5 
 10.0 
 11.5 
 
 Boucher. 
 Boucher. 
 Boucher 
 
 
 
 
 
 Phys. Rev., 19, pp. 189-209 (1922). 
 
 For example, we have found a pronounced resonance potential in 
 iodine at 2.34 volts. If this is due to the atom, by the simple quantum 
 relation we should expect a line at X 5300. This line should appear in a 
 
 
THERMOCHEMICAL RELATIONS 189 
 
 low voltage arc and should show absorption when a long column of 
 iodine is heated to a point where a considerable amount of dissociation 
 is present. Efforts to detect this line as well as the corresponding line 
 for arsenic vapor have been unsuccessful. Of course there are thousands 
 of lines present in this region, but these belong to the complicated mo- 
 lecular band spectrum and disappear if the temperature is high and 
 pressure low. 
 
 Assuming, in the critical potential measurements, that the electronic 
 impacts occurred with dissociated molecules, it is quite likely that the 
 velocity of the 2.34 volt electron is further increased on account of the 
 electron affinity of the iodine atom. The total kinetic energy absorbed 
 should then be not 2.3 volts but 2.3 + E. This might give rise to a 
 resonance line at 2200 A or possibly a band terminating in this region. 
 However we are confronted with the experimental fact that an electron 
 of higher speed, say 6 volts, may suffer a velocity loss of 2.3 volts and 
 leave the atom with a velocity of 3.7 volts. What becomes of the energy 
 corresponding to this velocity loss of 2.3 volts? 
 
 Various facts indicate that with polyatomic elements the ordinarily 
 observed critical potentials are usually characteristic of the molecule 
 rather than the atom. Accordingly the observed resonance potential 
 might represent the true resonance potential of the atom plus the work 
 required to dissociate the molecule. Similarly the ordinarily observed 
 ionization potential may represent the true ionization potential of the 
 atom plus the work of dissociation of the molecule. Smyth and Comp- 
 ton 11 observed two ionization potentials in iodine, the lower one being 
 very faint, and 1.4 volts less than the more pronounced critical velocity. 
 The work required to dissociate the iodine molecule is 1.6 volts. This 
 lower faint ionization appears to correspond to the 13.5 point for hydro- 
 gen and may be due to the atoms which have been dissociated by the 
 hot cathode. 
 
 Still further the molecule may be dissociated by the impact at the 
 observed resonance potential and the impacting electron may be drawn 
 into one of the atoms on account of the electron affinity. The char- 
 acteristic radiation should then be located in another part of the spec- 
 trum and might be a band, a line or a group of lines. If we consider the 
 electron affinity of the molecule many other simple possibilities readily 
 suggest themselves. 
 
 In practically all cases the resonance potentials of the polyatomic 
 elements lead to wave-length values which lie in a region of strong band 
 
 Phys. Rev., 16, pp. 501-13 (1920). 
 
190 ORIGIN OF SPECTRA 
 
 absorption. A discussion of the theory of band spectra, which in its 
 present initial stage of development is summarized by Sommerfeld, 12 
 cannot be here entered upon. The theory indicates that the connection 
 between absorbed energy of electronic impact and final radiation as 
 band structure may be involved and remote. The absorbed energy is 
 distributed between the quantized vibratory and rotational states of 
 the molecule. Brandt, 13 using the photo-electric method of measuring 
 resonance potentials, found for nitrogen some twenty inflections in the 
 radiation curve (similar to Figure 25) between 7.5 and 8 volts. On the 
 Lenz theory these might correspond to the same final but different 
 initial momentary, vibratory and rotational quantized states of the 
 molecule. 
 
 We call attention to the above facts to point out that one cannot 
 use the method of critical potentials to predict new series in polyatomic 
 elements, as the simple relations established for the metallic vapors no 
 longer apply. 
 
 If the resonance potential of iodine is related to the work of dissoci- 
 ation, the complicated band spectrum may appear considerably below 
 ionization. Experiments indicate that the reaction 2 1 I 2 produces 
 an emission of these bands. Wood 14 first showed that iodine vapor, 
 heated in a quartz bulb, emitted the complicated band spectrum. The 
 emission is better demonstrated by using a large graphite heater at 2000 
 C in the center of a glass bulb containing iodine at rather high pressure. 
 Strong convection currents of the vapor are set up. The molecules 
 stream from the bottom up the center, past the heater, where they are 
 dissociated, and then flow down to the bottom, following the walls of 
 the bulb. Above the heater and along the walls, especially in the upper 
 part of the bulb where recombination is taking place, the yellowish-red 
 illumination in the vapor is brilliant. There is no emission below the 
 heater where the gas is in the diatomic state, nor along the heater where 
 the dissociation is occurring. 
 
 It is certain that some types of band spectra may be excited by 
 electronic impact at a voltage less than the ionization potential. Leon 
 Bloch and E. Bloch 15 observed the positive bands of nitrogen at 12 volts 
 and the negative bands at 21.5 volts. They accordingly attribute the 
 positive bands to the neutral molecule and the negative bands to the 
 molecule which has been simply ionized. Meggers and the authors 16 
 
 " " Atombau," 3d Ed. (1922). See also Birge, Astrophys. J., 55, pp. 273-90 (1922). 
 
 " Z. Physik, 8, pp. 32-44 (1921). 
 
 14 "Physical Optics," 2d Ed. 
 
 Compt. rend., 173, pp. 225-7 (1921). 
 
 Unpublished work of Jan., 1921. 
 
THERMOCHEMICAL RELATIONS 191 
 
 investigated the emission spectrum of nitrogen in the presence of sodium 
 vapor which was introduced in order that the ionization of the latter 
 might increase the current. A discharge tube of the type illustrated by 
 Figure 22 was employed. The positive band group of nitrogen appears 
 at 7 volts as shown in Figure 31, and at 25 volts the negative group is 
 intense. The range from 18 to 25 volts was not studied. The field 
 recently opened in the experimental study of band spectra from the 
 quantum theory standpoint has already yielded fruitful results and 
 rapid development is assured within the next few years. 
 
Chapter IX 
 X-ray Spectra 
 
 INTRODUCTION 
 
 The radiation phenomena considered in Chapters ill, IV and V 
 involve primarily the valence electrons of atoms. The corresponding 
 phenomena for the electrons in inner atomic orbits will be considered 
 in the present chapter. 
 
 X-ray frequencies are in general higher than those of arc and spark 
 spectra since the electrons are closer to the nucleus. However, the 
 spectrum range extends to much longer wave-lengths than the ordi- 
 narily observed x-ray spectra, and overlaps part of the arc and spark 
 range. Measurements with the crystal grating spectrometer extend 
 from X = 12 A to X = .1 A or in terms of v/N from 70 to 9000. Meas- 
 urements by indirect means indicate x-ray wave-lengths as long as 
 700 A or v/N = 1.3 and no definite limit in this direction is known at 
 present. 
 
 A fundamental difference between x-ray phenomena and valence 
 electron spectra is that the former change with increasing atomic number 
 from element to element in a continuously progressive manner. This 
 regular sequence is evident in Figures 36 and 37, showing the emission 
 spectra of several elements on the same scale. The approximate law of 
 this progression, as stated by Moseley, is that the square roots of cor- 
 responding frequencies are proportional to the atomic number. The 
 physical basis for the regularity evidently involves a similar and un- 
 changing configuration of electrons within the atom combined with the 
 increasing nuclear field. We have derived in Chapter I a fairly accurate 
 equation for Ka on the basis of certain assumptions as to this con- 
 figuration. 
 
 Besides the regular change in frequency of x-rays, there is also a 
 periodic progression in the complexity of spectra as successive electron 
 levels are added to the atom structure. With each rare gas a new 
 electron level is completed and another x-ray series or group of series 
 
 192 
 
192 A 
 
 m 
 
192 B 
 
 K line Klimit R limit Br L lines of W 
 
 r i 
 
 FIG. 32. Photograph by de Broglie, showing absorption bands of silver bromide 
 superposed on the emission spectrum of tungsten. 
 

 X-RAY SPECTRA 193 
 
 begins. Table III, Chapter I, shows the order in which these levels 
 appear in the periodic table. In the first row we have one inner level 
 determining a K series; with neon a second level is completed and the L 
 series starts. Similarly we assume that beyond argon, krypton, xenon 
 and niton, we have the initiation of M, N, and P series. 
 
 However, our knowledge of x-ray spectra is not as extensive as the 
 above scheme would indicate. Spectroscopic data cover only the K 
 series from sodium, Z = 11, the L series from zinc, Z = 30, and the M 
 series from dysprosium, Z = 66. This range has been considerably 
 extended by experimental methods independent of spectroscopic analysis 
 as well as by combination relations of spectral lines, but and P 
 series remain largely hypothetical. 
 
 The phenomena of x-ray spectra will be considered under the sub- 
 jects: (1) Critical potentials for x-ray excitation, (2) Absorption phenom- 
 ena (including the transformations of absorbed energy), (3) Emission 
 lines and the combination principle and (4) Theoretical significance of 
 the system of absorption limits. 
 
 1. CRITICAL POTENTIALS FOR X-RAY EXCITATION 
 
 An important difference between outer and inner atomic levels is 
 that while there are outside of the atom various series of " virtual orbits" 
 (positions of equilibrium unoccupied by electrons in the normal atom), 
 within the atom all positions of equilibrium are normally filled. Hence 
 the necessary condition for excitation of x-rays is the removal of an 
 electron from the atom. Resonance potentials, single-line emission 
 spectra and line absorption spectra, all of which involve removal of an 
 electron to a virtual orbit, are absent or at least unobserved in high 
 frequency phenomena. 
 
 Another distinction is that x-ray frequencies of an atom are in- 
 dependent of its chemical or physical state, for the reason that the 
 energy levels of the inner structure are little affected by the outer elec- 
 trons which are alone involved in chemical reactions. 
 
 The above statements need qualification. There is no sharp dis- 
 continuity between the principles involved in outer and inner atomic 
 structure, but many factors, of importance near the surface, become 
 negligible within the atom. The transition stage probably lies in the 
 little known region between the ordinary ultra-violet and x-ray spectrum 
 range. 
 
 The potential required to excite an x-ray series can be accurately 
 
194 ORIGIN OF SPECTRA 
 
 determined with the Coolidge tube. D. L. Webster and his associates 1 
 have observed critical potentials for several x-ray series. The method 
 involves the measurement of the intensity of spectral lines at potentials 
 slightly above the critical point and the extrapolation of the intensity- 
 voltage curve to zero intensity. For the K series all lines start at one 
 potential and above this point maintain their intensity ratios constant. 
 Critical potentials thus measured agree within the experimental error 2 
 with limiting frequencies determined spectroscopically. 
 
 For the L series it was found that the lines occur in three groups 
 starting at potentials corresponding to the three observed limiting 
 frequencies. Four critical potentials have been distinguished in the 
 M series of lead. The possibility of separately exciting the different 
 groups of the L and M series is of fundamental importance in the inter- 
 pretation of emission spectra. 
 
 It is evident that with sufficiently sensitive measurements of intensity 
 it might be possible to measure critical potentials without resolving the 
 radiation into a spectrum. X-ray limits should then appear simply 
 as changes in slope in the total radiation-voltage curve. This method 
 has been most useful in extending x-ray data beyond the range of the 
 crystal grating. 3 Since all materials are opaque to radiation softer 
 than ordinary x-rays, the radiation is detected by its photo-electric effect 
 on electrodes within the x-ray bulb. In this manner the critical po- 
 tentials required to excite the softest characteristic x-rays can be meas- 
 ured. 
 
 Table XXXIX summarizes the data on critical potentials obtained 
 by this method. The results of the authors for nickel and tungsten 
 and all values given by Kurth and other observers are from measure- 
 ments of the radiation of solid anticathodes. The other potential 
 measurements of the authors have been obtained from a study of radi- 
 ation from a thermionic discharge in gas (or vapor) at low pressure. 
 The radiation intensity from a gas is very much greater than from a 
 solid target, at least in the low voltage range. It is essential to maintain 
 conditions such that electrons receive their full speed before collision 
 with the gas molecules (see description of experiments on low voltage 
 excitation of arc and spark spectra; Chapter V, Figure 22) . The photo- 
 electric current per unit cathode current, for radiation either of a gas 
 or solid, when plotted against applied voltage, gives a nearly straight 
 line with change in slope at critical potentials. 
 
 i Reference 1 at end of chapter. 
 
 See Chapter X. 
 
 3 Reference 2 at end of chapter. 
 
X-RAY SPECTRA 
 
 TABLE XXXIX 
 
 CRITICAL POTENTIALS AND CORRESPONDING FREQUENCIES OP 
 SOFT X-RAYS 
 
 195 
 
 Element 
 
 Z 
 
 4 
 5 
 
 6 
 
 7 
 8 
 
 11 
 12 
 
 13 
 
 14 ! 
 15 
 
 16 
 17 
 19 
 22 
 26 
 
 28 
 29 
 
 74 
 
 Data of 
 Mohler and Foote 
 
 Data of Kurth 
 
 Series limit 
 given by 
 author 
 
 Volts 
 
 V /N 
 
 Volts 
 
 V /N 
 
 Beryllium .... 
 Boron 
 
 116 
 186 
 
 272 
 
 374 
 
 478 
 
 35 
 17 
 46 
 33 
 
 126 
 110 
 95 
 152 
 122 
 198 
 157 
 23 
 19 
 
 80 
 . 60 
 
 8.57 
 13.7 
 20.0 
 
 27.6 
 35.3 
 
 2.58 
 1.25 
 3.40 
 2.44 
 
 9.30 
 8.13 
 7.01 
 11.2 
 9.02 
 14.6 
 11.6 
 1.70 
 1.40 
 
 5.91 
 4.42 
 
 290 
 33 
 
 519 
 50 
 
 123 
 150 
 
 504 
 145 
 757 
 
 227 
 50 
 
 1002 
 297 
 106 
 
 21.4 
 2.43 
 
 38.3 
 3.68 
 
 9.11 
 11.05 
 
 37.2 
 10.7 
 55.9 
 16.8 
 3.69 
 
 74.1 
 21.9 
 
 7.85 
 
 K 
 K 
 K 
 L 
 K 
 K 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 L 
 M 
 M 
 L 
 M 
 L 
 M 
 
 if 0) 
 
 M 
 
 L 
 M 
 
 Ncn 
 
 N 
 
 Carbon 
 
 Nitrogen 
 
 Oxveien 
 
 Sodium ... . 
 
 Magnesium. . . 
 
 Aluminum. . . . 
 Silicon 
 
 Phosphorous. . 
 Sulphur 
 
 Chlorine 
 
 Potassium. . . . 
 Titanium 
 
 Iron 
 
 Nickel 
 
 Copper 
 
 Tungsten 
 
 
 Data of Other Observers 
 
 Volts v/N 
 
 Richardson and Bazzoni Carbon 
 Molybdenum 
 Hughes Carbon 
 
 Boron 
 
 K 
 M 
 
 286 21.1 
 356 26.3 
 215 15.9 
 34.5 2.55 
 148 10.9 
 24.5 1.81 
 
 K 
 
 L 
 
 K 
 
 L 
 
 
196 ORIGIN OF SPECTRA 
 
 
 
 Experiments with gases show that ionization takes place at the 
 critical x-ray potentials. The increase in ionization is not as pro- 
 nounced as the radiation change and in only two elements has it been 
 studied, sodium and potassium. 
 
 It is seen from Table XXXIX that measurements of critical po- 
 tentials cover nearly the entire interval between arc spectra and the 
 range of the x-ray spectrometer. Most of the work has been concerned 
 with light elements, as these furnish the safest starting point in the 
 development of new methods. 
 
 The evidence that these radiation potentials are characteristic x-ray 
 limits is found both in the agreement of observed potentials with limits 
 computed from spectroscopic data (Figure 35), and in the Moseley 
 relation between critical potentials and atomic number (Figures 34 and 
 35). The relation of these data to x-ray spectra will be considered in 
 detail later. In the work with gases, x-radiation is superposed on arc 
 and spark spectra. Many fainter potentials not listed in Table XXXIX 
 were found, but it will require further study to classify them. 
 
 The results of Hughes are apparently inconsistent with those of other 
 observers, and there is no evident explanation of the difference. 
 
 2. ABSORPTION PHENOMENA 
 
 If a beam of continuous (heterochromatic) x-rays is passed through 
 a thin layer of any element, spectroscopic analysis of the transmitted 
 light shows a band absorption spectrum characteristic of that element. 
 There is also a non-selective absorption, probably caused by pure scatter- 
 ing of radiation. Only the selective effect will be considered here. 
 Figure 32 is a photograph of the emission of a tungsten anticathode in 
 which the K absorption bands of the elements silver and bromine in 
 the photographic plate are distinctly shown. The bands are regions 
 of continuous absorption terminating abruptly on the low frequency 
 side and fading out gradually with increasing frequency. The position 
 of the sharp edge of each band coincides with a limiting frequency 
 computed from critical potential measurements. 
 
 Energy absorbed in a band is expended in the ejection of an electron 
 from the atom. Part of the absorbed energy is given to the atom and 
 part to the electron. If ~v\ is the frequency of incident radiation and ~V Q a 
 limiting frequency characteristic of the absorber, then an absorbed 
 quantum of energy hv\ is expended: 
 
 (1) In work on the atom, hv Q ] 
 
 (2) In kinetic energy of the ejected electron; 
 
 i mv* = hvi - hv . (134) 
 
X-RAY SPECTRA 197 
 
 This is identical in form with the equation originally proposed by Ein- 
 stein to explain photo-electric phenomena of solids in the visible and 
 ultra-violet regions. 
 
 One consequence of Equation (134) is that each absorption limit I 
 determines the least frequency which will eject an electron from the / 
 given level of the atom. Duane 4 has verified this very accurately for 
 bromine and iodine. A beam of monochromatic x-rays was passed 
 through an ionization chamber containing the vapor and the current 
 measured for different frequencies. A sharp increase in the ionization 
 was found at a frequency equal to the K limit. 
 
 The energy hvo given to the atom is re-emitted as fluorescent radi- 
 ation when the ionized atom recombines. It was known even before 
 the days of x-ray spectroscopy that substances exposed to x-rays emitted 
 a characteristic fluorescent radiation. As the excitation of an atom by 
 radiation is identical, in its effect, with excitation by electron impact, 
 viz. complete ejection of an electron from one of the inner atom levels, 
 there is no need of any distinction between the resulting spectra. 
 
 The verification of Equation (134) requires the measurement of 
 velocities of photo-electrons, ejected by radiation of a frequency greater 
 than the absorption limit. The method of measurement developed by 
 Rutherford and recently improved by M. de Broglie 5 is as follows. A 
 thin layer of the material studied is placed in a narrow groove and illu- 
 minated by x-rays. A magnetic field parallel to the groove bends the 
 photo-electrons into arcs of circles of radii proportional to their speed. 
 This dispersed beam of electrons falls on a photographic plate giving a 
 "corpuscular spectrum" in which the position of any image is a measure 
 of the velocity of emission of a group of photo-electrons. If an element 
 with absorption limits K, L and M were illuminated by x-rays of fre- 
 quency v, the resulting spectrum, with low dispersion, would consist of 
 three lines corresponding to velocities v\, v 2 and ^3 given by the 
 equations 
 
 i mv\ = hv-K] 
 
 i mv\ = hv - L I (134a) 
 
 i jYifi-i = hv M 
 
 In practice, intense illumination is required so that a continuous 
 x-ray spectrum is used rather than monochromatic radiation. The 
 continuous spectrum of maximum frequency v then gives rise to a 
 
 * Reference 4 at end of chapter. 
 5 Reference 3 at end of chapter. 
 
198 
 
 ORIGIN OF SPECTRA 
 
 " corpuscular spectrum" consisting of bands terminating sharply on the 
 side of maximum velocity 
 
 J mv\ < (hv - K) (134b) 
 
 etc. 
 The incident x-rays also excite characteristic fluorescent radiation in 
 
 15 30 
 
 ATOMIC NUMBER 
 
 45 
 
 60 
 
 75 
 
 90 
 
 FIG. 33. Moseley diagram of absorption limits of the elements. Dots and crosses 
 are limits observed spectroscppically and by potential measurements. Circles 
 are values computed from emission spectra. 
 
 the material illuminated and these monochromatic rays give rise to a 
 corpuscular line spectrum superposed on the band spectrum. Thus 
 lines Ka, K(3, La. and Lp of the fluorescent radiation produce electrons 
 of velocities corresponding to frequencies Ka L, Kfi L, Ka M, 
 Kp -M,La- M, L0 - M . 
 
X-RAY SPECTRA 
 
 199 
 
 De Broglie states that the corpuscular spectra can be measured 
 with a precision comparable to spectroscopic methods. Evidently 
 the method is not subject to the limitations of the crystal grating and in 
 the future it may prove a very valuable means of studying atomic 
 structure. 
 
 As absorption limits can be measured with a precision of .1 % or 
 better through a wide spectrum range, they furnish our best means of 
 measuring electron energy levels within the atom. De Broglie opened 
 this field of research. The precision measurements of Duane and his 
 associates, together with the work of Fricke, Stenstrom, Hertz, and 
 others, furnish a basis for the classification and interpretation of all 
 x-ray spectra. 6 
 
 The K series absorption limits have been measured for nearly all 
 elements from magnesium Z = 12 to uranium Z = 92. As critical 
 potentials have been measured from beryllium Z = 4 to oxygen Z = 8, 
 inclusive, our knowledge of the innermost energy levels of the elements 
 is nearly complete. The K limit is in general observed as a single 
 discontinuity in the continuous absorption. 7 Figures 33 and 34 show 
 the K limits, for the light elements, plotted on the Moseley scale. The 
 points all fall on a smooth curve which is nearly linear from magnesium 
 to uranium. Between oxygen and magnesium there is a change in slope 
 of this line. The ionization potential of helium at 25.5 volts has been 
 included on these diagrams. It falls exactly on the extrapolated K 
 line and is evidently the starting point of the series. 
 
 The K limit of uranium is of peculiar interest, as it is the upper 
 limit of the range of atomic line-spectra. Duane's measurements give 
 the following values X = .1075 A; v/N = 8,476; critical potential 
 114,770 volts. Radiations of higher frequency than this exist. Some 
 of the hard 7 rays may be of very much shorter wave-length, but these 
 are undoubtedly vibrations from within the nucleus. They are not 
 strictly speaking characteristic of the 92 chemical elements but of the 
 200 or so different types of nuclei. 
 
 L absorption limits have been spectroscopically measured for ele- 
 ments Z = 55 to 92. Each of these elements shows three superposed 
 bands, of which the long wave-length limit is strongest. These will be 
 designated L 1, L 2 and L 3 in order of decreasing wave length. 8 
 
 8 Reference 4 at end of chapter. 
 
 7 Absorption limits of long wave-length in this and other series show a fine structure at 
 the edge of the band which will be discussed later. 
 
 8 The notation K I, L 1, etc., serves present purposes better than Kai, Lai, etc., used in 
 former chapters. It avoids confusion with^he line notation Km, Lai, etc. Similarly M and 
 N limits will be numbered in the order of their frequency, the lowest being 1. 
 
200 ORIGIN OF. SPECTRA 
 
 L limits for ten light elements between sodium 11 and copper 29 
 can be computed from critical potential measurements. Here too the 
 authors have observed several limits for each element, but the highest 
 potential corresponds to the doublet L 1, 2 and the other limits are new 
 series not found in heavy elements. Figure 35 gives the beginning of 
 the L series and Figure 33 the entire series. The ionization potential 
 of Neon at 16.7 volts falls on the line L 1, 2 and is assumed to be the be- 
 ginning of the series. 
 
 M series limits have been observed spectroscopically only in uranium, 
 thorium and bismuth. Five limits are known for the first two elements 
 and three for bismuth. Four critical potentials have been measured 
 for the M emission lines of lead and Table XXXIX gives potential 
 measurements of M limits for five light elements. The limits ascribed 
 by Kurth to the N series are probably M limits. Much of our knowledge 
 of the M series and outer levels is derived indirectly from the data on 
 emission lines. Detailed consideration of the relation of these critical 
 potentials to the system of absorption limits will be given later. 
 
 In the above treatment of absorption phenomena we have assumed 
 that the limits are single discontinuities in the continuous absorption. 
 Stenstrom and Fricke 9 have obtained spectrograms with relatively high 
 dispersion which indicate that this is not the case. Fricke describes the 
 structure of soft K limits as a distinct boundary on the long wave- 
 length side followed by an absorption line or band and sometimes by 
 two bands. The interval between the boundary and first line varies 
 from X = .002 A to .01 A and indicates an energy difference between the 
 levels of the line and boundary of from 2 to 25 volts. 
 
 Kossel 10 has suggested that this line absorption may be ascribed to 
 the virtual orbits outside the atom. But if this is true, the boundary 
 of the absorption cannot give the energy required to remove an electron 
 from the atom, since the lines are of higher frequency than the limit. If 
 the lines are so explained, the limit of the band may give the work re- 
 quired to displace a K electron to the incomplete valence ring. Fricke 
 states that the structure observed is apparently not consistent with the 
 above hypothesis. Another possible theory is that the lines are limits 
 for multiply ionized atoms. 
 
 The potential measurements of the authors gave no evidence of a 
 structure of this kind. In the case of potassium and sodium the princi- 
 pal radiation potentials agreed within experimental error (1 or 2 volts) 
 
 9 Reference 4 at end of chapter. * 
 
 10 Reference 5 at end of chapter. 
 
X-RAY SPECTRA 
 
 201 
 
 with ionization potentials for an x-ray level. This is probably the most 
 direct evidence that x-ray absorption is accompanied by ionization 
 
 2466 
 
 Atomic Number 
 
 FIG. 34. K limits observed by the authors and the ionization potential of helium. 
 
 and that the absorption limit corresponds exactly to the work of ioniza- 
 tion from an x-ray level. Our results, however, do not exclude the 
 
202 ORIGIN OF SPECTRA 
 
 possibility of excitation without ionization at other critical potentials. 
 Some faint radiation potentials (not listed in Table XXXIX) were 
 observed for elements of the first row, which may be in the future 
 identified with potentials required for excitation of single line K spectra. 
 It is probable that in the outer x-ray levels, the phenomena of line 
 absorption and resonance spectra become of importance. With valence 
 electrons, line absorption is the chief characteristic, and continuous 
 absorption beyond the series limit very faint, while with high frequency 
 spectra the second factor becomes predominant. In the intermediate 
 range we should expect to find the transition, although conclusive 
 experimental evidence of this is yet to be found. 
 
 It also may be predicted that limits of x-rays are not entirely in- 
 dependent of the chemical and physical state of an element. Indications 
 of a difference in K limits of various compounds of phosphorus and 
 chlorine have been observed. 11 On the other hand measured K limits 
 of four carbon compounds showed no detectable difference 12 (less than 
 1 volt). 
 
 The possibility of locating absorption limits by measurements of the 
 absorption coefficient of elements for radiation not resolved by the 
 spectroscope, is shown by Holweck. 13 The continuous x-rays from a 
 solid bombarded by thermions (electrons) are passed through screens 
 of very thin celluloid and the absorption coefficient of gases and solids 
 for the residual radiation is determined. Now the continuous radiation 
 has a maximum wave number v given by the applied potential V, viz. 
 v = 8100 V. If this radiation is passed through screens exhibiting 
 only general absorption (no bands) in the region studied, the lower 
 frequency radiation will be entirely absorbed and the transmitted frac- 
 tion will become more homogeneous, approximating monochromatic 
 light of wave number v. This is known to be true in the range of x-ray 
 spectra and Holweck, assuming it true at low voltage, was able to esti- 
 mate the position of absorption bands from curves of total absorption 
 vs. potential. Results are given in Table XL, together with comparison 
 data from other sources. As the technique of the measurements is 
 difficult, the agreement must be considered at present merely as a satis- 
 factory check on results by other methods. A most important phase of 
 Holweck's work is the study of the laws of non-selective absorption in 
 the low voltage range. We cannot consider this subject here except to 
 state that the results justify the fundamental assumptions of the method. 
 
 11 Reference 6 at end of chapter. 12 Reference 2 at end of chapter. 
 
 13 Reference 7 at end of chapter. 
 
X-RAY SPECTRA 
 
 203 
 
 70 - 
 
 10 
 
 14. 
 
 18. 
 
 26. 
 
 30 
 
 ATOMIC NUMBER 
 
 IG. 35. Soft L and M limits. Dots and crosses give results of potential measure- 
 ments. Circles are limits computed from K spectra. 
 
204 
 
 ORIGIN OF SPECTRA 
 
 TABLE XL 
 ABSORPTION LIMITS MEASURED BY HOLWECK 
 
 X-ray Limit 
 
 Volts 
 
 v/N 
 
 Comparison Data 
 
 Carbon K 
 
 290 approx. 
 
 21.4 
 
 20.0 Mohler and Foote. 
 
 Aluminum L. . . . 
 Aluminum K 
 Boron K .... 
 
 64 2 
 1555 10 
 160 approx. 
 
 4.7 
 115.0 
 11.8 
 
 4.8 Figure 35. 
 114.8 Fricke. 
 13.7 Mohler and Foote. 
 
 Gold ATI, 2? ... 
 
 160 approx. 
 
 11.8 
 
 9 Figure 33. 
 
 3. EMISSION LINES AND THE COMBINATION PRINCIPLE 
 
 The first survey of the field of x-ray emission spectra was made by 
 Moseley soon after the discovery of the crystal spectrometer by Bragg. 
 Since that time rapid progress has been made in the precision and range 
 of measurements and particularly in the discovery of new lines in known 
 series. 14 Figures 36 and 37 show typical K and L photographs. Many 
 more lines have been measured than can be seen in the reproduction, 
 and the complexity, particularly of the L groups, is increasing with 
 every improvement in technique. Measurements of line spectra have 
 been extended to somewhat longer wave-lengths than absorption limits. 
 
 An interesting recent development is the extension of the range of 
 the diffraction grating by Millikan. 16 He finds isolated groups of lines 
 in the extreme ultra-violet spectra of sodium, magnesium and aluminum 
 which he ascribes to their L series. The wave-lengths of the strongest 
 of these are 
 
 Na-372.2A, Mg-232.2A, A1-144.3A. 
 
 The above lines were designated as I/a, but for magnesium and 
 aluminum the wave-lengths are shorter than the limit LI. A 
 possible explanation of their origin which is consistent with other data 
 will be given later. Similar groups of lines are found for elements in the 
 first row of the periodic table. These are apparently related to the L 
 limits of carbon and oxygen found by Kurth. Though the theoretical 
 significance of these extreme ultra-violet emission spectra is as yet in 
 doubt, they at least promise an important field for future research. 
 
 The extensive and accurate data on high frequency spectra furnish 
 us the basis of our knowledge of the inner structure of the atom. An 
 
 14 Reference 8 at end of chapter. 
 
 16 Reference 9 at end of chapter. 
 
 
X-RAY SPECTRA 205 
 
 important step in this study is the development of a combination princi- 
 ple 16 which relates emission lines and absorption limits in a manner 
 analogous to the combinations found in arc or spark spectra. A system 
 of combinations was first proposed by Kossel, but the complexity of 
 absorption limits was not then known, and the scheme is too simple for 
 a satisfactory interpretation of the spectra. In the past year several 
 physicists have independently developed combination principles ade- 
 quate for the explanation of nearly all observed emission lines. 
 
 The initial condition for x-ray emission is an electron deficiency in an 
 inner atomic level. The emission of a spectrum line results when an 
 electron from an outer, orbit falls into the vacant place. The final 
 state with respect to this process is accordingly an atom with an electron 
 deficiency in a higher level and the process is then repeated until the 
 atom assumes the normal state. The quantum radiated is equivalent 
 to the difference in energy of the two successive states involved. The 
 energy of each state, referred to the normal as zero, is proportional to a 
 limiting frequency. Hence the frequency radiated should be equal to 
 the difference of two absorption limits. The following pages give the 
 experimental verification of this conclusion. 
 
 We shall consider in detail the x-ray spectra of tungsten consisting 
 of the experimentally determined K limit, 3 L limits and over 30 emis- 
 sion lines, the v/N values for which are listed in Table XLI. These 
 spectroscopic data with a few exceptions are from a table by Smekal 17 
 and data of Duane. 18 The notation is that of Siegbahn as revised 
 by Coster. 17 The system of combinations follows the scheme of 
 Wentzel. 17 
 
 In Figure 38 we have plotted as vertical lines the differences 
 between absorption limits and emission lines. Thus in the lower row 
 are plotted K 1 Kai, K I Ka Z) etc. This row of lines gives accord- 
 ing to the combination principle the energy levels involved in K emission 
 lines. The origin is the atom surface. The observed ZJ limits plotted 
 in the second row are seen to agree with the computed values. For 
 convenience L and M series are plotted on a larger scale. 
 
 In the computation of a limit from an L line we must first determine 
 which of the three L limits corresponds to the initial state. Experi- 
 ments by Hoyt 19 on the critical potentials of tungsten give the series 
 limits of a number of the lines (designated by * in Table XLI) and the 
 remaining lines are classified so that they are consistent with those of 
 
 16 Reference 10 at end of chapter. 
 
 17 Reference 10 at end of chapter. 
 
 18 Reference 4 at end of chapter. 
 i Reference 11 at end of chapter. 
 
206 ORIGIN OF SPECTRA 
 
 known origin. The M lines are assumed to originate as follows : Ma = 
 M 1 - N 1; Mp = M 2 - N 2; My = M 3 - N 3. On the right side 
 of Figure 38 are shown the series limits of the emission lines which 
 indicate the initial states involved. The plotted differences give the 
 final state for each emission line which also corresponds to an absorption 
 limit. All M lines are plotted on one row and the M limits used are 
 those computed from the L series lines. The upper row gives the mean 
 positions of five M and seven N levels. The intervals N 1,N 2 and N 3, 
 
 
 
 CO 
 
 N M 
 
 234567 12 345 
 
 t II III II . I I I 
 
 I - M 
 
 I II II I I -L, 
 
 III I I -L, 
 
 III. II I t-L, 
 
 I I I "K 
 
 40 80 12O ISO 2OO 
 
 V/N -L 
 
 1 2 3 
 
 | | | Observed 
 
 I II I II K 
 
 200 400 600 80O 1OOO 
 
 V/N 
 
 FIG. 38. Energy levels in the tungsten atom computed by the combination principle. 
 
 NQ for tungsten are smaller than the experimental error, but for uranium 
 and thorium they are of measurable magnitude. 
 
 In^Table XLIps given the origin of each line in accordance with 
 Figure 38. The limits are all unresolvable and close to the origin, so 
 they have not been included in the diagram. All but two very faint 
 lines are accounted for. It is seen that the series relationships furnish 
 a logical system of nomenclature for x-ray lines analogous to the notation 
 used for arc and spark spectra. 
 
X-RAY SPECTRA 
 
 207 
 
 TABLE XLI 
 X-RAY SPECTRA OF TUNGSTEN 
 
 Notation 
 
 Observed 
 r/JV 
 
 Series Notation 
 
 Computed 
 Limit v/N 
 
 Notation 
 
 K 1 
 
 51180 
 
 
 
 
 Ka3 
 
 4239 
 
 Kl - L3 
 
 879 
 
 L3 
 
 Ka2 
 
 4270.3 
 
 K 1 - L2 
 
 848 
 
 L2 
 
 Ka 1 
 
 4368 7 
 
 K I L 1 
 
 749 
 
 LI 
 
 K/3.. 
 
 4947.4 
 
 K 1 - M3 
 
 171 
 
 M 3 
 
 KB' . 
 
 4928 
 
 Kl - M 4 
 
 190 
 
 M 4 
 
 Ky 
 
 5050.9 
 
 K I - N 5 
 
 27 
 
 JV5 
 
 LI 
 
 75088 
 
 
 
 
 L2 
 
 849.42 
 
 
 
 
 L3 
 
 889.9 
 
 
 
 
 LI 
 
 544 02* 
 
 LI - M5 
 
 206 9 
 
 M5 
 
 La 2 
 
 613.85* 
 
 LI- M2 
 
 137.0 
 
 M2 
 
 Lai. . . 
 
 618 45* 
 
 L 1 M 1 
 
 1324 
 
 Ml 
 
 L?/...... 
 
 642.78* 
 
 L2 - M 5 
 
 207.0 
 
 M5 
 
 L4.. 
 
 701 66* 
 
 3 _ jif 4 
 
 1882 
 
 Af 4 
 
 L6Q . 
 
 708 00* 
 
 LI N 7 
 
 429 
 
 N 7 
 
 L81.. 
 
 712.39* 
 
 L2 - M2 
 
 137.4 
 
 M2 
 
 L/33.. 
 
 723 23* 
 
 L3 M3 
 
 166 7 
 
 M3 
 
 L/32 
 
 733.76* 
 
 LI- AT4 
 
 17 1 
 
 N4 
 
 L/3 8 
 
 7364 
 
 
 
 
 L37. 
 
 746 6* 
 
 L 1 - N2 
 
 43 
 
 N2 
 
 L/3 5 
 
 751.1* 
 
 L 1 - 
 
 
 
 
 
 
 7520 
 
 
 
 
 
 753 3 
 
 jr. Q /if 2 
 
 136 6 
 
 M 2 
 
 
 
 757.1 
 
 L3 - Ml 
 
 132 8 
 
 Ml 
 
 Ly 5 
 
 807.03 
 
 L2 - JV7 
 
 42.7 
 
 N7 
 
 Ly 1 
 
 831.81* 
 
 L2 AT4 
 
 17.9 
 
 N4: 
 
 
 844.2 
 
 L2 - N2 
 
 5 5 
 
 N2 
 
 I/T6. 
 
 8505 
 
 L2 - 
 
 o 
 
 
 
 Ly 2. . . 
 
 854.98 
 
 L3 - AT6 
 
 34.9 
 
 NQ 
 
 L-yS. . 
 
 859.97 
 
 L3 - AT5 
 
 300 
 
 AT5 
 
 
 873 5 
 
 L3 N 3 
 
 16 4 
 
 N 3 
 
 Z/y4. . 
 
 887.77* 
 
 L3 - Nl 
 
 2.1 
 
 ATI 
 
 Ma. 
 
 13056 
 
 M 1 ATI 
 
 20 
 
 Nl 
 
 M0 
 
 134.99 
 
 M 2 - AT2 
 
 20 
 
 N2 
 
 MT.. 
 
 149.62 
 
 M3 - N3 
 
 17 1 
 
 N3 
 
 
 
 
 
 
 * Denotes lines of experimentally determined series. 
 
208 ORIGIN OF SPECTRA 
 
 Figure 39 shows the M and N levels of uranium computed from 
 the L and M series. In this case the five M levels have been observed 
 spectroscopically so that the N limits computed from M lines are much 
 more accurate than for tungsten. Other heavy elements give similar 
 results and for atoms as light as caesium, Z = 55, several M and N 
 levels may be located from data on the L series. L limits may be com- 
 puted from K series lines down to magnesium, Z = 12. K spectra for 
 elements lighter than titanium, Z = 22, become complicated by addi- 
 tional lines Ka f , Ka z , Ken, Ka b , Ka & , and L limits computed from these 
 lines are all softer than L 1, 2. Figure 35 shows lines drawn through 
 
 N 
 
 1 1 I 1 
 
 M 
 
 12 34 567 
 II II II 
 
 123 45 
 
 1! 1 II. 
 
 II 1 -if 
 
 *> M 
 
 
 (I) || Observed 
 
 III 
 
 : ;| i i i ::;: u 
 
 II II 1 
 
 I 
 
 II 1 L, 
 
 i i i i 
 
 10O 200 500 40O 50O 
 
 V/N 
 
 FIG. 39. Energy levels in the uranium atom computed from L and M spectra. 
 
 the mean points computed from the close doublets a 3 , a 4 and a b) a 6 . It is 
 seen that the computed points agree with the observed critical potentials, 
 though only in one case, phosphorus, were the three potentials, cor- 
 responding to the three lines drawn, clearly separated. 
 
 Several theories have been proposed to explain these a lines all of 
 which assume that the simple combination law cannot be applied; i.e. 
 that the limit K 1 does not determine the initial state. The observation 
 of L limits agreeing with the computed frequencies, 
 
 L 5, 6 = K 1 - Ka^ etc., 
 

 208 A 
 
 
 
 
 
 4 
 
 ' J J 
 
 
 ' 
 
 . 
 
 
 * 
 
 ,' 
 
 J 
 
 
 
 
 J 
 
 , 3 
 
 
 
 
 
 
 
 
 _,_ 
 
 
 j , 
 
 
 
 
 
 
 
 1 
 
 
 
 
 ' 
 
 
 
 > 0,J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .45 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Se 
 
 
 
 
 
 
 
 
 } 
 
 ' 
 
 
 
 
 
 Br 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Rb 
 
 
 
 
 
 
 
 
 
 
 
 
 
 " 
 
 _J 
 
 Sr 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Nb 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Rh 
 
 FIG. 36. K emission lines photographed by Siegbahn. (Reproduction is a negative.) 
 The line at the left is a reference line. The strongest close doublet is K ai and 
 
208 B 
 
 Tl 
 
 Pb 
 
 Di 
 
 FIG. 37. L Spectra photographed by Siegbahn. Lines from right to left are: 
 a group, j8 group, 7 group and reference line. 
 

 X-RAY SPECTRA 209 
 
 cannot be explained by any such theory. For the same reason we can- 
 not ascribe these L limits to resonance potentials. If the K limit is an 
 ionization potential, L5,6 must be one also, provided the above relation 
 has a physical basis. 
 
 4. THEORETICAL SIGNIFICANCE OF THE SYSTEM OF ABSORPTION LIMITS 
 
 It is evident from Figure 33 that the usual assumption that the 
 atom structure is made up of single K, L, M, etc., levels is a very rough 
 approximation. In a heavy element the five M limits and seven N 
 limits each cover a range of frequency comparable to the interval sepa- 
 rating the two groups. For uranium we must have, in addition to the 
 sixteen limits shown, an undetermined number of and P levels. 
 
 Disregarding for the instant the complexity of the limits, we see 
 that the magnitude of the frequencies involved indicates the total 
 quantum number n, which must be assigned to each group of levels 
 K, L, M, etc. Thus the energy of a X-level is a little less than that of a 
 single electron in an n = 1 orbit around a nucleus of charge Ze. An 
 electron in an outer level has energy comparable to an electron in a 
 higher quantum orbit revolving around a charge (Z z)e, (z = electron 
 deficiency) so that to a first approximation the equation of a limiting 
 frequency is 
 
 V /N = (Z ~* )2 - (135) 
 
 While this equation is far from accurate, yet it indicates that n has the 
 values 1 for K, 2 for L, 3 for M , and 4 for N. 
 
 There are some striking regularities in the complicated groups of 
 absorbtion limits. 20 They may be classified in two ways: (1) Pairs 
 LlL2,MZM4,MlM2,N5N6,N3N4,SMdNlN < 2, which are 
 converging lines on the Moseley diagram. The wave-length difference 
 for each pair is constant for different elements. (2) The pairs L 2 L 3, 
 M 4 M 5, M 2M 3, N 6 N 7, N 4 N 5, N2N3 give parallel curves on 
 Figure 33. The law of their separation is then \/vi \/7t = constant. 
 
 It was shown in Chapter I that the separation L 1, 2 could be ex- 
 plained by the difference in relativity correction for two orbits, one of 
 radial quantum n r = and azimuth quantum n a = 2, the other n r = 1 
 and n a = 1. Sommerfeld finds that all doublets of the first type, AX = 
 constant, can be explained in the same manner. 
 
 20 Reference 1 1 at end of chapter. 
 
210 
 
 ORIGIN OF SPECTRA 
 
 The equation for this doublet separation, Equation (62) Chapter I, 
 can be written in the form 
 
 7 (Z - z) 4 [l + a (Z - z) 2 + b (Z - z) 4 ] (136) 
 
 where 7, a and b are constants involving the values of n a and n r used, 
 and z is the electron deficiency in the orbit concerned. Values of n a and 
 n r are chosen according to the scheme of Table XLII. 
 
 TABLE XLII 
 QUANTUM NUMBERS OF X-RAY LIMITS 
 
 Limit 
 
 K 
 
 LI 
 
 L2 
 
 L3 
 
 Ml 
 
 M2 
 
 M3 
 
 M4 
 
 M5 
 
 ATI 
 
 A'2 
 
 AT3 
 
 AT4 
 
 AT5 
 
 #6 
 
 #7 
 
 tin . 
 
 1 
 
 
 1 
 
 2 
 
 2 
 
 1 
 1 
 2 
 
 1 
 1 
 2 
 
 3 
 
 3 
 
 2 
 1 
 3 
 
 2 
 1 
 3 
 
 1 
 2 
 3 
 
 1 
 2 
 3 
 
 4 
 
 
 4 
 
 3 
 1 
 4 
 
 3 
 1 
 4 
 
 2 
 2 
 
 4 
 
 2 
 2 
 
 4 
 
 1 
 3 
 4 
 
 1 
 3 
 
 4 
 
 n r 
 
 n a + n r . 
 
 That the law AX = constant is consistent with Equation (136) is 
 easily seen. To an approximation, from Equation (135), it follows 
 that for a given line of a given series in all elements, 
 
 v = k (Z - z) 2 z/ 2 = fc 2 (Z - z) 4 . 
 
 By Equation (136), Av = k' (Z - z) 4 . 
 
 Since AX = Av/v 2 we have AX = k'/k 2 = constant. 
 
 A further test of Equation (136) is best made by solving for z, using 
 the values of n a and n r given in Table XLII. Sommerfeld has carried 
 this computation throughout the range of experimental data and finds 
 the value of z constant for corresponding doublets of different elements. 
 The following mean values are obtained for the different doublets. 
 
 Doublet 
 
 LI, 2 
 
 M3, 4 
 
 Ml, 2 
 
 A" 5, 6 
 
 N 3, 4 
 
 Nl,2 
 
 
 
 
 
 
 
 
 z. . 
 
 350 
 
 825 
 
 13 16 
 
 163 
 
 25.7 
 
 33.9 
 
 
 
 
 
 
 
 
 The quantity z is a measure of the resultant repulsive force of electrons 
 in the inner atom structure on an electron at the given level. To a first 
 approximation it is numerically equal to the number of electrons inside 
 the orbit considered. The value of z should then increase progressively 
 from the K ring outward, being always greater for levels of smaller 
 
X-RAY SPECTRA 
 
 211 
 
 energy. The above results fulfill this condition, viz. z (L 1, 2) < z 
 (M 3, 4) < z (M 1, 2) < z (N 5, 6) < z (N 3, 4) < z (N 1, 2). The 
 values are also of the expected magnitude. Thus there are 10 electrons 
 within the M group for which z = 8 to 13. That this deficiency re- 
 mains the same for different elements is likewise in agreement with our 
 conception of the inner structure of atoms. 
 
 The second class of doublets (inaptly termed irregular doublets) 
 for which V7i Vi/ 2 = constant, are more simply explained. We 
 obtain directly from Equation (135) : 
 
 (Z - z' 2 ) 2 
 
 Accordingly 
 
 (137) 
 
 (138) 
 
 That is, the second type of doublet separation can be ascribed to elec- 
 trons in levels of the same quantum number (n = n a + n r ) but differing 
 in electron deficiency, (z' and z distinguish deficiencies computed from 
 the two types of doublets.) Equation (137) is only an approximation 
 so that z'i and z' 2 may differ considerably from the z'a computed from 
 relativity doublets. However the difference z' 2 z'i = Az'i, 2 should 
 be the actual difference in electron deficiency if as we have assumed 
 this is the sole cause of the frequency difference. All available data on 
 these doublets give the following mean values. 
 
 
 L2, 3 
 
 M 2, 3 
 
 NQ, 7 
 
 N4, 5 
 
 AT 2, 3 
 
 A z' 
 
 1.21 
 
 3.39 
 
 2.3 
 
 4.7 
 
 9 
 
 
 
 
 
 
 
 A z 
 
 
 4.91 
 
 
 9.4 
 
 8.2 
 
 
 
 
 
 
 
 The lower row gives values of A z computed from differences in z given 
 by relativity doublets (z of M 1, 2 - z of M 3, 4 = Az of M 2, 3, etc.). 
 The agreement is not very close, but there is great uncertainty in some 
 of the data as well as in the approximations. That the two differences 
 are of the same sign and magnitude is a fair justification of the theory. 
 
 We conclude that the doublets of the first type; L 1 and L 2, M 1 and 
 M 2, etc.; all originate from two orbits at the same mean distance from 
 the nucleus but differing in ellipticity; while apparently the pairs of the 
 
212 
 
 ORIGIN OF SPECTRA 
 
 second type; L 2 and L 3, M 2 and M 3 etc.; are orbits of the same shape 
 but at different distances from the nucleus. 21 Thus the L 3 orbit is 
 inside of L 2 so that the electron deficiency for the latter orbit is in- 
 creased by the effect of electrons in L 3. There are then two L levels, 
 three M levels and four N levels; and at some of these levels are two 
 types of orbit differing in ellipticity and hence in energy because of the 
 relativity effect. This latter separation becomes negligibly small for 
 the limits of low frequency. The L limits softer than L 1 observed only 
 for light elements, do not fall within the above scheme. These lines on 
 Figure 35 are evidently parallel and hence form doublets of the second 
 type. 
 
 Two quantum numbers n a and n r suffice to explain the doublet 
 separation and, roughly at least, the absolute values of the frequencies in 
 x-ray spectra. If we attempt to find a selection principle in the emission 
 spectrum another quantum number must be used. Wentzel 22 has de- 
 veloped a system involving a third "grund quantum m" 23 which explains 
 the observed intensity relations and requires no change in the other 
 quantum numbers. As with arc spectra, transitions violating the 
 selection principle are improbable but not impossible. For details of 
 this principle of selection the reader is referred to the original papers. 
 
 The laws of doublet separation furnish the criteria for extrapolating 
 the curves of Figure 33 beyond the range of our data. Thus L 3 on the 
 Moseley scale is parallel to L 2. The graphs of the relativity doublets 
 converge as the atomic number decreases and the five M limits for light 
 elements approach three parallel lines, M 1, 2, M 3, 4, and M 5. As a 
 further guide for extrapolation we assume in analogy to the L series 
 that M 1, 2 begins with the ionization potential of argon at 15.1 volts. 
 
 21 But see in this relation Appendix II. 
 
 22 Reference 10 at end of chapter. 
 
 23 This is analogous to the "inner quantum" proposed to explain the selection principle 
 involved in doublets and triplets of arc spectra. It is found that, with the exception of certain 
 very faint lines, x-ray emission spectra, like arc and spark spectra, arise from transitions 
 fulfilling the Rubinowicz selection principle; viz., the change in n a is =*= 1 or 0. But the 
 converse is not true. All transitions fulfilling this condition do not appear. For instance 
 both Kaz = Kl - L2 and Ka ? = Kl - L3 involve transitions in which An = + 1. Km 
 is always a strong line but Ka.3 is unobserved except in the tungsten spectrum as measured by 
 Duane. Evidently there is in addition to the Rubinowicz limitation another limiting factor 
 independent of the values of n a and nr. Wentzel expresses the law of selection as follows 
 Assign to the x-ray orbits numbers m as given below: 
 
 m.. 
 
 K 
 
 LI 
 
 2 
 
 L2 
 
 L3 
 
 Ml 
 
 M2 
 
 M3 
 
 M4 
 
 M5 
 
 ATI 
 
 N2 
 
 N3 
 
 AT4 
 3 
 
 N5 
 
 NQ 
 
 N7 
 I 
 
 1 
 
 2 
 
 1 
 
 3 
 
 3 
 
 2 
 
 2 
 
 1 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 Then observed emission lines (very fault lines excepted) arise in transitions for which An a = =*=! 
 or 0, Am = 1 . At the present time we do not know tne physical meaning of m or of changes 
 in m. 
 
X-RAY SPECTRA 213 
 
 It is seen in Figures 35 and 33 that critical potentials ascribed by Kurth 
 to the N series, the potentials measured by the authors for potassium 
 and nickel, and the molybdenum point found by Richardson and Baz- 
 zoni all fall close to the M 1 line. The three higher potentials measured 
 by Kurth are close to M 5 and the point ascribed by the authors to 
 tungsten falls on the N 1, 2 line. 
 
 Of the L limits observed by Kurth the points for aluminum and 
 silicon fall exactly on L 3, while for heavier elements measured potentials 
 are close to L 1. The fact that the authors did not observe L 3 is ex- 
 plained by the difficulty in distinguishing a faint critical potential which 
 lies above a strong one. The failure of Kurth to observe the L 1, 2 
 limit indicates that there is a fundamental difference between soft 
 x-radiation of solids and gases. We suggest the hypothesis that radi- 
 ation from the outer x-ray orbits is at least partially suppressed in 
 solids for the same reason that arc and spark spectra are entirely missing. 
 In the second row of the periodic table the level L 1, 2 is close to the 
 atom surface and L 3 considerably below it. Hence in the solid state 
 only L 3 can freely emit radiation. Beyond the second row both L 1, 2 
 and L 3 are well within the surface and radiation from the former be- 
 comes strong. For the same reason, the emission spectra observed by 
 Millikan for sodium, magnesium, and aluminum may belong to the L 3 
 series. The lines are not then La but possibly Lfa or Z/j8 4 . If the above 
 hypothesis is admitted all serious discrepancies in critical potential 
 measurements are removed and the observations agree within experi- 
 mental error with the scheme of x-ray limits computed from high fre- 
 quency spectra. 
 
 CONCLUSION 
 
 The system of x-ray absorption limits indicates the energy levels 
 within the atom surface and must accordingly form the basis for any 
 theory of atomic structure. The large number of the absorption limits 
 suggests the difficulty of the problem. There have been several view- 
 points as to the interpretation of these results. One is that in any single 
 normal atom only one type of orbit appears in each K, L, M , etc., level. 24 
 This makes it possible to preserve the symmetry which it has been 
 customary to ascribe to atom models, but unfortunately this assumption 
 has other theoretical consequences/for example fine structure of Klines, 
 which are impossible to reconcile with experimental data. 
 
 We are apparently forced to the conclusion that all the shapes of 
 
 Reference 11 at end of chapter. 
 
214 ORIGIN OF SPECTRA 
 
 orbits indicated by the theory of relativity-doublets appear in every 
 atom. This is the viewpoint taken by Bohr 25 in his recently published 
 theory of atomic structure (see Appendix II). If we refer to Figure 1 
 which gives the possible shapes of orbits up to quantum number 4 it 
 will be evident that the simultaneous existence of all types of orbits 
 in a heavy atom results in a very complicated structure. In 
 addition to this complexity due to different shapes of orbits we have in 
 the second type of doublets evidence of a difference in size among orbits 
 of the same shape. Bohr, however, suggests that this frequency differ- 
 ence may be due to the existence of two possible configurations in the 
 excited atom following the ejection of an electron from one normal orbit. 
 In view of the apparent success of the explanation, on the basis of the 
 existence of two normal orbits, we must, at least for the present, give it 
 preference and conclude that absorption limits all correspond to energy 
 levels in the normal atom. 
 
 The test of these theories will rest largely on more extensive and 
 accurate data on absorption limits. As we have shown in this chapter, 
 the problem can be approached both by direct measurements and by the 
 computation of limits from emission spectra. The rapid progress of the 
 past year in both directions encourages the belief that a fairly complete 
 survey of the field will be available in the near future. As to the the- 
 oretical computation of energy levels, the apparent success of previous 
 attempts may be misleading. The simple symmetrical electron con- 
 figurations which have been assumed in such calculations bear little 
 resemblance to the complicated structure indicated by experiment. 
 The numerical agreement between computation and experiment over a 
 limited range of x-ray spectra (all published results are limited to the 
 K series) may be accidental. A complete solution of the problem is 
 inconceivable at the present time, but a reconsideration of the assump* 
 tions necessary for an approximate solution is imperative. 
 
 REFERENCES 
 
 1. Critical potentials in the x-ray region. 
 
 Summary: Webster, Bui. Natl. Res. Council, 1, p. 432 (1920). 
 
 L series of tungsten and platinum: Hoyt, Proc. Nat. Acad. Sci., 6, p. 639 (1920). 
 
 M series: Ross, Phys. Rev., 18, p. 336 (1921). 
 
 2. Soft x-ray limits from critical potential measurements. 
 
 Mohler and Foote, Bur. of Standards Sci. Paper No. 425. 
 Kurth, Phys. Rev., 18, p. 461 (1921). 
 Richardson and Bazzom, Phil. Mag. 42, p. 1015 (1921), 
 Hughes, Phil. Mag., 43, p. 145 (1922). 
 
 3. Corpuscular Spectra. 
 
 Rutherford, Rawlinson and Robinson, Phil. Mag., 28, pp. 277, 281 (1914). 
 M. de Broglie, Compt. rend., 172, pp. 274, 527, and 806; Compt. rend., 173, p. 527 
 (1921). 
 
 Reference 12 at end of chapter. 
 
X-RAY SPECTRA 215 
 
 4. Absorption spectra. 
 
 Summary: Duane, Bui. Natl. Res. Council, 1, p. 384 (1920). 
 
 de Broglie, J. phys., p. 161 (1916). 
 
 K series: Fricke, Phys. Rev., 16, p. 202 (1920). 
 
 L series: Hertz, Z. Physik, 3, p. 19 (1920). 
 
 M series: Stenstrom. Dissertation, Lund (1919). 
 
 Coster, Z. Physik, 5, p. 139 (1921), 
 
 5. Theory of structure of x-ray limits. 
 
 Kossel, Z. Physik, 5, p. 139 (1920). 
 
 6. Dependence of spectra on chemical composition. 
 
 Chlorine: Lindh, Z. Physik, 6, p. 303 (1921). 
 Phosphorus: Bergengren, Z. Physik, 3, p. 247 (1920). 
 
 7. Absorption coefficients for x-rays of long wave-length. 
 
 Holweck, Ann. phys., p. 1 (1922). 
 
 8. Data on emission spectra. 
 
 Siegbahn, Jahrbuch Rad. u. Elek., 13, p. 296 (1916). 
 
 Duane, loc. cit., 4. 
 
 Stenstrom, loc. cit., 7. 
 
 Hjalmar, Z. Physik, 7, p. 341 (1921). 
 
 Coster, Z. Physik, 4, p. 178 (1921). 
 
 9. Extension of the range of the diffraction grating. 
 
 Millikan, Proc. Nat. Acad. Sci., 7, p. 289 (1921). 
 
 10. Combinations in x-ray spectra. 
 
 Kossel, Verh. Deut. Phys. Ges., 16, pp. 899 and 953 (1914). 
 
 Duane, loc. cit., 4. 
 
 Smekal, Z. Physik, 4, p. 26; 5, pp. 91 and 121 (1921). 
 
 Dauvillier, Compt. rend., 172, pp. 915 and 1350 (1921). 
 
 Coster, Z. Physik, 6, p. 185 (1921). 
 
 Wentzel, Z. Physik, 6, p. 84 (1921). 
 
 11. On regular and irregular doublets. 
 
 Sommerfeld, " Atombau und Spektrallinien," 3d Edition, p. 605. 
 Hertz, Z. Physik, 3, p. 19 (1920). 
 
 12. On the structure of atoms. 
 
 Bohr, Z. Physik, 9, p. 1 (1922). 
 
 Published since this Chapter was Written 
 
 On the Spectra of X-Rays and the (Bohr) Theory of Atomic Structure. D. Coster, 
 Phil. Mag., 43, pp. 1070-1107 (1922). 
 
 The N Series Emission Spectrum of Uranium, Thorium and Bismuth. V. Dolejsek, 
 Z. Physik, 10, pp. 129-136 (1922). 
 
Chapter X 
 Photo-electric Effect in Vapors 
 
 It is well known that if a solid or liquid metal is illuminated with 
 light of sufficiently high wave number v, photo-electrons are emitted. 1 
 Below a minimum value of v no emission takes place, but as v is increased, 
 the emitted electrons leave the surface with increasing initial velocity. 
 The metals in the solid and liquid state are capable of absorbing the 
 entire energy of the quantum of incident radiation. This energy is 
 conserved and is represented by the kinetic energy of the emitted electron 
 plus the work required to bring the electron through the surface of the 
 metal. 
 
 By analogy we should expect a corresponding photo-electric effect 
 for atoms in the vapor state. If the vapor is illuminated with light 
 of the wave number corresponding to the highest convergence frequency 
 in its arc spectrum, 1 s for the alkalis and I S for the metals of Group II, 
 a quantum of this energy value should be sufficient to eject the valence 
 electron from the atom with zero velocity. If the wave number exceeds 
 this minimum value we might expect that the valence electron could 
 be ejected with a velocity or kinetic energy % mv z = hcv he- (1 S). It 
 is conceivable on the other hand that the atom would respond to only 
 the single wave number 1 S, the higher frequencies producing no effect 
 upon the valence electron. We shall see however that there is good 
 evidence against this latter hypothesis. 
 
 So far the ordinary methods of measuring the photo-electric effect 
 by observing the photo-electric current between two plates immersed 
 in the vapor which is illuminated by the ultra-violet source of light have 
 yielded very little of a definite nature. The amount of photo-electric 
 ionization has not been sufficient to have enabled any of the many 
 investigators in this field to differentiate it clearly from spurious effects. 
 In fact the very existence of a photo-electric effect should be responsible 
 
 i Hughes, "Photo-Electricity" Cambridge Univ. Press (1914). Supplemented by Bull. 
 Nat. Res. Coun., 2, pp. 83-169 (1921). 
 
 216 
 
216 A 
 
 FIG. 40. Absorption of sodium vapor showing the presence of continuous absorption 
 beginning at the convergence of the principal series and extending toward the 
 shorter wave-lengths. Bright lines are due to the source of radiation. 
 
 FIG. 41. The lower spectrogram shows the continuous absorption of sodium vapor 
 beginning at the limit of the principal series and extending toward the shorter 
 wave-lengths. The upper spectrogram shows the source of radiation alone. 
 
PHOTO-ELECTRIC EFFECT IN VAPORS 217 
 
 for a spurious current consisting of electrons liberated from the electrodes 
 by the diffused radiation from the vapor which must be an immediate 
 consequence of photo-electric ionization. The chief difficulties encoun- 
 tered, however, have been in the shielding of the electrodes from direct 
 and scattered radiation of the illuminating source, and the scattering by 
 impurities, dust particles, condensed groups of atoms, or ions, etc. 
 
 A probable exception to the above statement is suggested by the 
 recent note of Williams and Kunz 2 who found that caesium vapor was 
 ionized by light of wave-length 2530 A and that wave-lengths longer than 
 X 3130 were quite ineffective. Special care was taken to ensure the 
 absence of surface effects. The value of 1 s for caesium is X 3184. 
 
 The spectroscopic consequences of a photo-electric effect in vapors 
 are most interesting. If any considerable effect existed, and if it re- 
 quired for its production radiation precisely corresponding to the con- 
 vergence wave number of the principal series, we should expect to find a 
 strong narrow absorption line at this point in the absorption spectrum 
 of the normal vapor. No such phenomenon has been observed. 
 
 On the other hand if the photo-electric ejection of the valence electron 
 may be produced by the absorption of radiation of any wave number 
 greater than that corresponding to the highest convergence limit we 
 might expect to find a well-defined broad band in the absorption spectrum 
 terminating sharply on the long wave-length side at the convergence of 
 the series. In fact this method would immediately suggest itself for the 
 determination of series limits for elements for which the relations are 
 unknown. This precise phenomenon has not been observed. We shall 
 see that absorption is present but it is not in general very sharply defined* 
 
 If the ordinary photo-electric action is possible, illumination of the 
 vapor with light of wave number equal to or greater than that of the 
 highest convergence frequency should produce ionization. The ioniza- 
 tion should be followed by recombination so that with such monochro- 
 matic stimulation all lines of the arc spectrum should be excited. The 
 authors have tried this experiment with caesium vapor obtaining nega- 
 tive results. However, from the evidence presented below there is little 
 question but that the emission should be produced. It is possible that 
 the effect is present, but of insufficient intensity to be readily detected. 
 The experiment is a crucial one and worthy of extensive investigation. 
 
 Complete ionization, or certainly nearly complete, may be pro- 
 duced in successive stages as shown by Fuchtbauer's 3 experiments 
 
 2 Phys. Rev., 15, p. 550 (1920). 
 ' Physik. Z., 21, pp. 635-8 (1920). 
 
218 ORIGIN OF SPECTRA 
 
 with mercury vapor. As discussed in detail in Chapters IV and VI, 
 the mercury vapor illuminated by light from the mercury arc was found 
 to emit the arc spectrum. Wood observed absorption of the 57th term 
 in the principal series of sodium. The valence electron is accordingly 
 ejected to the 58 p orbit and the atom is thus able to emit most of the 
 arc lines. If the electron can be ejected to the 58 p orbit there is no 
 question but that it can be completely ejected by absorption of radiation 
 of slightly higher frequency, for the difference between the 58 p orbit 
 and complete ipnization is an extremely small quantity. 
 
 We have shown in Chapter IX that a limit in x-ray series is sharply 
 defined by the edge of an absorption band. For example, dense absorp- 
 tion begins abruptly at the K limit and gradually fades away toward 
 the higher frequencies. The reason that the band is well defined is 
 because the other x-ray orbits are occupied. The electron in the K- . 
 orbit can not absorb a lower frequency sufficient to displace it to an 
 L-orbit, for example, since the L-orbits are saturated and there is no 
 vacant place which the ejected electron may occupy. The displacement 
 must be to a virtual orbit which is unoccupied in the normal atom. In 
 the case of x-rays these virtual orbits are so far out that displacement 
 to any of them amounts to complete ejection as far as the energy or the 
 spectral frequencies are concerned. 
 
 The case is totally different with the spectroscopic phenomena 
 produced by the valence electron. Here all orbits outside the normal 
 orbit occupied by the electron are virtual or unfilled. The electron 
 may be displaced to any of an infinite number of virtual orbits by absorp- 
 tion of radiation. The main reason the lines of the principal series of 
 sodium were not detected by Wood beyond m = 58 was because of 
 insufficient resolution. The absorption is present but the 58 to oo 
 terms are all so close together that they appear as a continuous band 
 terminating at the convergence of the series. Now if the atoms could 
 not absorb radiation of higher wave number than this, that is if there 
 were no photo-electric effect, the absorption spectrum should terminate 
 sharply at the convergence frequency. We would have a dark band 
 from m = 58 to m oo and the clear bright background of the con- 
 tinuous source at the higher frequencies. The phenomenon usually 
 observed however is an apparently continuous absorption extending 
 from, say m = 58 to wave-lengths much shorter than that corresponding 
 to 1 s. That is, the apparent band spectrum due to the close linfe absorp- 
 tion joins on to the true band spectrum, at wave numbers greater than 
 1 s, and there is no abrupt change in the spectrum at 1 s. The band 
 
 
PHOTO-ELECTRIC EFFECT IN VAPORS 219 
 
 spectrum at wave numbers greater than 1 s indicates the existence of the 
 photo-electric effect in vapors. 
 
 Under certain experimental conditions it is possible to accentuate 
 the amount of continuous absorption over that of the line absorption 
 so that a slight discontinuity is observable at 1 s. Apparently one 
 condition for this result is high vapor density. Figure 40 shows three 
 absorption spectrograms for sodium vapor made from Professor Wood's 
 original negatives. The higher terms of the principal series show as 
 absorption lines on the right half of the figure. Unfortunately, the 
 bright lines from the cadmium spark used as the continuous source 
 detract somewhat from the appearance of the prints. However, one 
 sees that, because of insufficient dispersion and resolution, the lines 
 crowd together near the convergence forming what appears to be band 
 absorption. At the point A which marks the head of the series a genuine, 
 continuous absorption spectrum is present which extends to the left 
 for a considerable distance into the ultra-violet. The point to which 
 attention is specially directed is the fact that the absorption is con- 
 siderably more pronounced over the spectral region indicated by the 
 arrow than at the head of the series just to the right of the arrow. The 
 source, however, if photographed alone, is of uniform brightness in this 
 region. This illustration clearly demonstrates the presence of the con- 
 tinuous absorption beginning at the head of the series and extending 
 toward the higher frequencies, a fact pointed out by Wood 4 in 1909. 
 In his paper he states " One point of great interest noted with very dense 
 sodium vapor is the general absorption which begins exactly at the head 
 of the principal series and extends from this point down to the end of the 
 ultra-violet. The vapor is much more transparent to the light between 
 the absorption lines than in the region below the head of the series. 
 The head of the series actually shows much brighter on this account 
 than the rest of the spectrum below it." 
 
 This is again brought out by Figure 41, a photograph made by Dr. 
 George Harrison under similar conditions. Below the limit, the con- 
 tinuous absorption is much greater than anywhere between the principal 
 series lines from m = 9 to the limit. The upper spectrogram shows 
 the cadmium source alone, the intensity of which is fairly uniform. 
 
 We have found in Chapter VI that if the vapor pressure is high an 
 appreciable fraction of the atoms may be excited, the valence electron 
 being maintained in the 2 p orbit by absorption of the temporarily 
 imprisoned resonance radiation. Hence for such atoms there should be 
 
 Astrophys. J., 29, pp. 97-100 (1909). 
 
220 
 
 ORIGIN OF SPECTRA 
 
 a region of continuous absorption denned sharply on the red side at 2 p 
 or for sodium at about X = 4080. There is an indication of this at the 
 extreme left of the illustration. The wave-length concerned, however, 
 lies outside the portion of the spectrogram here reproduced. One 
 would expect that if such a continuous absorption were present, lines 
 of the subordinate series should be reversed. However, it is worthy 
 of note that under the above described conditions some continuous 
 absorption may be expected at 2 p and at higher wave numbers such as 
 2 s, 3 d, 3 p, etc. This absorption, of course, will be superposed on the 
 structured band spectrum arising in the molecule Na 2 and in general is 
 probably too faint to be detected. Furthermore the different bands 
 beginning at 3 p } 3 d } 2 s, 2 p, etc. probably overlap and give the appear- 
 ance of a continuous stretch of faint absorption. 
 
 O o 
 
 o o 
 
 Na 
 
 I I I I 1 
 
 12 13 
 
 19 
 
 19 
 
 Limit 
 
 FIG. 42. Transmission of sodium vapor for radiation near the limit of the principal 
 
 series. 
 
 Holtsmark 5 has made micro-photometric measurements on the 
 transmission of a photographic negative throughout the region of the 
 absorption spectra of sodium and potassium. The photographs were 
 similar to those in Figures 40 and 41 except that lower vapor pressure 
 was employed and there was no detectable transition from the line 
 absorption to the band absorption. The negatives were of uniform 
 density throughout this region. Figure 42 shows his results for sodium 
 where the wave-length with increasing values toward the left is plotted 
 against a function of the intensity of the light transmitted by the column of 
 vapor. 
 
 s Physik. Z., 20, pp. 88-92 (1919). 
 
PHOTO-ELECTRIC EFFECT IN VAPORS 
 
 221 
 
 The upper curve represents the observations on the portion of the 
 spectrum lying between the lines, the ordinal numbers of which are 
 indicated below. The lower curve from line 14 to the head of the 
 series represents the photometric measurements made on the absorption 
 lines themselves. The points to the right lying at higher frequencies 
 than the head are due to the continuous absorption. One notes that 
 the lower curve shows no abrupt change in passing the head of the 
 series. The line absorption goes over into the band absorption without 
 discontinuity. However, the comparison must be made with the upper 
 curve. If it were not for the line absorption crowding together, making 
 measurements between the lines impossible near the head, we would 
 find the intensity curve following the course of the dotted line with a 
 sharp break at the head. This is identically the type of curve char- 
 
 Limit 
 
 FIG. 43. Transmission of potassium vapor for radiation near the limit of the principal 
 
 series. 
 
 acteristic of x-ray absorption limits. The only reason it is so difficult 
 to detect in optical spectra is because the effect is in general obliterated 
 or greatly reduced by the line absorption which is absent with x-rays. 
 
 Figure 43 shows similar results with potassium. The upper curve 
 refers to the intensity between the lines and the lower curve to the 
 intensity in the continuous band beginning with the head of the principal 
 series. A sharp break appears at v = Is, the limit. 
 
 We have mentioned that if continuous absorption is present at 
 the head of the principal series we should also find it at the head of the 
 subordinate series when a sufficient number of atoms are, excited, having 
 the valence electron in the 2 p ring. Thus with hydrogen, while the 
 true photo-electric absorption of the normal vapor begins at the head 
 of the Lyman series in the far ultra-violet, that of the excited gas should 
 
222 ORIGIN OF SPECTRA 
 
 begin at the head of the Balmer series and extend toward the shorter 
 wave-lengths. In certain hydrogen stars as discussed in Chapter VII 
 an appreciable fraction of the hydrogen atoms have the electron in the 
 second orbit. Such stars should show a continuous band absorption 
 limited on the less refrangible side at v = % N-R or X = 3646. 
 
 Huggins 6 observed that "a characteristic feature of white-star 
 spectra consists in the rather sudden fall of intensity of the continuous 
 spectrum at about the place of the end of the series of dark hydrogen 
 lines. The spectrum, much enfeebled, continues to run on without any 
 further sudden enfeeblement until it is stopped by the absorption of our 
 atmosphere. This fall of intensity is most truly appreciated by compar- 
 ing the brightness of the continuous spectrum in the narrow intervals 
 between the last few hydrogen lines with the brightness of the continuous 
 spectrum a little beyond the termination of the series of lines." 
 
 Hartmann 7 has made a systematic photometric study of several 
 hydrogen stars and from numerous measurements concludes that there 
 is a general absorption from the head of the Balmer series to about 
 X 3400. 
 
 Horton and Davies were led to conclude from their experiments on 
 ionization potential, that helium, excited by 20.4 volt electronic im- 
 pact, may be ionized by absorption of the 21.2 volt radiation of helium. 
 If this observation be correct it indicates a photo-electric action analogous 
 to that described for hydrogen. 
 
 In conclusion we find that while attempts to detect a photo-electric 
 effect in vapors by electrical means have not yielded satisfactory results, 
 the spectroscopic evidence for the existence of the effect is perfectly 
 definite and that the phenomenon takes place precisely as predicted by 
 the quantum theory of absorption. 
 
 "An Atlas of Representative Spectra," p. 85. 
 
 * Physik. Z., 18, pp. 429-32 (1917). 
 
Chapter XI 
 Determinations of h Involving Line Spectra 
 
 Birge 1 has summarized up to July, 1919, the determinations of 
 Planck's constant h by seven independent methods and has concluded 
 that the most probable value is h =J).554-JQ- 27 erg sec. This is the 
 number employed for computation throughout this book. 
 
 Probably the most accurate means for the determination of h is by 
 the application of the quantum relation to general x-radiation. Duane's 2 
 most recent value by this method gave[6.556 10~ 27 . We shall, however, 
 confine our discussion to the methods, less precise at present, which 
 involve the spectroscopic measurement of frequencies belonging to line 
 series, for example, the limit of a principal spectral series, an x-ray 
 limit, or a particular emission line. 
 
 There are three direct means for this: (1) by the x-ray method in- 
 volving the correlation of the critical potential required to excite an 
 x-ray series and the wave number or frequency of the limit of the series 
 as determined by the absorption spectrum; (2) by use of the empirically 
 determined value ,of the Rydberg constant N w in Equation (7) ; (3) by N 
 measurements of ionization and resonance potentials and the correspond- / 
 ing spectral wave 'numbers, employing the quantum relation h&v 
 *V'1&. 
 
 CHARACTERISTIC X-RAYS 
 
 Table XLIII summarizes typical data on the determination of h 
 by this method. We have seen in Chapters I and IX that as the kinetic 
 energy of the impacting electron is increased by raising the accelerating 
 voltage, a critical value is reached which is just sufficient to produce 
 complete ejection of an electron from an x-ray ring. Because of this 
 ejection, for example from the X-ring, a vacant space is created into 
 which an L-electron falls with the resulting emission of Ka etc. One, 
 accordingly, observes the minimum potential, V, at which the K lines 
 
 * Phys. Rev., 14, pp. 361-8 (1919), see also Ladenburg, Jahrbuch Rad. u. Elek., 17, p. 93 
 (1920). 
 
 2 Duane, Palmer and Chi-Sun-Yeh, J. Opt. Soc. Am., 5, pp. 376-87 (1921). 
 
 223 
 
224 
 
 ORIGIN OF SPECTRA 
 
 are excited. This is correlated with the absorption limit X by the quan- 
 tum relation : 
 
 h 
 
 10 8 
 
 5.309 -10- 23 FX COT , 
 
 (139) 
 
 where e = 4.774 -IQ- 10 e.s.u. and c = 2.9986 -10 10 cm/sec., the wave- 
 length X being expressed in cm. 
 
 There is little doubt but that the method is capable of far greater 
 precision than is indicated by the values in Table XLIil. The technique 
 has not been developed because of the more satisfactory method involv- 
 ing the general x-radiation. The recent value for aluminum by Holweck 
 was obtained in a different manner as described on page 202. 
 
 TABLE XLIII 
 
 DETERMINATION OF h BY CHARACTERISTIC X-RAYS 
 
 Element 
 
 Limit 
 
 X-HFcm 
 Duane 
 
 Minimum 
 voltage 
 
 h-W 
 
 Investigator 
 
 Mo 
 
 K 
 
 .6184 
 
 19200 
 
 6.30 
 
 Wooten * 
 
 Rh 
 
 K 
 
 .5330 
 
 23300 
 
 6.59 
 
 Webster ** 
 
 Pd 
 
 K 
 
 .5075 
 
 24000 
 
 6.47 
 
 Wooten * 
 
 W 
 
 K 
 
 .1781 
 
 70-80000 
 
 6.7 
 
 Hull and Rice t 
 
 Pt 
 
 Li 
 
 1.070 
 
 11450 
 
 650 
 
 Webster and Clark ff 
 
 Al 
 
 L, 
 K 
 
 .932 
 7.947 
 
 13200 
 1555 
 
 6.54 
 6.56 
 
 Webster and Clark 
 Holweck, cf . Table 40 
 
 
 
 
 
 
 
 * Phys. Rev., 13, pp. 17-86 (1919). 
 
 ** Phys. Rev., 7, pp. 599-613 (1916). 
 
 t Proc. Nat. Acad. Sci., 2, pp. 265-70 (1916). 
 
 tt Phys. Rev., 9, p. 571 (1917). 
 
 THE RYDBERG NUMBER 
 
 Equation (7), derived theoretically, in which N^ denotes the Ryd- 
 berg series constant for an element having a nucleus of infinite mass, 
 gives directly for h: 
 
 (140^ 
 
 c (e/m) N 
 
 GO 
 
 The relation between N^ and N for a nuclear mass M is expressed by 
 Equation (8). From empirically determined values of N H and A 7 He 
 
DETERMINATIONS OF h 225 
 
 obtained by a consideration of the lines of hydrogen and ionized helium 
 respectively, Paschen 3 found that 
 
 #00 = 109737.11. 
 
 This value may be readily verified by use of Equations (8) and (10), 
 the independent determinations with hydrogen and helium agreeing 
 to the last significant figure given. 
 
 The value of e/m may be also derived from observations on the 
 wave-lengths of the hydrogen and helium lines as shown by Equation 
 (12). This optically determined quantity is e/m = 5.343 -10 17 e.s.u./g. 
 Substituting these values in Equation (140) we find: 
 
 h = 6.53 -10- 27 erg sec., 
 
 where the controlling error should be in the magnitude of the elementary 
 charge and in e/m. 
 
 lONIZATION AND RESONANCE POTENTIALS 
 
 If we use the values of the ionization and resonance potentials listed 
 in Tables X, XI and XXIV and the corresponding wave numbers which 
 are known with high precision from spectroscopic determinations, we 
 may employ the quantum relation to obtain a value for h as follows : 
 
 h _ Ve' 10* _. f 
 
 ~~#v L88347 
 
 The authors, in 1920, summarized their own data, to that date, which 
 included twenty independent points on various elements, each of course 
 a mean of a large number of measurements. 4 Equal weight was given 
 to each observation with the resulting mean h = 6.55 -10~ 27 . Since 
 then more points have been obtained by ourselves and others. We have 
 plotted in Figure 44 thirty-three values, listed in the tables referred to, 
 for which the spectroscopic frequencies are known. Assigning equal 
 weight to each determination the mean value, h = 6.544 0.015 prob- 
 able error, is obtained. 
 
 There is no doubt but that this method properly carried out will 
 yield results of a precision comparable to that obtained by the best of 
 the other methods. Up to the present time the primary object has been 
 to determine critical potentials for a large number of elements and little 
 attention has been given to the conditions favorable for the measurement 
 of h. For example, a metal like calcium which can be handled only with 
 
 3 See Chapter I. Computed from Paschen's values on N H and N Hft , cf. Ann. Phys. 50, 
 p. 935 (1916). 
 
 Foote and Mohler, J. Opt. Soc. Am., 2-3, pp. 96-9 (1919). 
 
226 
 
 ORIGIN OF SPECTRA 
 
 difficulty, is of little service in this regard. By using the recently 
 developed refinements in the measurement of critical potentials and by 
 
 10 
 
 8 
 
 CD 
 
 20,000 40,000 60,000 80,OOO 
 
 ti 
 FIG. 44. Determination of h by ionization and resonance potentials. 
 
 employing a method of magnetic dispersion to produce a univelocity 
 stream of electrons, high precision in h may be expected with an easily 
 controlled vapor such as mercury. 
 
Appendix I 
 Computational Data 
 
 TABLE XLIV 
 
 VALUES OF NUCLEAR DEFECT, s n , (Cr. Equation 44) 
 
 n 
 
 s n 
 
 n 
 
 Sn 
 
 1 
 
 
 
 14 
 
 6.159 
 
 2 
 
 0.250 
 
 15 
 
 6.764 
 
 3 
 
 0.577 
 
 16 
 
 7.379 
 
 4 
 
 0.957 
 
 17 
 
 7.991 
 
 5 
 
 1.377 
 
 18 
 
 8.624 
 
 6 
 
 1.828 
 
 19 
 
 9.27 
 
 7 
 
 2.305 
 
 20 
 
 9.92 
 
 8 
 
 2.805 
 
 21 
 
 10.57 
 
 9 
 
 3.328 
 
 22 
 
 11.24 
 
 10 
 
 3.863 
 
 23 
 
 11.92 
 
 11 
 
 4.416 
 
 24 
 
 12.60 
 
 12 
 
 4.984 
 
 25 
 
 13.29 
 
 13 
 
 5.565 
 
 26 
 
 13.98 
 
 227 
 
228 
 
 ORIGIN OF SPECTRA 
 
 TABLE XLV 
 NUMERICAL MAGNITUDES 
 
 h 
 
 6.554 -10-* 7 
 
 e 
 
 4.774- 10~ 10 
 
 7T 
 
 3.142 
 
 m 
 
 8.93 -10- 28 
 
 h* 
 
 4.295 -10- 63 
 
 e* 
 
 2.279 -10- 19 
 
 T 2 
 
 9.870 
 
 mo 2 
 
 7.97 -10- 63 
 
 h 3 
 
 2.815 -10- 79 
 
 e 3 
 
 1.088 -10^ 8 
 
 7T 3 
 
 31.01 
 
 N x hc 
 
 2.157 -10- 11 
 
 h* 
 
 1.845 -10- 106 
 
 e' 
 
 5.194- 10- 38 
 
 7T 4 
 
 97.42 
 
 h 2 
 
 6.04 -10^ 8 
 
 S-j^mo 
 
 *. 
 
 1.209 -10~ 131 
 
 e 6 
 
 2.48 -10- 47 
 
 V~, 
 
 1.772 
 
 e 
 mo 
 
 5.34 -10 17 
 e.s.u./g. 
 
 c 
 
 2.9986- 10 
 
 2 ire* 
 
 
 a 2 
 
 5.31- 10- 5 
 
 #06 
 
 109737-11 
 
 he 
 
 
 V oits = y = ^=^. 
 
 e \A XA 
 Volts = V = 10~ 8 = 1.2345 
 
 (\A measured in Angstroms) 
 v 10~ 4 (v = wave number) 
 
 v = r = (wave-lengths reduced to vacuo) 
 
 Acm A.4. 
 
 v = 8100 V v = frequency = c v 
 Number molecules/gm mol = 6.06 10 23 
 Number molecules/cm 3 at 760 mm and C = 2.705 -10 19 
 Faraday constant = 96500 10 coulombs 
 One 20 cal. = 4.183 -10 7 ergs 
 (20 cal./gm mol) -r- 23070 = Volts/molecule 
 (Kg cal./gm mol) -T- 23.07 = Volts/molecule 
 Ergs = 1.592 -10- 12 X volts 
 Ergs = 1.965 -10- 16 ^ 
 v = 5.088 X ergs-10 16 
 
 Gas constant = R = 8.315 -10 7 ergs/deg. C. (referred to mol of gas) 
 = 1.985 g cal./deg. C. (referred to mol of gas) 
 Kinetic energy of translation of av. molecule at C = 5.62- 10~ 14 ergs ^ 
 
 /V~ 
 
 Velocity of singly charged ion = 1.389-10 6 y -r: cm/sec: (V = volts, M = mo- 
 lecular weight) 
 
 Root mean square velocity = C = 1.579 10 4 \ / 7 7 /M cm/sec. (T = abs. temp., 
 M = mol. wt.) 
 
 Mean free path of electron in gas = I/TT r 2 n cm. (r = radius of gas molecule, 
 n = number of molecules /cm 3 ) 
 
U\ 
 
 APPENDIX I 229 
 
 VELOCITIES OF ELECTRONS, IONS AND MOLECULES 
 
 (Explanation of Figure 45) 
 
 The relation between the molecular weight, M, of an ideal gas, its 
 absolute temperature T, and the root mean square velocity C of a mole- 
 cule is given by 
 
 C = VZ RT/M = 1.579-10* VTjM cm/sec., 
 
 where R is the gas constant, 8.315- 10 7 ergs/ C. 
 
 I. To obtain C, knowing T and M: Lay a straight-edge from M on 
 scale (1) to T on scale (4). At the intersection with scale (2) read C 
 in cm/sec. Example: The helium atom (M = 4) at a temperature of 
 20 C (T = 293 K) has a root mean square velocity 1.38-10 5 cm/sec. 
 
 II. To obtain the thermal velocity of an electron: Lay a straight-edge 
 from the electron point on scale (1) to T on scale (4). Read its inter- 
 section with scale (2) and multiply by 100 (since a mass 10 4 times too 
 large has been used). 
 
 The relation between v, the velocity of a singly charged ion of mass 
 m, and the voltage V producing that velocity, is : 
 
 i mtf = eV 10 8 /c = eF/300, 
 
 also e/m = f/'M, where / = 96500 coulombs = 1 faraday = 9650c e.s.u. 
 of charge. 
 
 .'. v = 1.389 10 6 VVjM cm/sec. 
 
 III. To obtain v for a simply charged ion, knowing V and M (where 
 V lies between 0.1 and 100 volts) lay a straight-edge from M on scale 
 (1) to V on scale (6). At the intersection with scale (3) read velocity 
 of ion in cm/sec. 
 
 IV. To obtain the velocity of an electron after acceleration by a voltage 
 V lying between 0.1 and 100: Lay a straight-edge from the electron 
 point on scale (1) to V on scale (6), read its intersection with scale (3) 
 and multiply by 100 (since a mass 10 4 times too large has been used). 
 Example: A 4.9 volt electron has a velocity, 100-1.32-10 6 = 1 .32-10* 
 cm/sec. 
 
 (If the voltage V is greater than 100, proceed as follows.) 
 
 V. To obtain v for an ion, knowing V and M: Proceed as in III, 
 using 1/100 of the voltage on scale (6), and multiply the result by 10. 
 Example : The velocity of a singly charged mercury atom (M = 200) , 
 after falling through 110 volts, is 10 times 1.03 -10 5 = 1.03 -10 6 cm/sec. 
 
230 ORIGIN OF SPECTRA 
 
 VI. To obtain v for an electron, "knowing V and M. Lay a straight- 
 edge from the electron point on scale (1), to 1/100 of the voltage on 
 scale (6). Read the intersection with scale (3) and multiply by 1000. 
 Example: A 110 volt electron has a velocity 1000 times 6.2 -10 5 = 6.2- 
 10 8 , change of mass with velocity being left out of account. 
 
 Scales 1 (5) and (6) give directly the wave-length of the quantum 
 emitted by an atom when it collides inelastically with a V volt electron. 
 
 The reader will be able to work out many other combinations. The 
 principle of the chart is simple. It will be noted that all the scales 
 have a similar logarithmic spacing. Scales (1), (2), (4) belong together, 
 as do also scales (1), (3), (6), scale (1) doing double service to save space. 
 We have, for example : 
 
 log C = log (1.579 -10 4 ) + J log T - 1 log M. 
 
 In using the chart as in I, we subtract graphically ^ log M from \ log T. 
 The graphical addition of log (1.579 -10*) has been cared for by shifting 
 the origin of scale (2) with respect to the origins of (1) and (4). Similar 
 remarks hold true for the relation between v, V, and M . 
 
 The chart cannot be applied directly to multiply charged ions, but 
 it is easy to read the results for a singly charged ion and to multiply by 
 the appropriate factor as found from the formulae given above. 
 
 The authors are indebted to Mr. W. H. Holden for suggesting the 
 usefulness of such charts and to Mr. Arthur E. Ruark for preparing this 
 particular arrangement. If the reader has occasion to do much rough 
 computational work of this character, he will find that the few moments 
 spent in studying the principle of this chart will be amply repaid. 
 
230 A 
 
 4 
 
 Electron, 
 6 .000546. * 
 7 
 8 
 
 ?o 
 
 12 
 
 40 3 
 
 o> 
 
 50 "O 
 
 60 ^ 
 
 70 
 
 80 
 
 9O 
 
 100 
 
 -120 
 -HO 
 -160 
 180 
 -200 
 
 -300 
 
 400 
 500 
 600 
 700 
 600 
 900 
 
 3 
 
 S 
 
 'o 
 
 o 
 _o 
 
 ^ 
 
 ! 
 
 C3 
 tt 
 
 I 
 
 O 
 
 1.4- 
 1.2- 
 
 -1.2 
 
 2- 
 U 
 
 1.6- 
 1.4- 
 12- 
 
 2 
 
 18- 
 l.( 
 
 10 
 
 9 
 8 
 
 7 
 
 6 
 
 -2 
 
 1.8 
 
 1.6 
 
 1.4 
 
 1.2 
 
 ,e 
 
 10 
 
 ::-j 
 
 900( 
 
 aoc 
 
 7000 
 6000- 
 5000- 
 
 4000 
 3000 
 
 2000' 
 1800- 
 
 i; 
 
 1000- 
 aj 900 ' 
 *5 800- 
 O J^ 700- 
 
 3 
 
 2 
 
 1.6 
 1.6 
 
 1.4 
 1.2 
 
 -10 s 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 -4 
 
 2 
 
 1.9 
 -1,6, 
 
 
 
 O 
 O 
 
 I 
 
 < 
 
 c 
 
 *0> 
 
 ^ 200 
 Q>" " 
 
 u i< 
 
 2 M 
 
 2 M 
 
 |K 
 
 o> 
 
 U- 80- 
 
 co- 
 st 
 
 40- 
 30- 
 
 20- 
 M 
 
 16- 
 
 t : 
 
 I 7- 
 
 10- 
 
 90 
 80 
 70 
 60 
 50 
 
 40 
 
 30 
 
 -20 
 .8 
 
 16 
 -14 
 -\2 
 
 -1O 
 9 
 O 
 7 
 6 
 
 2 
 1.8 
 -L6 
 1.4 
 12 
 
 1 
 
 0.9 
 OB 
 
 a7 
 0.6 
 
 as 
 
 0.4 
 0.3 
 
 .2 
 
 0.18 
 -0.16 
 
 1.14 
 
 FIG. 45. Velocities of electrons, ions and molecules. 
 
APPENDIX I 
 
 231 
 
 **. 
 
 s a 
 
 g 
 
 m 
 
 
 PQ en. 
 in 
 
 CM 
 
 -< 05 
 
 S 
 
 Si 
 
 S3 
 
 l 
 
 i 
 
 
 _ 
 
 5 
 
 Ml 
 
 S 
 
 i 
 
 (S P5 
 
 
 
 
 
 LU 
 
 in 
 
 <M O 
 
 
 8? 
 
 y (N 
 00 CD 
 tf5 <^ 
 
 H 00 
 
 ro 
 
 ^ 
 H oo 
 
 i^ ro 
 
 (O CD 
 
 P 
 
 OJ 
 (O 
 
 ,0 
 
 H 04 
 in O) 
 
Appendix II 
 Bohr's Theory of Atomic Structure 1 
 
 The system of electron configurations in non-hydrogen types of atom 
 recently proposed by Bohr is a radical departure from the atomic models 
 heretofore suggested. As yet none of the mathematical steps in the 
 development of the theory have been published, and hence most of the 
 following outline will appear purely empirical. 
 
 In reality, however, the new theory is an attempt to avoid arbitrary 
 assumptions as to atomic structure. Bohr postulates that the normal 
 electron configuration about a nucleus Ze must be such as would result 
 by adding Z electrons, one at a time, to the structure, so that each 
 electron occupies that orbit which is most stable with respect to the 
 nucleus and previously bound electrons. This excludes the possibility 
 of either a ring configuration or of groups of electrons in polyhedral 
 symmetry. The ring structure appears to require the simultaneous 
 binding of all the electrons in the symmetrical group. On the basis 
 of the new theory each electron will occupy a separate orbit and will be 
 to a large extent independent of other electrons in the same group. 
 
 We can investigate directly only the last stages of the atom building 
 as shown in arc and spark spectra. A convenient approach to the 
 problem of the earlier steps in the formation of a heavy atom is found in 
 a study of successive elements in the periodic table. The stages are 
 marked, by the periodic appearance of groups of electron orbits of 
 increasing total quantum number, and by the subdivision of each 
 group into orbits of different degrees of ellipticity. 
 
 Periods in atom structure correspond to intervals between rare 
 gases in the periodic table. Table XL VIII shows the electron distribu- 
 tion in these gases and at certain intermediate stages. Table XLIX 
 gives the transitions in structure between the stages shown in Table 
 XL VIII. The following paragraphs are in explanation of the system 
 outlined in the tables. 
 
 *Z. Physik, 9, p. 1 (1922). 
 
 232 
 
APPENDIX II 
 
 233 
 
 To picture the different shapes of orbits it will be helpful to refer to 
 Figure 1, Chapter I, which illustrates possible types of hydrogen orbits 
 to quantum number 4. These are, at least to a first approximation, the 
 types of orbit appearing in heavier atoms, the essential difference being 
 that only one orbit is occupied in this figure while in general as many 
 orbits are occupied as there are electrons in the atom. 
 
 First Period. The theory of the hydrogen atom remains unchanged 
 and its line spectra show us the separate steps in the binding of the first 
 electron. The final state is a circular orbit of quantum number 1. 
 The binding of the first electron in helium or any heavier element is 
 similar except that the factor Z 2 enters into the energy equations. 
 
 TABLE XLVII 
 QUANTUM NUMBER NOTATION 
 
 Total 
 Quantum 
 n 
 
 Azimuthal 
 Quantum 
 n a 
 
 Radial 
 Quantum 
 n r 
 
 Bohr 
 Notation 
 nn a 
 
 Shape of 
 Orbit 
 
 1 
 
 1 
 
 
 
 li 
 
 circle 
 
 2 
 2 
 
 2 
 1 
 
 
 
 1 
 
 2 2 
 2i 
 
 circle 
 ellipse 
 
 3 
 3 
 3 
 
 3 
 2 
 1 
 
 
 
 1 
 
 2 
 
 3 3 
 3 2 
 3i 
 
 circle 
 ellipse 
 ellipse 
 
 The introduction of the second electron marks the departure from 
 former viewpoints. In the normal atom the two electrons are each in 
 one quantum orbits (circles to a first approximation) the planes of 
 which make with each other an angle of 120. (See Chapter III, section 
 on helium and Figure 11.) This configuration (I of Table XLVIII) 
 remains unchanged for the first two electrons in all heavier elements. 
 
 It is assumed that for any further additions to the atom structure 
 one quantum orbits are no longer possible. With groups of higher 
 quantum number, we will have the appearance of sub-groups differing 
 in orbital ellipticity. A notation is used by Bohr which is more con- 
 venient in this connection than specification of azimuth and radial 
 quantum number; viz., total and azimuth numbers, as shown in Table 
 XLVII. 
 
234 
 
 ORIGIN OF SPECTRA 
 
 TABLE XLVIII 
 STAGES IN THE BUILDING OF ATOMS DISTRIBUTION OF ELECTRONS IN SUB-GROUPS 
 
 Quantum Numbers of Sub-groups 
 
 
 
 i 
 
 ' 
 
 1 
 
 fl 
 | 
 
 "p 
 
 3 
 
 cr 
 
 1 
 
 bO 
 
 1 
 | 
 
 s 
 >< 
 
 1 
 
 1 
 
 .a 
 
 1 
 a 
 
 i 
 
 o 
 
 eS 
 
 3 
 
 a 
 
 3 
 
 I 
 
 -z 
 s 
 
 
 
 3' 
 a 
 
 w 
 
 i 
 
 00 
 
 1 
 
 >. 
 
 i 
 
 5 
 
 B 
 
 EO 
 
 1 
 
 * 
 
 * 
 
 . 
 
 10 
 
 coco 
 
 
 
 .5 
 
 TJ- CO CO 
 
 tS 
 
 ^f CO CO 
 
 j 
 
 00 00 
 
 s 
 
 n 
 
 CO CO 00 00 
 
 (M CO 
 
 * 
 
 ^ CO CO 00 00 
 
 ** 
 
 4 
 
 rP CO CO 00 00 
 
 COI> 
 
 CO 
 
 *** 
 
 5 
 
 I 
 
 CO 
 
 ^ CO CO CO CO CO CO 
 
 (M CO 
 
 CO 
 
 T^ CO CO CO CO CO CO 
 
 22 
 
 * 
 
 - 
 
 1 1 
 
 H^ 
 
 * 
 
 *^-*-***.^ 
 
 (M CO 
 
 - 
 
 
 
 w 
 
 
 Element 
 
 * * * 
 
 ^-i 03 -^ 
 
 ^ ^ 
 
 4 
 
 J g| 
 
 ^ ^ 
 
APPENDIX II 235 
 
 Second Period. In normal lithium the third electron is in a two 
 quantum elliptical orbit 2i. The binding process is seen in the arc 
 spectrum. In the three following elements the additional electrons 
 likewise fall in 2i orbits. We must assume that these have a space 
 configuration symmetrical with respect to each other and to the two 
 orbits of the helium-like sub-structure. 
 
 Additional electrons in nitrogen, oxygen, fluorine and neon fall in 2 2 
 circular orbits. The neon structure (II, Table XL VIII) must be excep- 
 tionally stable and symmetrical and represents the configuration of the 
 first ten electrons in all heavier elements. 
 
 Third Period. In the following row of the periodic table 3i and 82 
 orbits are added to the neon sub-structure in an order similar to the 
 building of the two quantum group in the second period. The binding 
 of the eleventh and twelfth electrons gives the line spectra of sodium 
 and magnesium. The period is closed with the stable argon structure 
 III. However, the outer structures of argon and heavier rare gases are 
 not completed groups, and, unlike the helium and neon structures, these 
 configurations appear in the sub-structure of only a few elements. 
 
 Fourth Period. Potassium and calcium have 4i orbits, giving them 
 properties like sodium and magnesium, but with further increase in the 
 nuclear charge a new type of transition appears. The 3 3 orbits become 
 more stable than 4i, so that successive electrons are added to the sub- 
 structure III, in an order not yet determined, until the three quantum 
 group is completed as in III'. This latter configuration does not occur 
 alone in any element, but is the sub-structure of the elements copper to 
 krypton. These have in addition to III', 4i and 4 2 orbits similar to 
 those of the superficial groups in the second and third periods. 
 
 Fifth Period. This period is built in a manner analogous to that 
 of the fourth. The 5i orbits give to rubidium and strontium the char- 
 acteristic properties of the alkalis and alkali earths, respectively, and 
 then ten electrons are added to the krypton sub-structure IV, producing 
 the structure IV'. From silver to xenon the eight electrons of the 5i 
 and 5 2 orbits are added to furnish the structure V of xenon. 
 
 Sixth Period. Beyond caesium and barium there is a more exten-. 
 sive change in the sub-structure. First the four quantum group is 
 completed by the addition of fourteen electrons (the rare earths) and then 
 ten electrons are added to the five quantum group to complete the 
 sub-structure V. From gold to niton eight electrons in 61 and 62 orbits 
 are added to form a characteristic rare gas structure VI. 
 
 Seventh Period. After niton another long period is initiated. 
 
236 
 
 ORIGIN OF SPECTRA 
 
 <NCO 
 
 4- 
 
 ~ 
 
 (Nrf 
 
 OHH 
 
 coco 
 
 CO'* 
 
 4- 
 
 UhH 
 
 <NCO 
 
 fflt-H 
 
 <N (M 
 
 4- 
 
 coco 
 
 4- 
 
 H- 
 
 3 c 
 
 a 
 
 1C CO 
 
 4- 
 
 : 
 
 1.1 
 
 
 f 
 
 COCO 
 
 4- 
 
 COIN 
 bC 
 
 CO 1-1 
 
 H- 
 
 csa 
 
 03 
 
 Sfc 
 
 COIN 
 
 
 COIN 
 
 4- 
 
 O^H 
 
 4- 
 
 4- 
 
 il 
 
 SCO 
 ^ 
 
 IJ 
 
 =.- 
 
 8 g .o 
 
 2 g 
 
APPENDIX II 237 
 
 Radium contains two electrons in 7i orbits. Other transitions cannot 
 be specified. The fact that no elements beyond uranium are known is 
 explained, not by any property of the electron configuration, but by the 
 instability of heavy nuclei, as evidenced by their radio-activity. 
 
 We will review briefly some of the properties of the new Bohr atoms 
 which can be tested by experiment. 
 
 X-ray Spectra. The evident interpretation of the origin of x-ray 
 series on the basis of the above outlined atomic structure is that the 
 K, L, M, etc., spectra originate in the groups of orbits of total quantum 
 number 1, 2, 3, etc., respectively, and that each series starts with the rare 
 gas in which the corresponding group of orbits first appears. This is in 
 exact accord with the conclusions based on x-ray data as to total quan- 
 tum number and origin of the different series (Chapter IX). Further- 
 more, the Sommerfeld theory of doublet separations shows that the 
 orbits of each group have all the degrees of ellipticity permitted by the 
 quantum theory. Thus we have experimental evidence for both the 
 existence and order of appearance of the types of orbit postulated by 
 Bohr. Table XLVIII gives in the lower rows the x-ray limits corre- 
 sponding to the different sub-groups. 
 
 Superficial Atomic Properties. The configurations of the last 
 bound electrons, shown in Table XLIX, must determine nearly all the 
 chemical and physical properties of the elements apart from x-ray 
 phenomena. It is seen that the first electrons appearing in each group 
 have orbits of azimuth quantum one. It is impossible to foresee what 
 the exact form of such an orbit will be, for it is in a field of force which 
 departs widely from a Coulomb field. Assuming though that Figure 1 
 gives the approximate form and relative size of the orbit, we conclude 
 that electrons in these orbits will all penetrate the entire atom structure 
 and at perihelion will be close to the nucleus of charge Ze. This is in 
 marked contrast to other theories, all of which have assumed that the 
 last bound electrons move in a field of approximately unit charge. At 
 aphelion the electrons will lie far outside the structure of previously 
 bound groups. The tendency of an atom to lose an electron (electro- 
 positiveness) will depend on the extension of the outer part of this orbit. 
 It will be greatest for the alkali metals and will decrease progressively 
 from left to right in each row of the periodic table. The number of 
 electrons which may be lost (positive valence) correspondingly increases. 
 
 The second sub-group formed has an azimuth number 2. These 
 orbits will not extend beyond previously bound groups and the electrons 
 are not readily lost. On the contrary, elements preceding the rare 
 
238 
 
 ORIGIN OF SPECTRA 
 
 gases, the electro-negative elements, tend to take up electrons to form 
 the stable rare gas configuration. The electro-positive or -negative 
 properties do not necessarily imply small or large ionization potentials. 
 The ionization potential is a measure of the total energy of an orbit ; the 
 electro-positive or -negative property depends on the extension or degree 
 of ellipticity of the orbit as well as upon the energy. These properties 
 are in strongest contrast in the second period (Li to Ne) where the two 
 sub-groups differ most in shape, and the contrast becomes progressively 
 
 .8 
 
 Total Quantum Number 
 5 4 
 
 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 42 4.3 44 45 4.6 
 
 Logarithm V 
 
 FIG. 46. Grotrian diagram for sodium on the basis of Bohr's new assignment of 
 
 quantum numbers. 
 
 less in the following periods. Thus in the row starting with silver the 
 two types of orbits 5i and 62 are only slightly different in shape and the 
 chemical differences are likewise less pronounced. 
 
 In the long periods where changes occur in the sub-structure and 
 not in the superficial groups we have successive elements with very 
 similar physical and chemical properties. It is impossible to present 
 in this outline a detailed consideration of the correspondence between 
 properties of elements and the proposed models. Bohr attempts no 
 explanation of the processes of chemical combination or crystal forma- 
 tion. 
 
APPENDIX II 
 
 239 
 
 TABLE L 
 QUANTUM NUMBERS OF SERIES TERMS 
 
 Series 
 Term 
 
 Sommer- 
 feld 
 Theory 
 
 Bohr Theory 
 
 Li arc 
 
 Na arc 1 
 
 Karc 2 
 
 Rb arc 3 
 
 Cs arc* 
 
 n 
 
 n r 
 
 n a 
 
 tt r 
 
 n a 
 
 rc r 
 
 rt a 
 
 Wr 
 
 n 
 
 n r 
 
 n a 
 
 n r 
 
 1 8 
 
 1 
 1 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 
 
 1 
 
 2 
 
 
 1 
 
 2 
 
 
 1 
 2 
 
 
 1 
 2 
 
 1 
 
 1 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 1 
 
 2 
 3 
 
 
 1 
 2 
 
 
 1 
 2 
 
 
 1 
 2 
 
 1 
 1 
 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 2 
 3 
 4 
 
 1 
 2 
 3 
 
 
 1 
 2 
 
 
 1 
 2 
 
 1 
 
 1 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 3 
 4 
 *5 
 
 2 
 3 
 4 
 
 1 
 2 
 3 
 
 
 1 
 2 
 
 1 
 1 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 4 
 5 
 6 
 
 3 
 4 
 5 
 
 2 
 3 
 4 
 
 1 
 2 
 3 
 
 1 
 1 
 1 
 
 2 
 2 
 2 
 
 3 
 3 
 3 
 
 4 
 4 
 4 
 
 5 
 6 
 
 7 
 
 4 
 5 
 6 
 
 3 
 4 
 5 
 
 2 
 3 
 4 
 
 2s 
 
 3s 
 
 2v. 
 
 3p 
 
 47?.. 
 
 3d 
 
 4d 
 
 5d 
 
 46.. 
 
 56.. . . 
 
 66 
 
 
 1 Similar numbers for Mg arc and spark. 
 
 2 Similar numbers for Cu arc and Ca and Zn arc and spark. 
 
 3 Similar numbers for Ag arc and Sr and Cd arc and spark. 
 
 4 Similar numbers for Au arc and Ba and Hg arc and spark. 
 
 Arc and Spark Spectra. A mathematical computation of the two 
 orbits of normal helium and of the stages in the binding of the second 
 electron is being worked out by Kramers and Bohr. The solution of 
 this very difficult three body problem has, we are assured, already 
 reached a stage that justifies the basic assumptions of the theory of non- 
 hydrogen types of atom. In heavier elements a rigorous mathematical 
 solution of the problem of the binding of the last electron offers difficul- 
 ties that are apparently insurmountable. The choice of quantum num- 
 bers assigned to the normal state (1 S) by the Bohr theory makes it 
 necessary to reject entirely Sommerf eld's theoretical computation of 
 spectral series formulae. Table L indicates the system of quantum 
 numbers assigned by Bohr to different series terms of elements in the 
 first and second columns of the periodic table. For comparison we 
 include in the table the numbers required by the Sommerfeld theory. 
 It is noted that the azimuth numbers remain the same in the two theo- 
 ries. The inter-orbital transitions involved in arc spectra of sodium on 
 the new Bohr hypothesis are shown in Figure 46. This should be 
 
240 ORIGIN OF SPECTRA 
 
 compared with Figure 9, which is based on the other theory. In Figure 
 46 the double p terms and transitions involving combination lines have 
 been omitted for the sake of simplicity. By our choice of coordinates 
 in these diagrams points and lines remain identical for the two theories, 
 but total quantum numbers are entirely different. Hence the expla- 
 nation of the features of Figure 9 applies, with the above noted exception, 
 to Figure 46, although the mathematical expression for the variable 
 term in a series formula would be entirely different. On the Bohr theory 
 total quantum numbers characterizing these series will differ for ele- 
 ments of the same family, as shown in Table L. 
 
 Though a quantitative test of the Bohr theory of spectra is im- 
 possible for heavy elements because of the mathematics involved, yet 
 a comparison of the relative magnitudes of different series limits in the 
 same element, and of corresponding limits in different elements, offers 
 a means of testing many of the assumptions as to the relative stability 
 of the different types of orbit. For the elements preceding and following 
 the long periods such comparisons are particularly interesting, but the 
 subject is too complicated for treatment here. 
 
 Conclusion. Bohr's new hypothesis of atomic structure was 
 developed primarily from considerations of atomic stability, and is thus 
 in marked contrast to other theories which in general postulate arbitrary 
 configurations suitable for the explanation of a limited range of physical 
 phenomena. It has been seen that in the field of x-ray spectra we find a 
 striking confirmation of Bohr's assumptions as to the types of orbit 
 appearing in the inner atom structure. It is only in the assumed space 
 configurations of these orbits and in the superficial structure (Table 
 XLIX) that the new theory can be open to question. 
 
 A space configuration of electrons is apparently essential for the 
 explanation of chemical and physical phenomena other than radiation. 
 The coplanar ring model assumed in the past for the mathematical 
 computation of spectral frequencies was adopted because of its simplicity 
 and was generally looked upon merely as an approximation to actual 
 electron configurations. It has been applied with apparent success 
 to a wide range of phenomena, notably, the theoretical derivation of the 
 Ritz formula and the computation of x-ray frequencies. 
 
 The new Bohr theory apparently rejects this model even as an 
 approximation, and the success of the theoretical deductions based on 
 ring configurations offers the chief objection to the acceptance of the 
 new viewpoint. In estimating the weight of this objection we must 
 remember that the different applications of the ring model involve 
 
APPENDIX II 
 
 241 
 
 many assumptions which are mutually inconsistent. The new theory 
 avoids the artificiality inherent in other models but as a consequence 
 it lacks the simplicity required for a direct mathematical test of its 
 validity. Thus we can foresee that the quantitative verification of the 
 details of this scheme of electron distribution may not be accomplished 
 in the near future. At the present writing the entire subject is in the 
 most elementary qualitative stage, but we are promised information 
 of more quantitative nature from Bohr in subsequent papers. 
 
INDEX OF SUBJECTS 
 
 Absorption lines, Chapter IV, 78-108. 
 of excited atoms, 93. 
 of ionized atoms, 103. 
 of normal atoms, 78. 
 of subordinate series, 97. 
 relation to critical potentials, 
 63. 
 
 Absorption phenomena, see x-rays. 
 
 Affinity for electrons, 177, 179. 
 
 , of excited argon, sodium and mer- 
 cury, 106. 
 
 , of excited helium, 105. 
 
 , of hydrogen molecule, 76. 
 
 Aluminum. 
 
 , K and L limits of, 204. 
 
 , raies ultimes of, 143. 
 
 , soft x-rays of, 195, 204. 
 
 Antimony. 
 
 , raies ultimes of, 144. 
 
 , resonance and ionization potentials 
 of, 66. 
 
 Arc spectra, 111, 119. 
 
 and spark spectra of elements, 
 
 42. 
 
 , notation on basis of Bohr's new 
 
 theory, 239. 
 
 of alkalis, 34. 
 
 of heavy atoms, 32-36. 
 
 of helium, 69. 
 
 of hydrogen, 17. 
 
 of metals of Group I, 134. 
 
 of metals of Group II, 125. 
 
 Arcs. 
 
 , below ionization potential, 73, 77; 
 115, 153. 
 
 , for determination of critical poten- 
 tials, 116. 
 
 , in nonatomic hydrogen, 77. 
 
 , in sodium, of high luminous effi- 
 ciency, 114. 
 
 , intensity of emission proportional to 
 current, 129. 
 
 , reversals, 82. 
 
 Argon. 
 
 , M limit, 212. 
 
 , negative ion, 106. 
 
 , resonance and ionization potentials 
 of, 68. ' 
 
 Arsenic. 
 
 , raies ultimes of, 143. 
 
 Arsenic, resonance and ionization po- 
 tentials of, 66. 
 Aspherical nucleus, 28. 
 Atomic numbers of elements, 231. 
 Atomic structure, 15. 
 
 , atoms with many electrons, 30, 31. 
 
 , Bohr's new theory of, 232-241. 
 
 , hydrogen, 16, 74. 
 
 , ionized helium, 16. 
 
 , normal helium atom, 70. 
 
 Balmer series, 17, 22, 25, 28. 
 
 , absorption of, 97, 98. 
 
 , fine structure of, 25, 28, 37, 59, 76. 
 
 Band spectra, 105. 
 
 , continuous band in iodine, 178. 
 
 , of helium, 106. 
 
 , of mercury chlorides, 185. 
 
 , of nitrogen, 190. 
 
 , relation to critical potentials, 190. 
 
 Barium. 
 
 , absorption of enhanced lines, 103. 
 
 , development of spectrum, 125. 
 
 , fundamental wave numbers of, 64, 85. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , reversal of series IS mP, 83. 
 , series in, 44. 
 
 , thermal ionization, 163, 170. 
 Beryllium. 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , soft x-rays of, 195. 
 Bismuth. 
 
 , raies ultimes of, 144. 
 , resonance and ionization potentials 
 
 of, 66. 
 Boron. 
 
 , K limit, 204. 
 , soft x-rays of, 195. 
 Broadening of spectral lines, 27, 91. 
 Bromine. 
 
 , critical potential of, 67. 
 , electron affinity of, 179, 182, 186. 
 , heat of dissociation of, 182, 186. 
 , K absorption band, 196. 
 
 Cadmium. 
 
 , absorption of X 3260 and X 2288 A, 81. 
 
 243 
 
244 
 
 INDEX OF SUBJECTS 
 
 Cadmium, development of spectrum, 125. 
 , fundamental wave numbers of, 64, 85. 
 , raies ultimes of, 142. 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , series in, 44. 
 , single line spectrum, 124. 
 , thermal ionization, 163. 
 , two line spectrum, 124. 
 Caesium. 
 
 , absorption lines of, 80. 
 , development of spectrum, 134. 
 , fundamental wave numbers of, 62. 
 , photo-electric effect in vapor, 217. 
 , possibility of higher resonance po- 
 tentials, 127. 
 , raies ultimes of, 142. 
 , resonance and ionization potentials 
 
 of, 62. 
 
 , reversal of subordinate series of, 108. 
 , reversed lines, 82. 
 , series in, 44. 
 
 , single-doublet and arc spectra, 129. 
 , thermal ionization of, 163. 
 Calcium. 
 , absorption of X 4227 A in furnace 
 
 spectra, 82. 
 
 , development of spectrum, 125. 
 , flame spectrum, 166. 
 , fundamental wave numbers of, 64, 84. 
 , in solar spectrum, 171, 172. 
 , in stellar spectra, 174. 
 , raies ultimes of, 142. 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , reversal of enhanced lines, 103. 
 , reversal of series 1 S-mP, 83. 
 , series in, 44. 
 
 , thermal ionization of, 160, 163, 170. 
 Carbon. 
 , ionization and resonance potentials 
 
 of compounds of, 188. 
 , K limit, 204. 
 , raies ultimes of, 143. 
 , soft x-rays of, 195. 
 Chlorine. 
 
 , critical potentials of, 67. 
 , electron affinity of, 179, 182, 186. 
 , heat of dissociation of, 182, 186. 
 , soft x-rays of, 195. 
 Chromium. 
 
 , in solar spectrum, 172. 
 , raies ultimes of, 144. 
 Cobalt. 
 
 , in solar spectrum, 172. 
 , raies ultimes of, 144. 
 Columbium. 
 , raies ultimes of, 143. 
 Copper. 
 , development of spectrum of, 134. 
 
 Copper, fundamental wave numbers of 
 
 62. 
 , ionization and resonance potentials 
 
 of, 62. 
 
 raies ultimes of, 142. 
 
 reversal of X 3248 and X 3275 A, 83. 
 
 series in, 44. 
 
 soft x-rays of, 195. 
 
 thermal ionization of, 163. 
 Cumulative ionization, 148-156. 
 
 Data, numerical, 227-231. 
 Displacement law for spectra, 42. 
 Dissociation. 
 
 of halogens, 182. 
 
 of hydrogen, 75, 76. 
 Doppler-Fizeau effect, 27, 88, 91. 
 
 e/m, value of, 18. 
 
 Emission lines, Chapter V, 109-147. 
 
 , metajs of Group I, 127. 
 
 , metals of Group II, 118. 
 
 , rare gases, 133. 
 
 Energy diagrams. 
 
 , Grotrian diagram; for hydrogen, 
 
 57; sodium, 58, 238. 
 
 , helium, 70. 
 
 , hydrogen, 52. 
 
 , ionized magnesium, 56. 
 
 , magnesium, 54. 
 
 , mercury, 101. 
 
 , sodium, 53, 58. 
 
 , sodium (Bohr's new theory), 238. 
 
 , tungsten (x-rays), 206. 
 
 , uranium (x-rays), 208. 
 Enhanced spectra, 113. (See also Spark 
 
 spectra.) 
 
 constants in series formulae, 40. 
 
 of metals of Group I, 134. 
 
 of metals of Group II, 119, 125. 
 
 , relation between a* and a, 41. 
 
 , relation between 1 and 1 S, 124. 
 
 , series notation for, 41. 
 
 Excited atoms, 79, 90, 150. 
 
 , electron affinity of, 105. 
 
 , life of, 92, 93. 
 
 , line absorption spectra of, 93-108. 
 
 , produced thermally, 157-176. 
 
 Fine structure, 25, 26, 27. 
 
 , doublets and triplets, 37. 
 
 , L-doublet separation, 49. 
 
 of Balmer lines, 37. 
 
 of x-ray spectra, 209-213. 
 
 , relation of L-doublets to arc 
 
 spectrum of neon, 136. 
 Flame spectra, 82, 84, 165. 
 , suppression of sodium lines with 
 
 excess of chlorine, 184. 
 Fluorescence, 90, 107. 
 
INDEX OF SUBJECTS 
 
 245 
 
 Fluorescence, of mercury, 104, 107. 
 of x-radiation, 197. 
 
 Gallium. 
 
 , raies ultimes of, 143. 
 
 Germanium. 
 
 , raies ultimes of, 143. 
 
 Gold. 
 
 , development of spectrum of, 134. 
 
 , fundamental wave numbers of, 62. 
 
 , N -limit, 204. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 
 of, 62. 
 
 , reversal of X 2428 A, 83. 
 , series in, 44, 83. 
 , thermal ionization of, 163. 
 Grating energy, 179. 
 
 of alkalf halides' 182. 
 
 of ZnS, 183. 
 
 h, determinations of, involving line 
 
 spectra, 223-226. 
 Helium. 
 
 , absorption of excited atom, 103. 
 , compounds of, 74, 106. 
 , development of spectrum of, 133. 
 , electron affinity of, 105. 
 , energy diagram, 70. 
 " , fine structure of ionized, 28. 
 , in stellar spectra, 174. 
 , K series, 199. 
 , metastable, 73. 
 , new ultra-violet lines, 77. 
 , ortho- and par-helium, 72. 
 , photo-electric effect in, 222. 
 , resonance and ionization potentials 
 
 of, 68, 73. 
 
 , resonance radiation of, 90. 
 , series in ionized atom, 17. 
 , series in neutral atom, 69-74. 
 , structure of ionized atom, 16. 
 , the normal atom, 69. 
 Hydrogen. 
 , arcs in, 77. 
 
 , continuous absorption in, 222. 
 , doublet separation, 29. 
 , electron affinity of molecule, 76. 
 , energy diagrams, 52, 57. 
 , halides, ionization potentials of, 186, 
 
 188. 
 
 , in solar spectrum, 171. 
 , in stellar spectra, 174. 
 , ionization potential of HCN, 188; 
 
 of water vapor, 188. 
 , life of excited atom, 96. 
 , molecule, 74-77. 
 , ratio of mass of nucleus and atom to 
 
 mass of electron, 18. 
 
 Hydrogen, resonance and ionization po- 
 tentials of, 68. 
 
 series in, 17, 22. 
 
 structure of atom, 16. 
 
 sulphide, ionization of, 187. 
 
 thermal ionization of, 161, 163. 
 
 work of dissociation of, 75, 76. 
 
 Impact damping, 92. 
 Indium. 
 
 , raies ultimes of, 143. 
 Iodine. 
 
 electron affinity, 179, 182, 186. 
 
 emission from recombination, 190. 
 
 emission spectrum, 178. 
 
 heat of dissociation, 182, 186. 
 
 resonance and ionization potentials 
 of, 67. 
 
 Ionization. (See also Ionization poten- 
 tials.) 
 
 by photo-electric action, 154, 217. 
 
 by photo-impact, 148. 
 
 by successive impact, 148. 
 Ionization potentials. 
 
 -- , determination of h, 225. 
 -- , higher, and x-ray limits, 196. 
 -- , of compounds, 179-191. 
 -- , of elements, 60-68. 
 Iridium. 
 
 , raies ultimes of, 144. 
 Iron. 
 
 , in solar spectrum, 172. 
 
 , raies ultimes of, 144. 
 
 , soft x-rays, 195. 
 
 Lead. 
 
 , raies ultimes of, 143. 
 
 , resonance and ionization potentials 
 of, 65. 
 
 Life of excited atoms, 92, 105. 
 -- , measurement of, 93. 
 Limits of series. 
 -- arc spectra, 125, 134. 
 -- enhanced spectra, 118, 125, 134. 
 -- significance of x-ray, 209. 
 -- spectral, 45; determining ioniza- 
 tion, 61, 111, 112. 
 
 x-ray, 46, 195, 198, 201, 203, 204. 
 
 , absorption lines of, 80. 
 
 , development of spectrum of, 134. 
 
 , doubly ionized, 16, 42; series in, 44. 
 
 , flame spectrum, 166. 
 
 , fundamental wave numbers of, 62. 
 
 r, ionization and resonance potentials 
 of, 62. 
 
 , raies ultimes of, 142. 
 
 , reversed lines, 82. 
 
 , thermal excitation of, 168. 
 
 , thermal ionization of, 163. 
 
246 
 
 INDEX OF SUBJECTS 
 
 Long lines, 141. 
 
 Lyman series, 17, 25, 59, 75. 
 
 Magnesium. 
 
 , absorption of enhanced lines, 103 
 
 , absorption of X 2852 and X 2026 A, 82 
 
 , complete arc spectrum, 121 
 
 , complete enhanced spectrum, 122 
 
 , development of spectrum, 118, 125. 
 
 , energy diagrams, 54, 56. 
 
 , fundamental wave numbers of 64 84 
 
 , in stellar spectra, 174. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 
 , series in, 44. 
 
 , single line spectrum, 118. 
 
 , single line spectrum of ionized 122 
 
 , soft x-rays, 195, 204. 
 
 , thermal ionization, 163. 
 
 , two line spectrum, 121. 
 
 Manganese. 
 
 , in solar spectrum, 172. 
 
 , raies ultimes of, 144. 
 
 , 1 S and ionization potential, 67 
 
 Mass. 
 
 , correction for finite, of nucleus, 17. 
 
 , of hydrogen nucleus, 15. 
 
 , ratio of, hydrogen nucleus and atom 
 
 to mass of electron, 18. 
 Mercury. 
 , absorption coefficient of vapor for 
 
 resonance radiation, 89. 
 , absorption of subordinate series, 99, 
 , absorption of X 1849 and X 2537 A. 
 
 81, 88, 89, 100, 108. 
 , development of spectrum of, 125 
 , energy diagram, 101. 
 , fluorescence, 104. 
 , fundamental wave numbers of, 64, 85 
 , higher critical potentials, 137. 
 , ionization potential of HgCl 2 , 188. 
 , metastable form of, 102, 106, 108 140 
 , molecule, 106. 
 , raies ultimes of, 143. 
 , resonance and ionization potentials 
 
 of, 64. 
 , resonance potential by probe wire 
 
 measurements, 114. 
 , resonance radiation, 86-89. 
 , series in, 44. 
 , single line spectrum, 124. 
 , thermal ionization, 163. 
 Molybdenum. 
 , raies ultimes of, 144. 
 , soft x-rays, 195. 
 
 Neon. 
 
 , development of spectrum, 136. 
 
 Neon, L series, 200. 
 
 , resonance and ionization potentials 
 
 of, 68. 
 Nickel. 
 
 , in solar spectrum, 172. 
 , raies ultimes of, 144. 
 -, soft x-rays, 195. 
 Nitrogen. 
 
 , complex critical potentials, 190. 
 , excitation of band spectra, 190. 
 , resonance and ionization potentials 
 
 of, 66. 
 
 , soft x-rays, 195. 
 Nuclear defect of a ring of electrons, 37, 
 
 227. 
 Numerical magnitudes, 228. 
 
 Orbits, 15. 
 
 , application of general quantizing 
 
 equation, 21. 
 , circular, of hydrogen and ionized 
 
 helium, 16, 23. 
 , elliptical, 19, 21. 
 , modifications arising in relativity 
 
 considerations, 24. 
 , of helium, 70. 
 Oxygen. 
 
 , resonance and ionization potentials 
 
 of, 67. 
 , soft x-rays, 195. 
 
 Palladium. 
 
 , raies ultimes of, 144. 
 
 Paschen series, 17, 25, 59. 
 
 Periodic table, 30, 231. 
 
 Phosphorus. 
 
 , raies ultimes of, 143. 
 
 , resonance and xonization potentials 
 of, 66. 
 
 , soft x-rays, 195. 
 
 Photo-electric effect in vapors, 216-222. 
 
 and ionization, 217. - 
 
 in caesium vapor, 217. 
 
 Photo-electric ionization, 148. 
 
 Platinum. 
 
 , raies ultimes of, 144. 
 
 Potassium. 
 
 , absorption lines of, 80. 
 
 , continuous absorption, 221. 
 
 , development of spectrum of, 134. 
 
 , fundamental wave numbers of, 62. 
 
 , heat of sublimation of, 182. 
 
 , ionization and resonance potentials 
 
 of, 62. 
 
 , raies ultimes of, 142. 
 , reversed lines, 82. 
 , reversal of subordinate series of, 108 
 , series in, 44. 
 
 , single line, arc, and enhanced spec- 
 tra, 129. 
 
INDEX OF SUBJECTS 
 
 247 
 
 Potassium, thermal ionization of, 163. 
 , soft x-rays, 195. 
 
 Quantum numbers, 16. 
 
 , definition of azimuthal and radial, 
 
 21. 
 
 -, determination of, 20. 
 
 , for alkalis, 34. 
 
 , for hydrogen series, 17. 
 
 , of series terms on basis of Bohr's 
 
 new theory, 239. 
 
 , of x-ray limits, 210. 
 
 Quantum theory, 15-50. 
 
 Radium. 
 
 , development of spectrum of, 125. 
 , fundamental wave numbers of, 64. 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , series in, 44. 
 Raies ultimes, 141. 
 
 of the elements (table), 142. 
 
 Relativity, of mass, 24. 
 
 hydrogen doublet, 29. 
 
 L-doublet, 49. 
 
 Resonance potentials. 
 
 , determination of h, 225. 
 
 , of compounds, 188. 
 
 , of elements, 60-68. 
 
 Resonance radiation, 86, 147. 
 
 Retarded potential, 28. 
 
 Reversed lines, 82. 
 
 Rhodium. 
 
 , raies ultimes of, 144. 
 
 Ritz equation, 32, 43. 
 
 Rubidium. 
 
 , absorption lines of, 80. 
 
 , development of spectrum of, 134. 
 
 , fundamental wave numbers of, 62. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 
 of, 62. 
 
 , reversal of subordinate series, 108. 
 , reversed lines, 82. 
 , series in, 44. 
 , thermal ionization of, 163. 
 Ruthenium. 
 
 , raies ultimes of, 144. 
 Rydberg number, N, N^, Nu, Nse, 17, 
 
 18, 19. 
 j determination of h, 224. 
 
 Scandium. 
 
 , in solar spectrum, 172. 
 , raies ultimes of, 143. 
 Selection, principle of, 26, 28, 35, 72, 86, 
 87, 88, 121, 140. 
 
 m absorption, 78. 
 
 in x-rays, 212. 
 
 Selection, principle of, representation in 
 Grotrian diagrams, 59. 
 
 , ls-3d in sodium and potassium, 
 
 130. 
 
 Selenium. 
 , resonance and ionization potentials 
 
 of, 67. 
 
 Series. (See x-rays.) 
 , absorption, Chapter IV. 
 , emission, Chapter V. 
 , graphic representation of, 51-59. 
 , in alkalis, 34. 
 , in heavy atoms, 32-36. 
 , in helium, 17. 
 , in hydrogen, 17. 
 
 , lines correlated with temperature, 
 169. 
 
 , notation and formulae, 43-46. 
 
 , notation on basis of Bohr's new 
 theory, 239. 
 
 , reversals, 82. 
 
 Silicon. 
 
 , raies ultimes of, 143. 
 
 , soft x-rays, 195. 
 
 Silver. 
 
 , development of spectrum, 134. 
 
 , fundamental wave numbers of, 62. 
 
 , K absorption band, 196. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 of, 62. 
 
 , series in, 44. 
 
 , thermal ionization of, 163. 
 
 Size. 
 
 of hydrogen nucleus, 15. 
 
 radius of hydrogen atom, 38. 
 Sodium. 
 
 , absorption of, 79. 
 
 , continuous absorption of, 219, 220. 
 
 , energy diagrams, 53, 58. 
 
 , development of spectra of, 129, 134. 
 
 . energy diagram (Bohr's new theory), 
 
 238. 
 
 , flame spectrum, 166. 
 , fundamental wave numbers of, 62, 87. 
 , in solar spectrum, 171, 172. 
 , ionization and resonance potentials 
 
 of, 62. 
 
 , metastable ion, 130. 
 , negative ion, 106. 
 , raies ultimes of, 142. 
 , resonance radiation, 86. 
 , reversal of subordinate series, 97, 108. 
 , reversed lines, 82. 
 , series in, 44. 
 , single line spectrum, 129. 
 , soft x-rays, 195, 204. 
 , subordinate series terms of higher 
 
 order, 117. 
 , thermal excitation, 165. 
 
248 
 
 INDEX OF SUBJECTS 
 
 Sodium, thermal ionization, 163. 
 Solar spectra, 169, 170. 
 Spark spectra, 39, 112. 
 
 , alkali earths, 118. 
 , helium, 17, 28. 
 
 , notation on basis of Bohr's new 
 
 theory, 239. 
 
 Spectroscopic analysis, 141. 
 
 Spectroscopic tables, 43. 
 
 Stark effect, 7, 27, 29. 
 
 Stellar. 
 
 , continuous band absorption in spec- 
 tra, 222. 
 
 spectra, 169, 172, 174, 176. 
 temperatures, 173, 176. 
 
 Stokes' law, 102. 
 
 Strontium. 
 
 , absorption of enhanced lines, 103. 
 
 , development of spectrum, 125. 
 
 , flame spectrum, 166. 
 
 , fundamental wave numbers of, 64, 85. 
 
 , in solar spectrum, 172. 
 
 , raies ultimes of, 142. 
 
 , resonance and ionization potentials 
 
 of, 64. 
 
 , reversal of series 1 S-mP, 83. 
 , series in, 44. 
 
 , thermal ionization of, 163, 170. 
 Sulphur. 
 
 , electron affinity of, 179, 183. 
 , heat of dissociation of, 183. 
 , heat of sublimation of, 183. 
 , resonance and ionization potentials 
 
 of, 67. 
 , soft x-rays, 195. 
 
 Tantalum. 
 
 , raies ultimes of, 143. 
 
 Tellurium. 
 
 , raies ultimes of, 144. 
 
 , resonance and ionization potentials 
 of, 67. 
 
 Thallium. 
 
 , absorption of vapor, 83. 
 
 , excitation of lines of, in mixtures of 
 Tl and Hg, 108. 
 
 , raies ultimes of, 143. 
 
 , resonance and ionization potentials 
 of, 65. 
 
 , reversals in arc, 83. 
 
 Thermal excitation, 157-176. 
 
 Thermochemical relations, 177-191. 
 
 Thermodynamics of excitation and ioni- 
 zation, 157-176. 
 
 Tin. 
 
 , raies ultimes of, 143. 
 
 Titanium. 
 
 , in solar spectrum, 172. 
 
 , raies ultimes of, 143. 
 
 , soft x-rays, 195. 
 
 Tungsten. 
 
 , complete x-ray spectra of, 205-207. 
 
 , energy diagram (x-rays), 206. 
 
 , raies ultimes of, 144. 
 
 , soft x-rays, 195. 
 
 Ultra-violet, continuous source of, 81. 
 
 Uranium. 
 
 , energy levels (x-rays), 208. 
 
 , K limit, 199. 
 
 Vanadium. 
 
 , in solar spectrum, 172. 
 , raies ultimes of, 143. 
 Velocities of electrons, ions and mole- 
 cules, 229. 
 
 Wave number, definition of, 17, 
 
 X-rays, 46-;50, 192-215. 
 
 , absorption limits (table), 204. 
 
 , absorption phenomena, 196. 
 
 , combination principle, 204. 
 
 , critical potentials for excitation, 193. 
 
 , determination of h, 223. 
 
 , diagram of K limits, 201. 
 
 , diagram of L and M limits, 203. 
 
 , diagram of x-ray limits of elements, 
 
 198. 
 
 , emission lines, 204. 
 , interpretation by Bohr's new theory, 
 
 237. 
 
 , N series, 215. 
 
 , relation to arc spectrum of neon, 136. 
 , significance of limits, 209. 
 , simple series nomenclature, 47. 
 , spark lines accompanying, 134. 
 , structure of band absorption, 200. 
 , table of soft x-rays, 195. 
 , values of v/N, 48. 
 
 Yttrium. 
 
 , raies ultimes of, 143. 
 
 Zeeman effect, 7, 29. 
 
 Zinc. 
 
 , absorption of X 3076 and X 2139 A, 82. 
 
 , development of spectrum of, 125. 
 
 , fundamental wave numbers of, 64, 84. 
 
 , heat of sublimation of, 183. 
 
 , ionization potentials of ZnCl2 and 
 
 zinc ethyl, 187, 188. 
 , raies ultimes of, 142. 
 resonance and ionization potentials 
 
 of, 64. 
 
 , series in, 44. 
 
 , single line and two line spectra, 124. 
 , thermal ionization of, 163. 
 Zirconium. 
 , raies ultimes of, 143. 
 
INDEX OF AUTHORS 
 
 Adams, Edwin Plimpton, 50. 
 Anderson, J. A., 72. 
 
 Bazzoni, C. B., 195, 213, 214. 
 
 Bergengren, J., 215. 
 
 Be van, P. V., 80. 
 
 van der Bijl, H. J., 155. 
 
 Birge, R. T., 19, 190, 223. 
 
 Bloch, E., 190. 
 
 Bloch, Leon, 190. 
 
 Bodenstein, M., 186. 
 
 Bohr, Nils, 7, 16, 26, 28, 30, 31, 35, 36, 
 
 50, 69, 71, 74, 77, 130, 186, 214, 215, 
 
 232-241. 
 
 Bormanri, Elisabeth, 183, 186. 
 Born, Max, 179, 183, 186. 
 Boucher, P. E., 188. 
 Brackett, F. S., 135. 
 Bragg, W. H., 204. 
 Brandt, Erich, 66, 190. 
 de Broglie, M., 192 B, 197, 199, 214, 215. 
 BuddeJ Hans, 183. 
 
 Cario, 108. 
 
 Catalan, M., 67. 
 
 Child, C. D., 156. 
 
 Chi-Sun-Yeh, 223. 
 
 Clark, H., 224. 
 
 Coblentz, W. W., 172, 173. 
 
 Compton, K. T., 8, 67, 68, 135, 148, 
 
 151, 153, 168, 189. 
 Coster, D., 205, 215. 
 Curtiss, R. H., 97. 
 
 Darwin, C. G., 28. 
 
 Dauvillier, A., 215. 
 
 Davies, A. C., 67, 68, 75, 95, 136, 222. 
 
 Davis, Bergen, 137. 
 
 Dempster, A. J., 96. 
 
 Dixon, A. A., 67. 
 
 Dolejsek, V., 215. 
 
 Duane, William, 197, 199, 205, 212, 215, 
 
 223, 224. 
 
 Duffenback, O. S., 77. 
 Dunoyer, L., 87. 
 Dunz, Berthold, 43. 
 Dushman, Saul, 26. 
 
 Edwards, E., 81, 137. 
 Einsporn, E., 120, 137. 
 Einstein, A., 197. 
 
 Fairchild, C. O., 99. 
 
 Fajans, K., 182. 
 
 Foote, Paul D., 36, 60-68, 75, 76, 81, 
 
 108, 116, 118, 124, 128, 129, 130, 132, 
 
 186, 187, 188, 190, 194, 195, 200, 201, 
 
 204, 213, 214, 217, 225. 
 Fortrat, R., 79. 
 Fowler, A., 39, 43-46, 50, 64, 65, 66, 67, 
 
 69, 136. 
 Franck, J., 7, 68, 71, 73, 74, 77, 90, 91, 
 
 92, 105, 106, 108, 120, 124, 133, 137, 
 
 177, 183, 186. 
 
 Fricke, Hugo, 72, 199, 200, 204, 215. 
 Fuchtbauer, Chr., 100, 155, 217. 
 
 Gehrcke, E., 28. 
 
 Gerlach, W., 77, 183. 
 
 Gossling, B. G., 188. 
 
 Goucher, F. S., 137. 
 
 de Gramont, A., 141. 
 
 Grotrian, Walter, 59, 105, 106, 114, 136, 
 
 138, 239. 
 Guthrie, D. V., 81, 83. 
 
 Harrison, G. R., 80, 219. 
 
 Hartley, W. N., 141. 
 
 Hartmann, J., 222. 
 
 Henderson, J. P., 124. 
 
 Hertz, G., 124, 199, 215. 
 
 Hicks, W. M., 45. 
 
 Hjalmar, E., 215. 
 
 Holden, W. H., 230. 
 
 Holtsmark, J., 220. 
 
 Holweck, F., 202, 204, 215, 224. 
 
 Horton, Frank, 67, 68, 75, 95, 136, 222. 
 
 Howe, H. E., 81. 
 
 Hoyt, F. C., 205, 214. 
 
 Huggins, William, 222. 
 
 Hughes, A. L., 66, 67, 68, 77, 195, 196, 
 
 214, 216. 
 Hulburt, E., 81. 
 Hull, A. W., 224. 
 
 Ireton, H. J. C., 124. 
 Jolly, H. L. P., 129. 
 
 Kannenstine, F. M., 73. 
 Kayser, H., 97, 103. 
 Kemble, E. C., 70, 74. 
 Kiess, C. C., 141. 
 
 249 
 
250 
 
 INDEX OF AUTHORS 
 
 King, A. S., 82, 103, 108, 169, 170. 
 
 Klein, O., 108. 
 
 Knipping, P., 68, 71, 73, 133, 186, 188. 
 
 Konen, H. M., 43. 
 
 Kossel, W., 42, 200, 205, 215. 
 
 Kramers, H. A., 29, 239. 
 
 Kunz, J., 217. 
 
 Kurth, E. H., 76, 194, 195, 204, 213, 214. 
 
 Ladenburg, R., 99, 223. 
 
 Lande, A., 71. 
 
 Langmuir, Irving, 30, 75, 152, 186. 
 
 Lau, F., 28. 
 
 Lenz, W., 106, 190. 
 
 Lewis, E. P., 81. 
 
 Lewis, G. N., 30. 
 
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 Lockyer, Norman, 141. 
 
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 Lorentz, H. A., 91, 92. 
 
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 Merton, T. R., 28. 
 Meggers, W. F., 8, 36, 81, 82, 85, 97, 108, 
 
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 Mie, Gustav, 96. 
 Millikan, R. A., 204, 213, 215. 
 Milne, E. A., 171. 
 Mixter, W. G., 183. 
 Mohler, F. L., 36, 62-68, 75, 76, 81, 87, 
 
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 Pier, M., 186. 
 Planck, M., 16, 24, 223. 
 Pollitzer, F., 183. 
 
 Raleigh, Lord, 24, 91. 
 
 Randall, H. M., 65. 
 
 Rawlinson, W. F., 214. 
 
 Reiche, F., 71, 73, 74. 
 
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 Richardson, O. W., 195, 213, 214. 
 
 Robinson, H., 214. 
 
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 Rosseland, S., 108. 
 
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 Rubinowicz, A., 26, 36, 212. 
 
 Russell, H. N., 171, 172, 175. 
 
 Rutherford, Ernest, 15, 197, 214. 
 
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 Saunders, F. A., 84, 85. 
 
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 Silberstein, Ludwick, 28, 50. 
 
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 Sommerfeld, A., 7, 20, 24, 26, 28, 32, 36, 
 
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 Starck, G., 186. 
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 Stimson, F. J., 141. 
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 Tate, J. T., 60, 63. 
 Thomson, A., 165. 
 Tolman, R. C., 8, 157, 158, 164. 
 
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 Waidner, C. W., 8. 
 
 Webster, D. L., 194, 214, 244. 
 
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 Wooten, B. A., 224. 
 
 Young, J. F. T., 83. 
 Zahn, H. ; 98, 166, 167, 168. 
 
re i i 137 
 
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