in I 1111 ,. iiljjiii i! fflliiiilM pjjpjil l >. mwm\\%MW ! PIP i iiiiiHlB UNIVERSITY OF CALIFORNIA DEPARTMENT OF CIVIL ENGINEERING BERKELEY. CALIFORNIA Engineering Library UNIVERSITY OF CALIFORNIA DEPARTMENT OF CIVIL, ENGINEERING BERKELEY. CALIFORNIA WITHIN THE ATOM A POPULAR VIEW OF ELECTRONS AND QUANTA BY JOHN MILLS M FELLOW, AMERICAN PHYSICAL SOCIETY AUTHOR "THE REALITIES OF MODERN SCIENCE' ILLUSTRATED NEW YORK D. VAN NOSTRAND COMPANY EIGHT WARREN STREET 1921 Mr Engineering Library COPYRIGHT, 1921, BY 0. VAN NOSTRAND COMPANY PRINTED IN THE UNITED STATES OF AMERICA PREFACE THIS volume is intended for readers who wish to obtain a familiarity with the basis of modern physical science. Without mathematical formula- tion it deals with modern theories as to matter and energy, emphasizing the granular structure and electrical nature of matter, and the apparently corpuscular character of energy. The reader need have no previous knowledge of electricity, mechanics, or chemistry. For the appre- ciation of the evidence of certain critical experi- ments upon which modern scientists base their be- lief in electrons and in quanta of energy some knowledge of electricity, however, is required. To supply this in a quick and easy manner, the usual historical order of presentation is abandoned and the correctness of modern theories is assumed at the start. There are postulated the electron and its counterpart, the proton. In terms of these there are then described those few phenomena of elec- tricity which are essential to the later consideration of the evidence. In this way, it is hoped most rapidly to introduce the reader to modern theories as to the invisible workings of the physical universe. J. M. WYOMING, N. J. June, 1921. CONTENTS CHAPT1 2R PREFACE PAGE iii INTRODUCTION vii I ATOMIC STRUCTURES 1 II SATISFIED AND UNSATISFIED SYSTEMS . . 11 III THE PERIODIC TABLE OF ATOMIC SYSTEMS . 20 IV MASS AND INERTIA OF ATOMIC SYSTEMS . 37 V RADIOACTIVE DISINTEGRATIONS . ^ 48 VI CONDUCTION OF ELECTRICITY THROUGH GASES 57 VII CONDUCTION THROUGH SOLIDS AND OTHER ELECTRICAL PHENOMENA 69 VIII THE PROOF FOR THE EXISTENCE OF AN ELECTRON 84 IX ISOLATING A PROTON 99 X X-RAYS AND ATOMIC NUMBERS .... 115 BETWEEN CHAPTERS A DIALOGUE . 135 XI PHOTO-ELECTRIC EFFECTS AND THE QUAN- TUM OF ENERGY 139 XII LIGHT RADIATION AND ATOM -MODELS . 155 XIII MORE EVIDENCE FOR THE QUANTUM HY- POTHESIS 168 XIV ENERGY AND ITS AVAILABILITY .... 184 APPENDIX THE MAGNITUDES OF ELECTRONS AND QUANTA 195 GLOSSARY . . . 207 INTRODUCTION IN the constellation of Orion is the bright reddish star Betelgeuse. For centuries it served with other stars as a guide to mariners and as an object for consideration by philosophers and myth makers. Although we still retain the name given to it by the Arabs and still see it as the right shoulder of the mighty hunter, science has removed all but the nomenclature of the earlier animistic interpretation and substituted cold quantitative facts. Since our school days we have known that Betelgeuse is a sun, essentially like that which illuminates our earth. Very recently we have been told by Pro- fessor Michelson of Chicago as to its astounding magnitude three hundred times the diameter of our own sun. The methods by which he arrived at this relationship involve* interesting theories and required precise experimentation. Like the news- papers, however, of the day following his announce- ment let us be content for the moment with the fact itself. In the midst of the universe in which Betelgeuse is but a speck exists a smaller sun on a planet of which there crawl what Bertrand Russell aptly called tiny lumps of impure carbons and water. What a shock to the "ego-centricity" of these car- bon compounds to realize their quantitative in- significance in comparison with Betelgeuse. vii viii WITHIN THE ATOM About this larger sun there are probably en- circling planets. Are there organic compounds on any of these and how do they arise from inorganic compounds as the ageing planet slowly cools? Are there conditions of temperature and atmospheric content which are accompanied by such chemical changes? If organic substances can be formed will life appear on the planet? What intimations of the evolution of life can be found in modern science? Our questions grow by association, overlapping one another, repeating and varying their content; and our apparently unbound speculation leads only to further questions. Some answers and much ma- terial for thought are vouched by modern science although the specific question as to the mechanism and process hi the evolution of life remains un- answered. What in fact do we mean by life? The cater- pillar in its cocoon awaits the proper temperature for its metamorphosis: the radioactive atom spon- taneously emits an electron and becomes a new substance. Both caterpillar and radioactive atom are but stages in a sequence of events, the one to be followed by more caterpillars all of which will differ slightly from the original and the other by more atoms which will differ radically from the original. The comparison is not too seriously in- tended although it is safe to say that the offspring of the radium atom will be moving in fast circles ages after the descendants of the moth have per- ished from the face of the earth. When we have reached a satisfactory definition INTRODUCTION ix of life shall death be its negative? Are life and death merely convenient terms which we loosely apply to phases in a wide process of continuous change? and what are the entities which are con- served during the change? To the last question science today may apparently give answer for in energy and in electricity it has two entities which are conserved in amount. The former manifests itself by changes in the location of the latter, for electricity is the only known constituent of the ponderable matter of which our universe is com- posed. Whether we are interested in speculative ques- tions like those just mentioned, in less speculative but yet unsolved questions like the mechanism for the transmission of stimuli by nerves, or in the purely practical matter of the efficient organization and operation of the multiplicity of machines which condition our daily lives, we must seek explanations in terms of energy and electricity. The reduction of the number of unknowns with which science deals is a recent advance which has followed discoveries like those of radium and X-rays. Widely different branches of science are now known to be dealing with the same funda- mentals of electricity and energy. For the first time in centuries there exists the material which a genius could synthesize into a universal science, in which physics and chemistry, biology and geology, will lose their identities in a common set of principles. So rapid, however, has been the advance of sci- ence toward this simplification of terms and prin- x WITHIN THE ATOM ciples that few except those immediately concerned are aware of the possibilities. With the change of base and point of view which has followed the dis- covery of the electron, and the consequent interre- lation of branches of science long held apart, there have arisen innumerable questions which occupy the time of those best able to expound the new science. Our schools follow but tardily in their elementary classes the conclusions of researchers in science and our text-book writers must comply with existing distinctions between branches of science. The fundamental concepts of the new science are easy to grasp and may be stated in relatively simple terms, although the quantitative relationships are to be expressed only in mathematical symbols. The complete synthesis may be upon us some day as unexpectedly as were Einstein's hypotheses and presumably to find us as unprepared. For its critical consideration but few will be competent. For a more popular appraisal many of us may be prepared if we have learned to think of all scientific problems in terms of electricity and energy. Unfortunately the popularizer of these concepts must run some risk of false statement for he is limited first by his own knowledge and interpreta- tion of the accepted body of scientific truth, and second by the necessity of purely verbal expression. Word pictures are all that he may give and the selection and emphasis of their material may carry implications which tune shall disprove. One difficulty which confronts those who would impart the concepts, evidence, and conclusions of INTRODUCTION xi modern science to readers untrained or impatient of mathematical formulation, arises from a weakness which is characteristic of modern research itself. Science today is quantitative rather than qualita- tive. It expresses the relationship of the intensities of two phenomena, as for example the intensities of the electric current and of the illumination of an incandescent lamp, and compensates for its in- ability to answer the question "how" by its wealth of data as to "how much." Research monograph and text-book alike emphasize the observable quan- titative relationship and rarely venture far into the speculative hinterland where "how" must precede "how much." As we teach science today in our schools the effort of learning the quantitative rela- tionships too frequently leaves neither the instruc- tor nor the student leisure for fruitful inquiry or speculation as to the mechanism itself. Rare indeed is the Faraday whose pictures of in- visible processes satisfy and vivify quantitative relationships during a century of fruitful research. That particular genius was discovered by Sir Humphrey Davy, himself a broad and versatile mind. One wonders whether our phonographic classroom methods and the machine processes of our laboratory instruction can create an environ- ment for that inspiration of another Faraday which the present development seems to require. Faraday's pictures were in the nature of working hypotheses as to an all-embracing and continuous medium an elastic ethereal medium. Assuming that an ether existed, the attraction or repulsion of xii WITHIN THE ATOM electrified bodies was explainable, in terms of the strains which the bodies introduced into the me- dium, without recourse to a theory for action at a distance. During the later half of the 19th century, the assumed medium became of first importance and scientifically electricity was in danger of becoming a phenomenon of the very medium which had been assumed to explain its own phenomena. The emphasis on the medium, however, had happy re- sults for it led Maxwell to the conclusion that light was an electro-magnetic phenomenon. With the discovery of the electron the appar- ently indivisible particle of electricity the ether rapidly lost its importance and finally with the work of Einstein it has ceased to be a necessary postulate in physical science. The terminology of the older physics of the ether is unavoidable, however, if one approaches the new physics of electrons in the historical order of its evolution. Such a method of presentation has the advantage that the experimental evidence* may be set forth in conjunction with each statement of fact. On the other hand, the method demands on the part of the reader a knowledge of the phenomena and laws of electricity, mechanics, and chemistry which is seldom possessed by the hypothetical per- son "the general reader." This deficiency may, of course, be supplied by devoting to that purpose the earlier chapters of an exposition, but several of these would raise memories of high school text- books. The facts which must be acquired would INTRODUCTION xiii of necessity be presented in a conventional manner. It would, therefore, be necessary to return to them, after treating the fundamentals of the new science, and attempt a corrective interpretation in the new terms. The process would not only be wasteful of time but difficult of attainment for first impres- sions, even of science, lie deep in the mind. It is perhaps better to start out boldly, stating the physical basis of the new science and building as far as practical on its firm foundation. For cer- tain portions of the superstructure only sketches are available, and for others not even such indica- tions. Occasionally there may be sketches of sev- eral draftsmen neither of whom seems destined to be accepted as the final designer. Enough material, however, may be inspected by the reader so that he may appreciate the problem of the new science and the point of view. Only when the structure is partially completed should the reader be expected to recognize its relation to the science of his own school days, for the new science starts with the invisible and intangible entity of electricity. WITHIN THE ATOM CHAPTER I ATOMIC STRUCTURES THE story is told of the debutante who met the renowned astronomer, the lion of the evening, with an appreciative remark as to the wonders of as- tronomy, "And do you know I think the most wonderful thing is how we know the names of the stars." Now imagine, if you can, two types of particles, each invisible, intangible and infinitesimal in the ordinary senses of these words, and indeterminate in form and substance. For one type, wonderfully enough, we know the name "electron," but for the other type there is no agreement. We are free to choose from a number advanced by various scientists and shall arbitrarily adopt the term "proton." Electron and proton are complementary. To- gether they may merge in a union so close that their combined size is less than that of the electron alone. Such a statement may sound absurd but experi- ments seem to indicate that the union of two or more protons with one or more electrons is a smaller particle than is a single isolated electron. The form 1 THE ATOM and size of the electron and proton must then be different in combination from that of the free elec- tron and free proton respectively. We apprehend at the start two types of particles both invisible but both independently observable by certain effects which they produce. To these we ascribe complementary properties. In so doing we meet at once a serious difficulty of existing language for there is a paucity of terms by which we may describe the particles without connotations of an animistic bias. The protons and electrons are com- plementary, mutually supplying each other's needs. Electrons, however, are mutually antagonistic and depart from each other's presence unless restrained. The same is true of protons. It is only by virtue of the complementary properties of proton and elec- tron that two or more electrons, for example, are constrained to the same infinitesimal space. A close union of a group of protons and electrons is conceivable from a social parallel for it may re- semble geometrically the careful seating of guests at a large dinner. Between those of opposing in- terests might be placed others whose interests are mutual with those of their immediate neighbors. The dinner guests have various degrees of sym- pathy and antipathy for each other. Between elec- trons, however, there is but one degree of antago- nism since all experiments point to the exact similarity of all electrons without regard to then- individual histories. The same apparently is true of protons although the isolation of the latter has been a more recent advance and there is not as ATOMIC STRUCTURES 3 large a volume of evidence in this case. We are probably entirely safe in assuming that protons are indistinguishable and are interchangeable to an ex- tent that would excite the admiration of the piece- part manufacturer of the present days of quantity production. Any grouping of antagonistic elements, for ex- ample, electrons, can persist only by virtue of the presence of the complementary type, in this case protons, and by virtue of such geometrical arrange- ment that the opposing tendencies of the elements of the same type are neutralized by the complemen- tary tendencies of elements of a different type and in part by tendencies which are discussed on page 76. According to some theories, however, two elec- trons or two protons are pictured as mutually at- tracted when they are very close together, although at larger separations they are repellent. Similarly an electron and a proton would start to repel each other after they had approached to within a certain small distance of each other. In any case the permanence of a group of protons and electrons will depend upon the geometrical arrangement. The picture which we may form is like that of some state of society where man shuns man, and woman avoids woman, but unrestricted promiscuity prevails. Pro- miscuity, however, carries no stigma for individu- ality is entirely lacking. In many ways their society approaches an angelic state, for its members are not confined to a terres- trial plane but hover and flit about in space, subject to the opposing tendencies which were just men* 4 WITHIN THE ATOM tioned. Nor are their antagonisms destructive like those of humans, despite the fact that electrons may rush about with a speed almost that of light. Actual collisions between like elements are always avoided by swerving to one side or in the extreme instances of head-on approach by retracing their paths. A deathless existence these particles lead and although there is marriage and giving in mar- riage the unions are fruitless. The number of elec- trons or of protons in our universe is believed to be eternally fixed so that their immortal society may alter only in its configurations. Such new configurations as these elements may assume are formed under the action and in con- formity with the laws stated figuratively above. In more classical terms these may be expressed by saying that like elements repel and unlike attract. To place this idea completely beyond the animistic bias two words of recent coinage and incompletely sanctioned usage may be employed. Electrons pellate, protons pellate, but an electron and a proton tractate. The law reminds one of that for the action of electrical charges, since like charges repel and un- like attract. It may be admitted at once that elec- trons are elements of so-called negative electricity and protons elements of positive electricity. It is preferable, however, to consider further this ques- tion of configuration of these elements before at- tempting to relate our present treatment with the familiar facts of electricity. We shall nevertheless ATOMIC STRUCTURES 5 find it most convenient to speak of electrons and protons as the "electrical elements." The electrical elements are found associated in configurations which increase rapidly in complexity as we pass from the simple union of one proton and one electron to systems which involve hundreds or thousands of elements. When more than one pro- ton is involved two types of systems are possible. In the simpler type all the protons are associated in a compact group which comprizes also sufficient electrons to secure a certain degree of stability for the coalition. Such other electrons as may be asso- ciated with the system under consideration are external to the compact group or nucleus as we shall call it. This simpler type of system we shall call atomic, and to the question of its stability we shall return later. The second type of system is that which involves two or more nuclei and associated external elec- trons. Again we postpone the question of degree of stability and class such systems as molecular. For completeness we should mention at this point also systems which may be formed by combinations of the two main types. A number of similar sys- tems, for example, molecular systems, may become closely associated by a temporary relinquishment of individual freedom and form a federation, to borrow a term which closely fits. As long as the external conditions remain as they were this federa- tion may persist but its component members may on occasion and without prejudice assume again 6 WITHIN THE ATOM their individual existences. Polymeric systems of this kind are of frequent occurrence. As the opposite of polymerization there is dis- sociation, the process of separating a polymeric or even a molecular system into the smaller systems which compose it. With the latter process particu- larly we shall have more to do later. For the moment, however, we shall consider only the simplest type of system, namely the atomic, which is formed by a nucleus and a number of elec- trons external to it. In the nucleus there are al- ways more protons than electrons. It is this excess of protons that serves by virtue of their inherent complementary characteristics to retain in the region immediately external to the nucleus a num- ber of electrons. Consideration will be further limited by exclud- ing for the present all systems in which the total number of electrons, including those external to the nucleus as well as those comprized by it, is unequal to the number of protons in the nucleus. Systems in which there is numerical equality be- tween protons and electrons we shall call normal atoms or, more conventionally, uncharged atoms. We shall further find it convenient to classify such atomic systems by the number of electrons external to the nucleus, or what amounts to the same thing by the excess of protons in the nucleus. This num- ber will be designated the "atomic number." The largest known atomic number is 92 and this corresponds to the chemical element uranium, a metallic element found in pitchblende. It was in ATOMIC STRUCTURES 7 residues of this mineral, from which the uranium had been extracted, that Professor and Mme. Curie discovered the element radium. Radium has an atomic number of 88. Another chemical element, which has a large atomic number, is thorium, a rare metal used in making incandescent gas mantles. Its atomic number is 90. Atomic systems with such high atomic numbers are very rare in the collector's sense of the word. Let us imagine a period long past in the history of our universe when such systems predominated even to the exclusion of systems of smaller atomic num- bers. Their nuclei were crowded spaces filled with antagonistic electrical elements insecure coalitions ready if necessary to sacrifice some of their mem- bers. Whether under external influence or solely from internal causes these coalitions started to expel their members. The electrons left as indi- viduals, ejected with enormous velocity, or in com- pany with protons with smaller velocities as be- fitted a larger party. Such a party was apparently composed of four protons and two electrons, and to it we give the name "alpha particle." Under some conditions the reduced coalition would be left so unstable by such action that a further expulsion would be necessary in the next few seconds. Sometimes days would elapse and under other conditions years or even ages might pass before such violent readjustments again took place. Today we may observe the same process in the case of atomic groups of high atomic numbers 8 WITHIN THE ATOM the so-called radioactive elements. The changes in nuclear composition appear in the case of these elements to be independent of external conditions and to occur solely because of the need of readjust- ment on the part of the elements of the nuclear coalition. By a sequence of expulsions of electrons and of alpha particles the highly complex nuclei of the prehistoric atomic systems were reduced in number of electrical elements and increased in stability until finally the apparently stable atomic structures of our ordinary chemical elements were attained. In other words, we may consider the chemical elements like tin, lead, sulphur and oxygen to be "end- products" of a long series of radioactive changes. The character of these changes and the alterations in the properties of the atomic systems which result will be discussed in considerable detail in later chapters. Although the disruption of the complex nuclear structure of a radioactive atom is spontaneous in the sense of occurring without the stimulus of ex- ternal agents, similar disturbances do not occur simultaneously in all the individual atoms of a large group. Some of the atoms of a bit of uranium, for example, or of radium, are always breaking down. The product of the disintegration may be removed by trained experimenters and hence the rate at which it is formed may be measured. Know- ing the rate at which disintegration is occurring, it is a matter of simple mathematics to calculate the average life, that is the time required until half ATOMIC STRUCTURES 9 the original atomic systems will have disintegrated. This is using the term "average life" as actuaries do, for of course some of the atoms may last for ages without dissociating. In the case of radium the average life is estimated as about 1600 years; that is, it should require that time for half the atoms of any bit of radium to become changed into atomic systems of smaller numbers of elements. Curiously enough the next atomic system, a gaseous element known as "niton," has a short average life of only five or six days. The atomic number of niton is 86, for it is the result of the ejection of an alpha particle from the nucleus of the radium system, which has an excess of 88 protons. The alpha particle is itself an atomic system, al- though it is not a normal or uncharged atom since it involves more protons than electrons. If two external electrons are associated with it, it becomes a normal atom, namely that of helium, a light in- active gaseous element which has recently attracted public attention as a desirable substitute in filling balloons for the lighter but active element hydrogen which burns with oxygen. It was perhaps by such spontaneous changes in the composition of the nuclei of atomic systems, as are illustrated today by radium, that the known chemical elements were produced. The definition, however, of the term "chemical element" is no longer as simple as it was in the days before this disintegration theory was advanced and accepted by scientists. Until we have discussed with further 10 WITHIN THE ATOM detail the possible changes which may occur in atomic systems, we may use the term in its usual sense, and say that the eighty, or so, known chem- ical elements are the products of radioactive dis- integration for which the further disintegration is so slow as to be negligible or inappreciable. For all practical purposes, however, we may assume that our chemical elements are end-products of pre- historic disintegration. CHAPTER II SATISFIED AND UNSATISFIED SYSTEMS IT is difficult to describe the interactions of the electrical elements without recourse to words which have an emotional significance. Words like stable and unstable, or active and inert, might be used but they have scientific connotations which are bet- ter avoided at present. In continuing the discussion of atomic systems we shall use words which are frankly animistic and classify these systems as sat- isfied, unsatisfied, or dissatisfied. The radioactive systems which were described in the previous chap- ter are evidently violently dissatisfied systems. A failure of satisfaction may be the result of a deficiency in the quantity or in the quality of the desired good. Quantitatively an electrical system is satisfied if there is an equality in the number of protons and electrons which comprise it. Satisfac- tion as to quality, on the other hand, depends upon the configuration of the component elements of the system. Dissatisfaction when it occurs is deep seated a neurotic condition of the nucleus which may re- sult without any external stimulus in violent out- bursts and a veritable orgy of smashing china and throwing things about. This excitable state is 11 12 WITHIN THE ATOM characteristic of those atomic systems which have retained their youth and been unchanged by the years. When they shall have become as lead, a long peaceful life will confront them, in which they may be at times unsatisfied but practically never dissatisfied. During the formative years of their discontent the nature of their dissatisfaction adapts itself to their condition, being now concerned with quantity and again with quality or configuration. At times they throw off alpha particles and thus find themselves with an excess of electrons which are a source of dissatisfaction in their innermost and nuclear hearts. The electron which is then ex- pelled from the nucleus is sometimes spoken of as a beta particle. By expulsions of alpha and beta particles the radioactive systems lose much of their energy and all appearances of radicalism. For a time, however, we shall deal with the con- servative atoms which never become more than mildly unsatisfied. Systems which are unsatisfied in the numerical equivalence of protons and elec- trons show the effect of electrical charges. The consideration of these effects also must be post- poned and our attention fixed upon systems which are satisfied in this quantitative relationship but are unsatisfied in the configuration of their com- ponent elements. Such absence of satisfaction as then exists is solely a matter of the arrangement of the electrons external to the nucleus since, if the source of the trouble were in the latter, dissatisfac- tion would be manifest unmistakably. The electrons which are external to the nucleus SATISFIED AND UNSATISFIED SYSTEMS 13 of an atom are separated from it and from each other by relatively large distances. Perhaps as good a picture of an atomic system as may be easily formed is obtained by a comparison with our solar system. The distances between sun and planets and between the various planets are very large as compared to the diameters of any of the planetary bodies. If we now imagine the sun to be very small as compared to the earth and then imagine all the distances and sizes to be proportionally reduced until the system is invisible even with the most powerful microscope we have a possible picture of an atomic system. The sun is first made smaller because the nucleus is small compared to the elec- tron. Some dimensions of such a system are quite accurately known for they are determinable by methods which will be described later. The diameter of the atom depends upon its con- struction, being smaller for some chemical elements than for others. If we wished, for example, to keep out of the way of a hammer thrower, starting his turns, we would assume that his diameter was that of the circle through which the hammer head swung. In much the same way the diameter of any atom is that of the circle of which the center is the nucleus and the radius the distance to the outer- most electron. The hydrogen atom is composed of only one proton and one electron. The two elements are probably whirling about each other in space much like a rapidly whirling dumbbell except that there is no direct connection between the ends of the 14 WITHIN THE ATOM dumbbell. Its diameter is about two hundredths of a millionth of a centimeter, but this is about one hundred thousand times as large as that of the electron so that the diameter of an electron is about two tenths of a millionth of a millionth of a centi- meter. The other atoms are not so simple. The helium atom, of which we have spoken before, consists of a nucleus and two external electrons. The atom of sodium has eleven, and that of chlorine seventeen electrons, external to the nucleus. We do not know as much about the arrangement of the electrons in the atomic structures as we should like or as we probably shall in the near future. For the purpose of discussing the effects of the configuration of the external electrons we may, however, draw one or two parallels of a kindergarten nature which will serve in default of more authoritative pictures. The system of nucleus and external electrons may be likened to a few children playing a circle game about a teacher. Suppose that the game goes best with eight in the ring but is possible with any num- ber between six and ten. If ten are playing, that is if the teacher's responsibility is for ten, as might be the case for electrons if the nucleus has ten excess protons, then there is some crowding. An oppor- tunity for two children to join an adjacent but less crowded circle will be welcomed by the children, and by the teacher also, if she can satisfy her quantita- tive obligations by supervising their play in a neighboring circle. An atom with a circle crowded by electrons is in SATISFIED AND UNSATISFIED SYSTEMS: 15 an unsatisfied condition which is favorable to losing electrons. If it does so it will have more protons than electrons. This tendency towards an excess of protons is ordinarily described by calling the atom electropositive. It can supply electrons to any other atom which can accommodate them in its circle. If it does so, however, the two atoms must remain together for each nucleus has responsibility for a definite number of the total of electrons.' For such a combination into a molecule the second kind of atom must have a complementary need, having fewer electrons than can be satisfactorily accommo- dated in its ring. Its tendency to acquire added electrons is indicated by calling it electronegative. If an atom has a ring of electrons just sufficient to play their circle game without crowding there will be no need for loaning or borrowing from an adja- cent atom, and hence no occasion for combination into a molecule. The elements with atoms of this character are "inert" substances such as the gases helium, argon, neon and krypton. Niton is also an example of such an arrangement. Niton, however, is inert only as far as concerns its possibility of com- bination with other atoms, for, due to its radio- active properties, it can very markedly influence the chemical behaviour of other substances. So far as concerns the combination into molecular systems of two different kinds of atomic systems, we should expect electropositive atoms to unite with electronegative ones. Common salt, Nad, is the combination of the electropositive sodium atom, which would spare one electron, with the electroneg- 16 WITHIN THE ATOM ative chlorine atom, which would accommodate an extra electron. In forming the molecule the electrons probably redistribute themselves about the two nuclei. Under certain conditions the combination so formed may be broken up into two new systems, which are slightly different from the original sodium and chlorine atoms. If salt is dissolved in water some of its molecules separate into these two parts. One has the nucleus of a sodium atom and the other that of a chlorine atom. The number of electrons about each of these nuclei is not that of the normal atom. In the process of separating, the electron which was borrowed by the ring about the chlorine nucleus is not returned. The chlorine nucleus and its ring with an excess electron is not a chlorine atom, nor is the sodium nucleus with its ring, which has lost an electron, an atom of sodium. When ordinary table salt breaks up in solution, it does not give the elementary sub- stances of sodium and chlorine, neither of which is a possible food. These new atomic systems move about in the solution exactly as do unsplit molecules. To them is given a new name, that of "ions" since they are go-ers. Sometimes they come together in their wanderings and for a tune form again a salt molecule but later they may break apart. The phenomena of solution and in fact all matters having to do with the motions through space of atomic or molecular systems must be postponed. The dissociation of the molecular system of sodium chloride into atomic systems has been cited as a step SATISFIED AND UNSATISFIED SYSTEMS 17 toward the fuller study of the combination of atomic systems into molecular systems. When the sodium ion, that is the positive ion, comes into the imme- diate neighborhood of the chlorine, that is the nega- tive ion, recombination will again occur although a dissociation may immediately follow as the result of those external influences which we are at present assuming without explaining. Ions are atomic systems unsatisfied in quantity rather than in configuration of electrical elements. Combination of atomic systems into molecular sys- tems is, therefore, seen to occur as the result of either type of unsatisf action. For historical reasons both of the kinds of combination, which we have pictured above, are called chemical combinations without regard to our more recent knowledge that they are entirely electrical phenomena. The ability of an electropositive atom, for ex- ample sodium, or of a negative ion, for example the chlorine ion, to enter into a molecular combination depends (as we have seen) upon the possession of one (or more) electrons in excess of those requisite to satisfaction in configuration or in quantity, re- spectively. We may therefore express the ability x>f an atomic system to combine, which is conven- tionally termed its valence, in terms of the number of electrons which measure its unsatisf action. Thus we may say that the atomic systems mentioned .im- mediately above have a positive valence of one. The atoms or ions which become the partners in such combinations have a complementary need of elec- 18 WITHIN THE ATOM irons. They may be described as having a negative valence of one. For a satisfied system, that is for an inert atom, the valence is, of course, zero. The satisfaction of that need on the part of an atomic system which is expressed quantitatively by its valence may be obtained in a number of ways. A monovalent atomic system like sodium requires only another monovalent system, like chlorine, which has a complementary need to form a satisfied molecular structure. A divalent atom, on the other hand, may be satisfied by a union with another divalent atom or with two monovalent atoms. In the latter case the two necessary atoms may be of the same kind or different. In the molecular system oj: water the divalent oxygen atom is combined with two similar monovalent hydrogen atoms. The symbol H 2 0, in which the subscript indicates the number of atoms of the type to which it is affixed, is a convenient representation of this combination. In similar man- ner the molecular system formed by the divalent oxygen atom with two unlike atoms of sodium and hydrogen is symbolized as NaOH. Many atomic structures attain satisfaction by combining into molecular form with others of their own type. Thus hydrogen normally exists in a diatomic molecular state represented as H 2 . The same is true of oxygen which forms a molecular sys- tem of O 2 . In such cases we find a combination of two atomic systems with similar rather than comple- mentary needs. The rearrangement of the electrons about the two nuclei, apparently, results in a more SATISFIED AND UNSATISFIED SYSTEMS 19 stable configuration than exists in the individual atomic structures although sometimes not as stable as it might be. A spark will explode a mixture of hydrogen and oxygen and result in two molecules of water being formed from one molecule of oxygen and two molecules of hydrogen. The operation is con- veniently symbolized as 2 + 2H 2 > 2H 2 O. The atomic system of oxygen is the great joiner and has fraternal relations with all except the most deadly dull and inert atoms. 1 It belongs to thou- sands of complex molecular societies. Associated with hydrogen it enters as water of crystallization into secret organizations of molecules of which it is not a bona fide member but from which it may be expelled only by heated action. Even then all the water molecules do not leave with equal readiness for some resist expulsion with considerable tenacity. It was largely by a study of combinations of oxygen with nitrogen that Dalton arrived at his well known laws as to molecular composition. The substance of these laws has been tacitly assumed in our earlier discussion. The unit in chemical combinations is the atomic system; and molecular systems are formed only from whole numbers of atomic systems. 1 And fluorine. CHAPTER III THE PERIODIC TABLE OF ATOMIC SYSTEMS AN atomic system is formed by a nucleus and a number of electrons external to it. In the configura- tion of these external electrons is to be found the secret of the ability of one atomic system to combine with one or more other systems to form a molecular system. The valence, which measures this ability to combine, may be positive or negative depending upon whether the system under consideration is un- satisfied as the result of too many or of too few electrons for a stable configuration of the external electrons. In the nucleus there is always an excess of protons and the number by which this excess is specified is known as the atomic number. The largest known atomic number is 92. On the basis of atomic num- bers, therefore, a classification may be established of 92 types of atomic systems. These types may then be cross-classified on the basis of valence. As we proceed from one type of atomic system to that with the next atomic number there is a change of one in the number of excess protons in the nucleus and a corresponding change of one in the number of external electrons. For example, let us enter our system of classification by atomic numbers 20 PERIODIC TABLE OF ATOMIC SYSTEMS 21 at the eleventh type, which is that of the sodium atom. We must picture this atomic system with eleven excess protons in the nucleus and eleven ex- ternal electrons, the actual configuration of which is still problematical. Despite the fact that there is a quantitative balance between the protons and the electrons, of complementary properties, there is a lack of satisfaction in the portion of the system comprised by the external electrons. In the system of next smaller number there are ten external electrons; and with the reduction in number the unsatisfaction has disappeared, for the tenth typical system is that of neon, an inert atom. The equivalence of number of protons and electrons still remains for both kinds of electrical elements have undergone the same reduction in number. The external electrons, however, no longer crowd each other. What would one naturally expect as the atomic number is further reduced? Eleven electrons crowd, ten do not, but nine are too few for satisfaction of the requirement of stability. The atomic system of the ninth type, known as fluorine, despite its quantitative satisfaction, is unsatisfied in configura- tion by one electron. Like the sodium system it also has a valence of unity but negative instead of positive. The satisfied atomic system is thus seen to occur as a transition between systems of negative and posi- tive valence. Such transitions occur at the atomic systems of helium, neon, argon, krypton, xenon, and niton for which the atomic numbers are respectively, 22 WITHIN THE ATOM 2, 10, 18, 36, 54 and 86. For convenience the names of the various types of systems corresponding to the atomic numbers below 22 are given in the accom- panying table. TABLE I THE NAMES AND NUMBERS OF THE ATOMIC SYSTEMS 1 Hydrogen H 12 Magnesium Mg 2 Helium* He 13 Aluminum Al 3 Lithium Li 14 Silicon Si 4 Beryllium Be 15 Phosphorus P 5 Boron B 16 Sulphur S 6 Carbon C 17 Chlorine Cl 7 Nitrogen N 18 Argon* A 8 Oxygen O 19 Potassium K 9 Fluorine Fl 20 Calcium Ca 10 Neon* Ne 21 Scandium Sc 11 Sodium Na 22 Titanium Ti * Transition system The atomic system for which the atomic number is one less than that of a transition system has a negative valence of one, and the system of the next greater number has a positive valence of one as in the case just mentioned of the sequence fluorine, neon, and sodium. Progressing toward higher num- bers the positive valence increases, and toward lower atomic numbers the negative valence. In progress- ing from one satisfied system to the next as, for example, from neon to argon, there must therefore be another kind of transition from negative valence to positive. Between these satisfied systems there are three types with positive valence of one, two and three, respectively, namely, sodium, magnesium, and aluminium, and three types, namely, chlorine, sulphur and phosphorus, with the corresponding values of negative valence. PERIODIC TABLE OF ATOMIC SYSTEMS 23 The middle system of the sequence, which we are considering, is like a hostess who is planning a din- ner. Shall she invite four more guests or four less? The decision will depend upon circumstances, that is upon who the guests are to be, but the number she will add or scratch from her list is preferably four, since that will make a satisfactory grouping. Some- times she makes one choice and again the opposite choice and the same is true of the atomic system of silicon. Its valence is four but it is amphoteric for it partakes of the character of both electroposi- tive and electronegative elements. The simile of the hostess, however, is inadequate, because the electrons are disposed about the nucleus in a space of three dimensions. The pictures of their disposition, which have been proposed from time to time, are all incomplete and none has been gen- erally accepted by scientists. The successful picture must account for the known facts of chemistry and also for those facts of physics which relate to the radiation of light from atomic structures. The maxi- mum number of electrons which may be concerned in atomic phenomena is, of course, definitely known since the atomic numbers are well substantiated facts. The grouping of these electrons, however, is still in the stage of hypothesis and the picture which will now be given is merely that which today most satisfactorily accounts for the largest number of the known phenomena. We imagine * that the electrons are disposed about the nucleus as if they lay in the shells of one of those 1 According to Lewis and Langmuir. 24 ' / WITHIN THE ATOM Chinese toys which consists of a concentric series of wooden egg-shaped shells. Let the innermost egg represent the nucleus. In the next or first shell there may be one or two electrons, one in the case of hydro- gen and two in that of helium. The latter condition would obviously admit of a stable structure in which electrons on diametrically opposite sides of the nucleus were held in the system, because they trac- tate with this nucleus, despite the fact that they pellate with each other. Because of this electrical stability, the atomic system of helium is inert. Except for the hydrogen system all atomic struc- tures have these two electrons. The unsymmetrical configuration of the hydrogen system accounts for its extreme activity as a chemical element, and also for its formation of diatomic molecules of hydrogen gas. When an atomic system contains more than two external electrons, all electrons in excess of two are disposed on shells external to that which was just described. The next outer shell is believed to be twice as far from the nucleus, and hence to have four times the superficial area. In it a total of eight electrons may be located. The atomic system which has one electron in this second shell is that of lithium. This atom readily parts with its third electron and assumes the more stable configuration of the helium atom. That is what takes place when the molecular system of lithium chloride, LiCl, dissociates into a lithium ion and a chlorine ion. Geometrically a lithium ion is similar to the stable helium atom, but it does not act at all similarly because the nucleus of lithium PERIODIC TABLE OF ATOMIC SYSTEMS 25 has three excess protons instead of the two of helium. With two electrons in the second shell the atomic system is that of beryllium which has a positive valence of two since it takes the loss of two electrons to convert it into the stable configuration of the helium system. Boron is a system with three elec- trons in this shell. When the number is four, there is reached the important system of carbon which enters into all organic compounds. Its four external electrons in pellating with each other probably take places such as to form the corners of a solid figure of four equal sides. Nitrogen has five, oxygen six, fluorine seven, and neon eight electrons in this second layer. In the last case the electrons will dis- tribute themselves four on each hemisphere, so that they form the corners of a cube at the center of which is the inner shell with its two electrons and within this the nucleus. The inertness of the neon atom is well accounted for by this symmetrical and stable arrangement of external electrons. The system of fluorine with its seven electrons in the second shell may be considered either as having seven too many for such stability as is possessed by the helium system, or one too few for the stability of the neon system. In other words, it has either a positive valence of seven or a negative valence of one. Oxygen has six and two respectively. The re- arrangement which is required to make these sys- tems stable, that is satisfied in configuration, is less if electrons are added than if they are subtracted, so that such systems tend in combination to attain their satisfaction by borrowing from the other com- 26 WITHIN THE ATOM ponents of the molecular systems in which they are associated. In the dissociation of such molecular systems the atom tends to retain its satisfaction by a failure to return the borrowed electron which amounts to an actual theft. Dissociation, therefore, results in the formation of negative ions, that is those with a quan- titative excess of electrons. In a large number of cases of molecular systems the electrons are shared so that borrowing and theft do not occur. It seems probable, however, that in- dividual electrons may not be shared but only pairs of electrons. 1 It is further believed that in the shar- ing of pairs of electrons the adjacent atomic groups so combine as to form as nearly as possible stable arrangements roughly similar to that of the neon atom, that is groups of electrons at the eight corners of a cube, at the center of which is a kernel com- posed of two electrons and a nucleus. This hypo- thetical process is peculiarly adapted to explain, for example, the large number of compounds which are formed by oxygen with nitrogen. As the number of external electrons is increased beyond ten a new outer shell is required. Let us picture this third shell as practically coincident with the second. The first electron to be disposed in it occupies a position with much the same precarious- 1 Chlorine, which forms a diatomic molecule, C1 2 , is a good illustration of the sharing of electrons between the atoms of molecular systems. Each chlorine atom lacks one electron of the number required for satisfaction in configuration. Hence, each atom shares one of its electrons with the other atom of its molecule. The requirements of configuration are thus satisfied, and in effect a pair of electrons is shared. PERIODIC TABLE OF ATOMIC SYSTEMS 27 ness as did the first electron of the second shell, and hence, sodium, the eleventh system, has much the same properties as lithium, the third. For similar reasons there is a periodic recurrence of the properties of beryllium when we reach the twelfth system, that is magnesium, and correspond- ing recurrences until we reach argon, where the shell has its complement of eight electrons. Again we have a stable structure. A new shell, a fourth, is required for electrons in excess of eighteen. This may not be superimposed, as was the third shell upon the second, for these inner shells now hold too many electrons to permit so near a position for additional electrons. The fourth shell is presumably three times as far from the nucleus as is the first and hence its area is nine times as great and its capacity for electrons eighteen instead of two. The first three of the atomic systems which are formed by the addition of electrons in this new shell also partake of the properties of the corresponding three in the two series previously considered. The area of the fourth shell is larger, however, and it is not filled until eighteen electrons are in it. The atomic system which exists when this fourth shell has four electrons has no such amphoteric properties as have silicon and carbon. It has no choice in its method of obtaining stability since to progress to stability would require the addition of fourteen elec- trons, while to regress would require only the loss of four. Similarly the next atomic system, with five electrons in this shell, can have only a positive 28 WITHIN THE ATOM valence. To assume the nearest stable structure, that of argon, would require the subtraction of all five electrons. Here we are met by a choice of kinds of satisfac- tions. A satisfaction of configuration requires the loss of five electrons. As each electron is lost the unsatisfaction as to the discrepancy between num- bers of protons and of electrons becomes more marked. As long as a net balance of satisfaction is attained by losing electrons there will be a tendency to do so. This balance of desires is generally met before all five are lost, for two and three are the usual valences of the vanadium system which we are con- sidering. TABLE II THE NAMES AND NUMBERS OF THE ATOMIC SYSTEMS 18 Argon* A 37 Rubidium Rb 19 Potassium K 38 Strontium Sr 20 Calcium Ca 39 Yttrium Y 21 Scandium Sc 40 Zirconium Zr 22 Titanium Ti 41 Niobium Nb 23 Vanadium V 42 Molybdenum Mo 24 Chronium Cr 43 25 Manganese Mn 44 Ruthenium Ru 26 Iron Fe 45 Rhodium Rh 27 Cobalt Co 46 Palladium Pd 28 Nickel Ni 47 Silver Ag 29 Copper Cu 48 Cadmium Cd 30 Zinc Zn 49 Indium In 31 , Gallium Ga 50 Tin Sn 32 Germanium Ge 51 Antimony Sb 33 Arsenic As 52 Tellurium Te 34 Selenium Se 53 Iodine I 35 Bromine Br 54 Xenon* X 36 Krypton* Kr * Transition system The names of the atomic systems with numbers between 18 and 54 are given in Table II. From this PERIODIC TABLE OF ATOMIC SYSTEMS 29 it will be seen that the systems corresponding to those with 8, 9, and 10 electrons in the fourth shell, namely, those of atomic numbers from 26 to 28, are those of iron, cobalt, and nickel, the three elements commonly known as magnetic. They constitute a family of elements with much in common besides their magnetic property. Although they have about half as many electrons in their outer shells as is required for stability they have a sufficient number to form fairly symmetrical systems. Thus iron with eight electrons might have them disposed at the corners of a cube like that of the outer shell in neon or argon. Nickel also may attain considerable stability with its ten electrons. Their valences, how- ever, would not be zero for the shells are incom- pletely filled. These substances are not inert and yet they possess certain structural advantages over their neighboring systems sufficient to form an oppor- tunistic goal, toward which these other systems may struggle in their quest of satisfaction in form. For this reason some of the systems on both sides of this group partake somewhat of their qualities. For this reason also, starting with the copper system, which is next higher than nickel, the valences again form an ascending series, being one (or two in some cases) for copper, two for zinc, three for gallium, and four for the amphoteric germanium. Beyond germanium, where the shell lacks only four electrons of its complement, satisfaction is most easily obtained by adding electrons and attaining to the form of the inert, stable system of krypton (36). 30 ;, WITHIN THE ATOM The elements from arsenic (33) to bromine (35) correspond, therefore, to those immediately below the other inert elements of neon and argon. Thus bromine belongs to the same family and reacts in the same general way to its electronic surroundings as do chlorine (17) and fluorine (9). In a similar manner the elements rubidium (37), strontium (38) and yttrium (39), which have atomic numbers immediately above that of krypton, tend to revert in configuration to that structure and thus to lose electrons just as do the corresponding systems of the preceding series, namely, potassium (19), calcium (20), and scandium (21). Between the atomic numbers of 40 and 50 the gen- eral characteristics of the atomic systems correspond to those of the previous series for which the numbers are 22 to 32. Again we find the structures of higher number tending to reach satisfaction in configuration by assuming that of the next highest stable system. Thus iodine, the fifty-third system, would attain satisfaction in gaining an electron and becoming in form like xenon, the fifty-fourth, in the same man- ner as chlorine, the seventeenth, would assume the form if not the substance of argon, the eighteenth system. Beyond xenon the names of the atomic systems are given in Table III. A new shell is now required and we imagine one with four times the diameter of the first, sixteen times its area, and a capacity for thirty-two electrons. The first six elements in this new series correspond to the first six hi the two im- mediately previous series. The seventh, of atomic PERIODIC TABLE OF ATOMIC SYSTEMS 31 number 61, is as yet undiscovered. Of the last seven, the one with an atomic number of 85 is also undis- covered. Otherwise the higher elements of this series are like those immediately below the transition sys- tems of xenon and krypton. TABLE III THE NAMES AND NUMBERS OF THE ATOMIC SYSTEM 54 Xenon* X 74 Tungsten W 55 Cesium Cs 75 56 Barium Ba 76 Osmium Os 57 Lanthanum La 77 Iridium Ir 58 Cerium Ce 78 Platinum Pt 59 Praseodymium Pr 79 Gold Au 60 Neodymium Nd 80 Mercury Hg 61 81 Thallium Tl 62 Samarium Sa 82 Lead Pb 63 Europium Eu 83 Bismuth Bi 64 Gadolinium Ga 84 Polonium Po 65 Terbium Tb 85 66 Dysprosium Ds 86 Niton* Nt 67 Holmium Ho 87 68 Erbium Er 88 Radium Ra 69 Thulium Tu 89 Actinium Ac 70 Ytterbium Yb 90 Thorium Th 71 Lutecium Lu 91 Uranium XH Ur Xn 72 92 Uranium Ur 73 Tantalum Ta * Transition systems. Of the thirty-one atomic systems between xenon (54) and niton (86), the first seven (55-61) corre- spond to systems (37-43) and (19-25). The last seven (79-85) correspond in chemical properties to systems (47-53) and (29-35). Both the lower series, (19-35) and (37-53), have intermediate transition systems of which the iron-cobalt-nickel group (26- 28) is the more noteworthy. These intermediate transition systems are believed to be somewhat analogous to the transition systems formed by the 32 WITHIN THE ATOM inert gases in that they have fairly stable electronic configurations, but they differ by being chemically active because they are not completely satisfied as to configuration. In the series which we are now considering there are two such intermediate transition groups, namely, (62-64) and (76-78). Of these the latter, represent- ing osmium, iridium, platinum, is the more impor- tant. The other group contains three rare earths, namely, samarium (62), europium (63), and gadoli- nium (64). Between these two intermediate groups of transi- tion systems there are nine known and two unknown systems, (72 and 75). With the exception of tan- talum (73) and tungsten (74) these are all rare earths metallic elements with positive valences of three. The pictures of electronic configuration which have been proposed to account for the elements be- tween (62) and (77) are not as yet generally ac- cepted and need not be discussed. It is perhaps sufficient to record the fact that chemical properties do not vary sharply with increase in number of planetary electrons when the shell has more than eight electrons, but is not within eight of its comple- ment. Beyond the last inert system, that of niton, there are only a few known systems, and the series termi- nates with uranium from which by radioactive proc- esses many of the lower systems were undoubtedly derived. These few remaining systems require elec- trons in a seventh shell, which we imagine to be Rare, FlQ. 1 Atomic systems at the periodic table. Place numbers corre- spond to atomic numbers. Systems similarly situated, as indi- cated by radial lines, have similar chemical properties. 33 34 WITHIN THE ATOM superposed upon the sixth and to have the same capacity. We may now make a schematic picture of the series of atomic structures as if there were a group of tables to be filled by guests. These tables are roughly concentric as shown in Fig. 1. One by one the atomic systems are seated and the order of their seating is given by the atomic numbers attached to their places. The first table seats only two. The next table eight on each side. The third table, seat- ing eighteen on each side, must place some atomic systems in positions which do not correspond with any of those at the second table. There is, however, a correspondence between atomic systems which are opposite one another at the same table. The fourth table differs in some ways from any of the inner ones and on one side it is only partially filled. In this representation atomic systems which have corresponding characteristics will be found to lie on the same radial line. That corresponding to the stable systems is marked zero. The others are marked with Roman numerals for the convenience of those who wish to compare with the usual tabular presentation of the periodic series of the chemical elements. Intermediate transition systems are indi- cated by VIII. To a very large extent the elements correspond in positive valence to the Roman nume- rals, thus the elements of group I all have positive valences of one although copper may also have two and gold may have three as values of valence. For groups beyond IV, the exceptions become more frequent as is evident from Table IV, where the PERIODIC TABLE OF ATOMIC SYSTEMS 35 PB| *<* o Oi ' a fcO 0*? * PH oo 43 ? - FlG. 34 Curves showing relation of intensity of radiation and frequency of radiating source at different temperatures. portional to the absolute temperature. There is thus a displacement of the frequency of maximum radiation toward the ultra-violet portion of the con- tinuous spectrum as is shown graphically hi the curves of Fig. 34. MORE EVIDENCE FOR THE QUANTUM 175 The other law, due to Stefan and Boltzmann, states that the total radiation from a heated body varies as the fourth power of the absolute tempera- ture; thus if the temperature is doubled the rate at which energy is emitted is increased sixteen times. It is also illustrated by the curves of Fig. 34. We are now ready to consider the occasion for Planck's development of the quantum theory. Up to the beginning of this century, when he made his contribution no adequate theory had been developed to explain, or to picture, the experimental relations. These had been observed by careful experiments on enclosures the radiation from which was measured through a small peephole by delicate devices sensi- tive to heat. There was, however, no theory on the basis of which formulae could be logically developed which contained the relations of actual experiment. Planck solved the difficulty by reasoning the steps of which have never met with general approval but the conclusions of which are firmly established in the science of today. The chief difficulty in the way of the existing theories concerned the manner in which a radiating body shares energy with its ethereal surroundings or absorbs it from them. It was commonly assumed that energy must be, or rather ought to be for the condition was contrary to fact interchanged in a continuous manner. A radiating surface was recog- nized as composed of a number of oscillators, but these were supposed to absorb or emit continuously, that is, in truly infinitesimal successive amounts, 176 WITHIN THE ATOM from or to the ether. For such assumptions there was a recognized basis in theories of mechanics and electrodynamics. Of this a mechanical illustration may be quoted from Jeans. Suppose we construct a vibrating system by con- necting a number of corks together by elastic bands. Imagine a complicated system, if you will, with a large number of cross connections between various corks. Now disturb this by pulling some of the corks from their equilibrium positions and then allow the natural oscillations to occur. Let this system with its several different oscillations be placed on water. The corks simulate a vibrating system. The water, with its almost infinite number of tiny molecules, and hence infinite possibilities for forms of vibration, simulates the ether. We know what happens. Equilibrium between these two systems is impossi- ble. The energy of the corks is all absorbed by the water. It goes into vibrations far more rapid than those of the corks, for it goes to increase the motions of the invisible molecules of the water. If the ether were like this in behaviour all the energy of the bodies in a temperature enclosure would be abstracted by it. And the energy in the ether would be distributed mostly in the vibrations of highest frequency instead of having a distribution with a definite maximum as is shown in Fig. 34. In effect Planck's solution of the difficulty con- sisted in postulating a condition which would fit the observed phenomenon. To an economist or an actuary each experimental curve of Fig. 34 looks something like a so-called MORE EVIDENCE FOR THE QUANTUM 177 probability curve, such a curve, for example, as one would plot if the vertical distances represented numbers of men and the horizontal distances repre- sented corresponding lengths of life. If the various oscillators in the radiating body differ in their abili- ties to absorb or emit radiant energy, each being capable of only a definite amount, then the frequency of maximum radiation should depend upon the char- acteristics of these oscillators just as the maximum in a plotted curve of mortality statistics depends upon the characteristics of the class for which it is con- structed. To a very large extent, as we shall see, Planck's theory constituted a theory of probability for electrical oscillators. As you remember, he assumed that an oscillator could handle only a quantum of energy; and by quantum he meant an amount proportional to the frequency of vibration, the amount hn. Oscillators of low frequency, even if relatively numerous, will handle but a small portion of the total energy and contribute but little because the amount which each individual oscillator may handle is small. On the other hand, oscillators of large frequency will respond only if there is available a relatively large amount of energy since their quanta are greater. To function, however, the higher frequency oscillator must re- ceive its quantum all at once; it cannot make it up from several successive smaller quanta. Since large quanta will probably occur only infrequently, this re- quirement means that there will be little total energy associated with the oscillators of high frequency. The maximum radiation, therefore, will occur in the 178 WITHIN THE ATOM middle range of frequencies, as the experimental re- sults indicate. Upon the assumption of quanta Planck's relations are calculable under the ordinary laws of probability as was shown by Jeans some time later. For pur- poses of following the latter's method one limits his consideration to a narrow region of frequencies. The quantum will be essentially the same for all the fre- quencies within this narrow band. It is then pos- sible to calculate the probability that any given os- cillator of this frequency will have zero energy or the energy of one quantum or that of two, and so on. Summing up the energy which a large number of similar oscillators would probably have at this fre- quency, Jeans obtains the basic expression of Planck, namely, an expression for the probable average energy of an oscillator at any desired fre- quency. It was Einstein, as a discrete, or indiscreet, elec- tron remarked between chapters, who applied this re- lationship with considerable success to the problem of the specific heat of solids. Different substances, but equal quantities by weight, are found to require different additions of heat, that is energy, to produce equal increases in temperature. The amount is specific to each sub- stance, and hence, the term "specific heat" is applied to the amount of heat required to change by one de- gree the temperature of unit mass of a given sub- stance. The common unit for expressing this mag- nitude is the calorie which represents approximately the amount of energy necessary to raise one gram of MORE EVIDENCE FOR THE QUANTUM 179 water one degree Centigrade, and exactly, that re- quired for the degree increase in temperature be- tween 15 and 16 degrees Centigrade. Temperature, of course, is a numerical answer to the question "how hot." As has been implied above, it measures the difference in hotness of substances the molecules of which differ on the average in the kinetic energy which is associated with their hap- hazard motions. If body "A" is hotter than body "B," the molecules of "A" have, on the average, more kinetic energy than those of "B". It is for this reason that a hot and a cold body when placed in contact come ultimately to a common temperature. By molecular collisions at the contiguous boundaries a portion of the energy of "A" is imparted to "B" until finally the molecules of both substances have the same average value of kinetic energy. Because of differences in molecular structure one may predict at once that different substances will have different specific heats. A fairer basis of com- parison, however, than amounts of heat for equal masses would be the amount required for equal num- bers of molecules. Molecules of similar structure should require equal amounts of energy for equal changes in temperature, that is, they should have equal "molecular heats." Thus we should expect monatomic molecules to be alike in this respect. In a monatomic structure the mass is almost en- tirely concentrated in the nucleus, which is the center about which any molecular rotation must occur. From the familiar example of flywheels, we know, however, that if a rotating body is to have associated 180 WITHIN THE ATOM with it large amounts of energy, the mass must be separated from the axis of rotation by a large dis- tance. Because monatomic molecules are not con- structed on the plan of flywheels, for the planetary electrons are negligible in mass as compared to the nucleus, they have no appreciable energy of rotation. When heat is added to monatomic gases it all goes to increase the kinetic energy of translation of the mole- cules. A diatomic molecule, however, would be expected to acquire and to store energy in a rotation or spin- ning of its figure-eight-shaped structure and particu- larly in a vibration of the component atoms with re- spect to each other. In the haphazard motion of such molecules when collision occurs, the atomic partners may be set spinning, or they may momen- tarily be crowded together, and thus vibrations may be set up within the molecular system itself. It ap- pears evident that collisions will lead to such trans- fers of energy, and hence that some of the specific heat of diatomic substances will represent spinning and vibratory motions, in addition to the haphazard translations of the individual molecules. The molecular specific heat of a substance should, therefore, depend upon the molecular structure, being greater "for structures which have greater variety in possible types of motion more degrees of freedom, as it is technically said. There is nothing, however, to indicate that the molecular specific heat should be different at different temperatures. We should expect that it would require the same fraction of a calorie to change a substance from 100 to 101 MORE EVIDENCE FOR THE QUANTUM 181 degrees as from 200 to 201 degrees. Of course, if a change in molecular state occurs as, for example, from liquid to vapor, the number of degrees of free- dom may be changed and we may be dealing in effect with a different substance. As long, however, as there is no change of state, it would appear that the specific heat of any substance should be constant without regard to temperature. For monatomic gases it is; also for metals in a va- por state; but for all other substances the specific heats are found to be markedly decreased as the tem- peratures at which they are measured are lowered. Here again no adequate theory had been presented prior to the application of the quantum hypothesis. The theory is still too incomplete to account for any- where near all experimental facts, but the successes of the quantum hypothesis are sufficient to indicate that the final solution must involve its use. Planck had derived an expression for the probable average energy, involving a large number of similar oscillators. This Einstein applied to the study of the specific heats of solids. The formula is too com- plicated for complete discussion, and it must suffice to say that it involves the absolute temperature of the substance. A mathematical operation was then required to find the rate at which this energy changed with temperature, that is to find the specific heat, which is the change in energy content of a body per degree of temperature. The expression so obtained was in form to permit the calculation of the specific heat of solid substances at any desired temperature if the frequency of the oscillators was known. 182 WITHIN THE ATOM Several methods were then devised by Einstein and others for obtaining this frequency experi- mentally. Of these, only one will be discussed. This depends upon a number of principles which have al- ready been mentioned. In the derivation of the for- mula for specific heat it had already been assumed, for simplicity, that all the oscillators of a homoge- neous body were essentially alike. It remained to excite them in such a way that their characteristic or natural oscillations could be detected and their FIG. 35 Cross-section of apparatus for studying residual rays. Radiation from a source T is successively reflected from bodies of the same substance. The residual rays are analyzed by the spectrometer, diagrammatically indicated at L. frequency measured. You will remember that re- flection is really re-radiation. Any reflected radia- tion must then include most prominently those ra- diations which are of the same frequency as the os- cillators would themselves naturally emit. The phenomenon is one of resonance, so-called that is the phenomenon of greatest response when the ap- peal strikes the proper personal note. If, therefore, a substance is illuminated by a con- tinuous spectrum of radiation, such as would arise MORE EVIDENCE FOR THE QUANTUM 183 from a black body which is emitting temperature radiation, the reflected radiation will contain more intensely the frequencies natural to the oscillators of the body. Now let this reflected radiation fall on another body of the same substance as the first. The general scheme is illustrated in Fig. 35, where the progress of the beam of radiation is indicated by the dotted lines. (A mirror, M, is interposed at one point to deflect the beam.) At the second reflecting sur- face there is a further selection of the natural fre- quencies, and a further discrimination against all others. By successive reflections there are thus ob- tained so-called "residual rays," which are those natural to the oscillators under examination. When the natural frequency is known the calcula- tion of specific heat by Einstein's method may be completed. For certain substances his formula was found to give results wonderfully in accord with the experimental findings. For other substances there was an unsatisfactory lack of agreement. Neverthe- less, the formula agreed in such cases with the general trend of the relations between specific heat and tem- perature. It indicated a certain correctness of the general method of approach which other investi- gators have been rapidly extending. Thus inquiry in another field of physical science was stimulated and is being advanced by the fruitful hypothesis that energy is transferred in discrete bundles, the magni- tudes of which are dependent only on the frequencies of the atomic and electronic oscillators which are concerned. CHAPTER XIV ENERGY AND ITS AVAILABILITY IN the earlier chapters of this book the orderly structure of matter was emphasized. In the later chapters some evidence was presented which favors a concept of "atomicity" for energy. Throughout, it is to be hoped that the text has conveyed an idea of the inherent structural order of nature. Now we must distinguish between order in structure and order in process. The processes of nature, are orderly only in the sense that they constitute phases of an inevitable sequence of events. They may and in- deed always do result in a certain disorder which we shall now consider. Of chaotic conditions we have had some intimations from the motions of molecules, particularly those of gaseous substances, and from the electrical elements which are responsible for con- tinuous spectra. The orderly processes of nature whereby disorder results have been formulated in a law commonly known as the second law of thermodynamics. It would be preferable to speak of a first and second law of energy rather than of thermodynamics, but they retain the titles, descriptive of their evolution, for both arose at a time when the relation between heat and energy was inadequately conceived. Both laws 184 ENERGY AND ITS AVAILABILITY 185 express relations which have been grasped more or less intuitively, particularly the second law. The first law states an equivalence between work (energy) and heat; and in mathematical symbols it contains an empirical constant for converting units of heat into units of energy. Prior to the statement of this law heat and mechanical work had seemed unrelated phenomena and different units had been adopted for the two magnitudes. Of these the calorie has already been defined ; the other unit is the erg. Whenever, under experimental conditions energy, associated with molar bodies disappeared, there was found a definite increase in heat which bore the proper numerical relationship to the amount of energy. For many years, however, it has been recognized that heat is merely a descriptive term for the kinetic energy of molecular bodies. Today we conceive of energy as associated with all electrons and protons, with their configurations and their motions; and the first law becomes our statement of belief in the con- servation or indestructibility of the entity energy. The second law, which followed the work of Sadi Carnot about 1824, has also outgrown its earlier narrower application to heat engines and become a general law of energy. At various times it has re- ceived many expressions, of which the most service- able are formulated in symbols and involve a con- cept known as entropy. To this we shall return in a moment. In so far as the second law is a matter of experi- ence it records the impression that there are certain 186 WITHIN THE ATOM natural processes. Water flows down hill; electric- ity moves from points of higher to points of lower potential; by radiation, and by actual molecular im- pacts if possible, a net amount of energy is trans- ferred from a hot to a cold body; impacts of molar bodies and all phenomena of friction result in transfers of energy to molecules. In fact, all natural processes, directly or ultimately, result in greater kinetic energy on the part of molecules. All me- chanical operations involve friction and hence all contribute to increase the kinetic energy of molecular and submolecular systems. Similarly, the con- duction of electricity and many x chemical reactions result in greater activity on the part of the tiny grains of our physical universe. Sometimes the second law is stated by saying that although work (the expenditure of energy in con- nection with molar bodies) may always be converted into a definite equivalent of heat the reverse trans- formation is always incomplete. This was the earli- est expression of the law and it was reached by a con- sideration of heat engines. Even if there were no friction whatever, a heat engine could never be 100 per cent efficient unless its lowest temperature was zero on the absolute scale of temperature. The prop- osition was originally proved by Carnot, who dealt theoretically with an ideal engine and found that the efficiency depended upon the ratio of the lowest tem- perature, say that of the atmosphere, to the highest temperature, say that of the boiler. The efficiency 1 When we consider the surroundings as well as the reacting substances all reactions result in increases of entropy. ENERGY AND ITS AVAILABILITY 187 is always less than 100 per cent by the number of per cent represented by this ratio. Since temperatures are measured from the absolute zero it is evident that all actual conversions of heat into work are remark- ably inefficient. Of the mechanical energy derived from heat energy there is always a certain amount which is expended in friction, so that the actual effi- ciency is even less than the "thermodynainic effi- ciency" which has just been explained. Energy once converted into heat and embodied in molecular motions can never be completely recov- ered. Strictly speaking, therefore, all natural proc- esses are irreversible because things can never be as they were. The fundamental cause of this so-called "thermodynainic irreversibility" is to be found in the characteristics of molecular systems. Any material systems which we may use in experi- mental investigations involve billions and billions of molecules. With these we can. only deal statistically treating of average effects. Because of their large number, however, the desired average effects may be studied by the laws and methods of probability, the mathematical science of chance. In this field Maxwell made one of his many con- tributions to science. He determined the distribu- tion of velocities, among the molecules of a gas, which would satisfy the experimentally observed condition that the pressure on the walls of a retain- ing vessel is constant when the temperature is con- stant. He found that no matter how collisions oc- curred there would be a definite average velocity (perpendicular to the surface of the container) and 188 WITHIN THE ATOM that the proportion of the total number of molecules which had any particular velocity, either greater or less than the average, was definite and calculable. If a plot is made, showing the percentage of mole- cules striking the container and their corresponding velocities, the result is the form of probability curve shown in Fig. 36. We have already met one application of the theory of probability in the development of an expression for the average energy of a large number of oscil- lators, each restricted according to the quantum hy- pothesis. Velocity FIG. 36 Diagrammatic representation of Maxwell's distribution of molec- ular velocities. We shall now sketch briefly an application of the method of probabilities by which Boltzmann arrived at a concept of entropy, the characteristic magnitude in terms of which the second law is most satisfac- torily expressed. Imagine looking across two paral- lel tennis courts. The players are warming up for two sets of doubles and each member of a team is volleying with an opponent so that four balls are constantly in the air. We shall distinguish between the balls by the letters a, b, c, and d. The distribution of the balls with reference to the line of the nets changes from instant to instant. At one moment all four may be on the east side, and a ENERGY AND ITS AVAILABILITY 189 moment later three on that side and one on the west. There are obviously five possible distributions, namely : all east, all west, three east and one west, or vice versa, and two on each side of the net. For any distribution there is one or more "com- plexions," as they are called. Thus the distribution of three east and one west might be the result and would correspond to any one of four complexions, for there are four different ways in which we may have three balls on one side and one on the other. If we tabulate the various possible complexions we have the result given below : Distribution Complexion East West East West 4 abed 3 i abc abd acd bed d c b a 22 ab ac ad be bd cd cd bd be ad ac ab i 3 a b c d bed acd abd abc o 4 abed The distribution of two balls on either side of the net is the most probable distribution. Out of six- 190 WITHIN THE ATOM teen possible complexions this distribution contains six, and that with the next largest number contains four. For purposes of later analogy we also note that this distribution of two and two represents a sort of an equilibrium condition. We might also note that from the standpoint of an attendant, who is accustomed to seeing balls neatly packed in dozens, the distribution is not that of order. Now forget the players, letting the balls represent molecules of a gas and let their number be enormous- ly increased. There will still be a distribution which will contain the maximum number of complexions and this will be the most probable distribution. It will also be the most probable state for the gas, the final "equilibrium state" toward which systems of gas molecules inevitably tend. It will be the state with the largest number of complexions and the greatest number of ways in which the gas molecules may be associated, the state of greatest disorder. As Boltzmann defined it, "thermodynamic prob- ability" is a number which expresses how much more probable a given state is than some "standard" or perfectly ordered state in which the substance occu- pies the same volume and has the same energy. For example, from the preceding table we see that the probability of the most "mixed-up" state is six times that of the state where all the balls are on one side of the net. The mixed-up state is most prob- able. There is always a natural trend toward the greatest disorder, toward the state of final equilib- rium. When four balls are on one side of the net there is ENERGY AND ITS AVAILABILITY 191 greater energy associated with this side than with the other. Hence, if we were dealing with molecules we would expect to obtain some of this energy by allow- ing them to pursue their natural haphazard motions and by their impacts to drive before them a molar body like the piston of an engine. Haphazard mo- tions will carry the balls across the net and they can do mechanical work, as, for example, upon a racquet held in their way. In the equilibrium state, how- ever, no mechanical work can be recovered, for on the average a racquet held over the net would receive as many and as hard impacts from one side as from the other. We now see that we cannot utilize or obtain from a gas, in the state analogous to four balls on one side, all the energy which its molecules appear to be able to expend, since the natural process upon which we rely proceeds only to a final equilibrium state corresponding to that of two balls on either side of the net. Unfortunately for the purposes of easy exposition, thermodynamic probability and entropy are not synonymous. There is, however, a definite relation between them. If one increases the other also in- creases but not in direct proportion. With this understanding we may proceed to use the term en- tropy in place of thermodynamic probability. All systems tend to a final state of maximum en- tropy, that is a condition of greatest molecular dis- order from which no mechanical work may be de- rived. Not only no mechanical work but also no chemical or electrical changes can be brought about by such a system of itself in such a manner as to per- 192 WITHIN THE ATOM mit energy to be derived from these changes. The equilibrium condition is a "run-down condition" which offers no hope to human beings who would control ni*4ure's store of energy. Although energy is still associated with the system its availability has disappeared. Human beings need never be concerned with the conservation of energy since that is apparently in- herent in the entity itself. Their concern is with its availability. When energy transformations occur naturally, and in final analysis all transformations so occur, there is a reduction in availability, or as the scientist says, an increase in entropy. There is no known or anticipated scientific process, despite all the discoveries of radioactive substances, whereby this inevitable and natural increase in entropy may be avoided. It does seem unnecessary, however, that man should accelerate the irreversible trans- formations of nature. This he does whenever he fails to take from a natural process, as, for example, from the combustion of coal, the full amount of use- ful energy which is his equity in accordance with the second law of thermodynamics. The final end of any conservative system, one which does not have energy communications with its neighbors, is not stagnation but disorder. Orderly systems may have no more energy than disorderly systems but their energy is partly available. In- evitably any orderly system tends to a state of maxi- mum disorder. In the process of attaining this state its own entropy is increased. Only a certain amount of its energy is available and the expenditure of this ENERGY AND ITS AVAILABILITY 193 margin is man's concern. It may be expended with foresight, as when a waterfall is utilized to make chemical compounds in which available energy is stored for later release, for example, in -nitrogenous fertilizers. It may be expended without foresight in the innumerable ways which history records. Every fire or explosion, every inefficient process, represents an increase in the world's entropy the sum total of its disorder. APPENDIX THE MAGNITUDES OF ELECTRONS AND QUANTA To a considerable extent the exposition of the previous text has been unrelated to our daily experi- ences. It has dealt with minute protons and elec- trons, with quanta of energy, and with granular structures so fine that they are only to be inferred and never to be seen. In this Appendix it is now proposed to assemble some numerical expressions whereby the tiny magnitudes involved in the modern science of electrons and quanta may be related to the grosser magnitudes with which we are familiar. In terms of the fundamental scientific units, namely, the centimeter (1 cm. 0.394 inch), the gram (1 g.=0.0353 ounce), and the second, the sizes and masses of the electrical elements are extremely small and their number in any sensible volume ex- tremely large. Where extremes are to be met, numerical expression is most conveniently accom- plished by a slight modification of our common decimal system. Consider first the expression of numbers greater than ten. Ten is one times ten; a hundred is one times ten times ten; and one thousand is one times the successive product of three tens; and so on as in 195 196 WITHIN THE ATOM the table below. The number of successive products of ten are represented by exponents of the proper value as shown. io i X io = i x io 1 loo = i X io X io = i x io 2 1000= i X io X io X io = i X io 3 10000=1 X io X io X io X 10= i X io* one million = i X io 6 one billion = = i X io 9 one million million = = i X io 12 one billion billion = i X io 18 On the same basis, any number like 606 is 6.06 times a hundred or as illustrated below : 606 = 6.06 X io 2 6060 = 6.06 X io 3 60600 = 6.06 X 10* When later we find that the number of molecules in two grams of hydrogen gas is 6.06X10 23 we shall be able to convert this expression into 606 thousand billion billion, and thus, perhaps, get some apprecia- tion of an enormous number. For numbers smaller than unity the system is equally simple. We write 1/10 as IO" 1 ; and 1/100 as 1/10 2 and then as 1X10" 2 , as in the following table: o.i = i X i/io = X io- 1 o.oi = i X i/ loo = o.ooi = i X i/io 3 = one millionth = = one billionth = = one billionth of a billionth = X X X X io- 18 MAGNITUDES OF ELECTRONS AND QUANTA 197 The use of these negative powers of ten is illustrated below: 0.254 = 2.54 X 1/10 = 2.54 X 10' 1 0.0254 = 2.54 X 10' 2 0.00254 = 2.54 X 10' 8 0.000,002,54 == 2.54 X 10' 6 In addition to the convenience and brevity which this system offers it serves to indicate most quickly the order of magnitude of a number and its signifi- cant figures. Consider for example the value of Avo- gadro's constant, that is the number of molecules in one "mole" of any substance. * The most exact value for this constant is 6.062 X 10 23 , as found by Millikan. From the second portion of this expression we recognize at once that the constant is of the order of hundreds of thousands of a billion billions. The first portion of the number contains the significant figures. If Millikan's determination had been less precise he might have found 6.06 XlO 23 , or with still less accuracy 6.0 XlO 23 . In the latter case he would not have written the number as 6.000X10 23 for that would have implied the same precision as does his actual value, that is a precision to the fourth signifi- cant figure. By the number of significant figures an experi- menter indicates the correctness of his results so far as concerns the precision with which he has made his measurements. He does not, of course, mean that *A mole is a number of grams equal to the molecular weight of the substance ; thus in the case of hydrogen, H 2 , a mole is two grams, but in that of oxygen, 0>, it is 32 grams. Without regard to substance all moles will contain the same number of molecules. 198 WITHIN THE ATOM there may not be present in his determination sources of error, inherent in the experimental con- ditions, which may have rendered his results wrong even in order of magnitude. By proper attention to significant figures throughout any necessary calcula- tions he arrives at a final result each figure of which is really significant and not merely a result of an arithmetical process. Taking a simple example, suppose he wishes to compute the circumference of a circle the diameter of which he has measured as 10.0 cm. He multiplies this diameter by Jt, but he uses for n, 3.14 and not 3.14156 or some still more accurate value. By his expression of the diameter as 10.0 cm. he means in substance that he has measured it with a centi- meter scale which is divided into tenths of a centi- meter, and that he does not know its value closer than a tenth of a centimeter. To write the circum- ference as 31.4156 cm. would imply a greater accur- acy than he has either right or desire to imply. When, therefore, we consider Millikan's value for Avogadro's constant we interpret it to mean that he has determined the number of molecules in a mole to the fourth significant figure. His value, then is in doubt by approximately 0.001 XlO 23 or a mere matter of a hundred or so billion billion molecules. He is right, however, to within about one-hundredth of one per cent. A more exact knowledge than this would probably avail us but little since there are few physical conditions where we may detect a percent- age difference as small as this, and few physical con- MAGNITUDES OF ELECTRONS AND QUANTA 199 stants which are expressible by more than four sig- nificant figures. We are now in a position to express numerically some important physical magnitudes. We shall not, however, go into any detail as to how they have been determined. Further, we shall allow the numerical values to create their own impressions instead of adopting conventional expedients to heighten them. For example, one might count the average number of letters on a page of the encyclo- paedia, divide this number into Avogadro's constant and find the number of pages which would be re- quired to contain a number of letters equivalent to this number of molecules, and then calculate the number of billions of complete sets 1 and so convey an impression. With more tediousness he could take the volume of atmospheric gas inspirated by an av- erage man in a single breath and by using Avogadro's constant express the number of molecules for this familiar case in terms of volumes of the encyclo- paedia. Arithmetical dexterity and interest will produce strange results by such a method, and the arithmetic is facilitated by the use of powers of ten. Sizes : Known distances in the physical universe extend from 10 24 cm., representing the distance from the earth to the further nebulae, to 10' 13 , representing the order of magnitude of the diameter of an elec- tron. With the microscope one can observe dis- tances in ordinary light of the order of 10' 5 cm., and can detect illuminated specks of somewhat smaller 1 The advertisements say 4.4 x 10 8 words per set. Hence, allow- ing six letters to the word, almost a billion billion sets. 200 WITHIN THE ATOM dimensions. The diameter of a molecule of oxygen is 2.99 X 10' 8 cm. For hydrogen the diameter is less, being 2.17X10' 8 cm. The best indications of the diameter of an electron give 2X10' 13 cm. Masses: The mass of a hydrogen molecule is 3.33 XlO' 24 g., and the mass of any other molecule is larger in proportion to its molecular weight, thus that of the oxygen molecule is 52.8 XlO' 24 g. The mass of the atom of hydrogen is half that of its mole- tule and this is also the mass of the proton. The mass of an electron is only about 1/1845 of the pro- ton and is thus 9.01 X10' 28 g. Velocities: The greatest velocity in the physical universe is that of light or of other forms of radiant energy. Light quanta apparently travel 2.999 X 10 10 cm. per second. Beta particles have been measured with velocities as high as 9/10 of this. Alpha particles, with their greater mass, are ejected with smaller velocities in the order of 1/10 the velocity of light. In a volume of gas under practically atmospheric conditions of pressure and temperature (so-called standard conditions) molecules travel with velocities which are dependent upon their masses. Hydrogen molecules travel fastest, about a mile a second or 1.69 XlO 5 cm. per second. Oxygen molecules with sixteen times the mass travel one-quarter as fast as hydrogen molecules, that is 4.2X10 4 cm. per second. Free Path of Gas Molecules: Under these stand- ard conditions the atoms of a volume of hydrogen would travel on the average about 1.76 XlO' 5 cm. be- tween successive collisions. On the average, there- MAGNITUDES OF ELECTRONS AND QUANTA: 201 fore, a hydrogen atom would make ten billion col- lisions per second. If the gas is less dense, for ex- ample, if the container has been exhausted until the pressure is 2.64 X10" 10 of the normal atmospheric pressure, the number of molecules per c.c. has been similarly reduced and the mean free path is increased by 3.8 XlO 9 times. For oxygen, for example, the mean free path under atmospheric conditions is 9.4 XlO" 4 cm. and under the above conditions of rare- faction 3.54 XlO 4 cm. The velocity has not been altered by the reduction in pressure for the temperature has been assumed unchanged, and hence the kinetic energy is not al- tered. The molecule will now make only about one collision a second. Such extreme conditions of rare- faction are producible today by vacuum pumps which employ molecules to bombard other molecules and thus drive them from the desired enclosure. When the bombarding molecules have done their work they are removed by condensing them into drops of liquid. Avagadro's Constant: A mole of any gas occu- pies a volume of 2.241 XlO 4 c.c., that is, about 22 liters (about 0.79 cubic foot) under standard con- ditions of temperature and pressure. In this mole there are, as has been said, 6.062 XlO 23 molecules. Per cubic centimeter, therefore, there are about 2.705 XlO 19 molecules. Under the conditions of rare- faction which were mentioned above as attainable by the modern mercury vapor vacuum pump the num- ber per c.c. is reduced to about 7 XlO 9 , so that the nearest we can come to a perfect vacuum is a mere 202 WITHIN THE ATOM matter of several billion molecules in each cubic centimeter. Energy Units : The unit of energy is the erg. It represents twice the kinetic energy which is asso- ciated with a mass of one gram which is moving at the rate of one centimeter a second. It represents roughly one- thousandth of the work required to raise a gram vertically one centimeter. It is too small a unit for convenience in practical mechanics. For example, in lifting an ounce vertically a distance of 1-inch one does 7.07 X 10 4 ergs of work. The familiar unit of energy, known as the foot-pound, is equiva- lent to 1.35X10 7 ergs. The joule which is used in electrical engineering is 10 7 ergs. The calorie which is the convenient unit for measuring energy which appears as heat is equivalent to 4.19X10 7 ergs. Quanta: Although the erg is too small for many practical purposes it is large compared to many of the amounts of energy with which the scientist is concerned. This is particularly so in the case of quanta. Planck's constant is 6.56X10' 27 and the number of ergs representing a quantum at any given frequency is the product of this constant, h, and the frequency n. For example, about the highest fre- quency of visible light is 7.5 XlO 14 vibrations per second, so that the corresponding quantum is 5.0 X 10" 12 erg. The frequency at which a heated body radiates the maximum amount of energy is about 1.5X 10 14 , which is in the infra-red region. The cor- responding quantum is only 9.9 XlO" 13 erg. Gamma rays have the highest known frequencies, about 10 20 vibrations per second. In this case the MAGNITUDES OF ELECTRONS AND QUANTA 203 quantum has its maximum known value of about 6 XlO- 7 erg. Kinetic Energy of a Gas Molecule: The kinetic energy which, on the average, is associated with each molecule of a gas under standard conditions of pres- sure and temperature (0C.) is 5.62X10" 14 erg, and for every degree increase in temperature the kinetic energy of translation is increased by 2.06 XlO' 16 erg. Electrical Units: For measuring electrical phe- nomena three systems of units are used, but we shall restrict ourselves to the so-called practical units known to electricians and the consumers of electrical energy. The Electron: The practical unit of quantity of electricity is the coulomb. It represents the amount of electricity which would be transferred in a silver- plating solution of silver nitrate every time that 0.001118 gram of silver is deposited on the cath- ode. If a coulomb is passed through an electrolyte under conditions where hydrogen is liberated the mass of hydrogen gas is 1.038X 10" 5 gram. To liber- ate a gram of hydrogen requires the passage of 96,- 500 coulombs. In terms of the coulomb the charge of an electron (or of a proton) is 1.591 XlO" 19 coul- omb. Current: When there is a transfer of electricity through any conductor at the rate of one coulomb per second a current of one ampere is said to be flow- ing. It is thus evident that a current of one ampere represents a flow across each and every cross-section of the conductor of 6.3 XlO 18 electrons each second. Electrical Potential: When a coulomb of elec- 204 WITHIN THE ATOM tricity is transferred between two points by an ex- penditure of one joule of energy (10 7 ergs) the points are said to differ in electrical potential by one volt. The lighting circuit of a house or office usually oper- ates at a voltage of 115. Power: By multiplying the voltage across and the current through any piece of electrical apparatus we find the number of joules per second which are being expended in the apparatus. For joules per second, however, there is used a single word, namely, watts. When energy is being expended at the rate of one joule per second the power in the circuit is one watt. An ordinary house light, rated as 40 watts, takes a current of 40/115 ampere or a little more than a third of an ampere, and represents a flow of electrons at the rate of about 2.X10 18 a second. lonization Potential: The kinetic energy which an electron acquires in free passage between two points differing in potential by one volt is about 1.59 XlO' 11 erg. lonization potentials are of the order of 10 volts so that it requires about 1.6X10" 10 erg to knock an electron free from an atomic structure. The ionization potential differs with the type of atom and some atoms require two or three tunes as much energy in the impact as do others. To ionize by removing two electrons requires more energy but the amount is still absurdly small compared to any of the energy expenditures of our daily lives. X rays : In an X-ray tube the electrons freed at the heated cathode are pulled across the intervening MAGNITUDES OF ELECTRONS AND QUANTA 205 space to the target under voltages of the order of 150,000. As a result each electron delivers to the target an energy of about 2.4 XlO' 6 erg. This is about the highest value of energy which physicists have yet been able to impart to an electron. The Inconstancy of Mass: Mass or inertia, as defined on page 40, depends upon energy and speed. Neglect for the moment the conventional units used in this Appendix and return to the simple units of the previous text. An electron moving with unit speed (1 cm. per sec.) has unit energy and under these conditions the electron has unit inertia. If it moves with twice the speed it has four times the en- ergy ; with three units of speed, nine units of energy; and so on, the energy of the moving electron being equal to the square of its speed as long as this speed is small as compared to the velocity of light (3X10 10 cm. per second). Under these conditions the inertia or mass of the electron is constant and is measured by the ratio of the number of units of energy to the square of the number of units of speed. Actual comparisons have been made of the ener- gies of electrons at different speeds and it has been found that as higher speeds were attained the energy was increasing enormously faster than was the square of the velocity, that is, that the inertia of an electron is not constant but always greater for greater speeds, although the differences are imper- ceptible at speeds small as compared to light. For this reason the mass may be said to be inconstant. The same relation holds for molar bodies as well as 206 WITHIN THE ATOM electronic if we accept, as we must, the so-called "special relativity theory." This subject, however, demands a whole book to itself, and it has received many such in recent days. GLOSSARY ABSOLUTE ZERO A temperature of 271.3 below zero on the Centigrade scale, equivalent to 456.3 below zero Fahrenheit. ABSORPTION SPECTRUM A spectrum showing by their absence what radiations a given substance fails to transmit. ACIDS Electrolytes for which one product of dissociation is a hydrogen ion. ALPHA PARTICLES The combination of four protons and two electrons which is expelled from the nucleus of a radioactive atom. An alpha particle is identical with the nucleus of a helium atom. ALPHA RAYS A stream of alpha particles. AMPERE A unit of electrical current. See Appendix. AMPHOTERIC A term applied to chemical elements which react either as electropositive or electronegative depending on the other reactants. ANODE The plate or other terminal in a conducting gas or liquid at which electrons or negative ions are collected. The positive electrode. ANTI-CATHODE The anode or target in an X-ray tube. ATOM An atomic system which is uncharged having equal numbers of protons and electrons. ATOMIC NUMBER A number equal to the number of positive charges 207 208 WITHIN THE ATOM (protons) of a nucleus in excess of the number of nega- tive charges (electrons). ATOMIC SYSTEM A nucleus and associated planetary electrons. It may be either a normal atom or an ion. ATOMIC WEIGHT The number representing, on a scale which assigns 16 to oxygen, the average mass of the atom of any chemi- cal substance. ATOM-MODEL A theoretical configuration of the electrons in an atom which would account for its properties. BASES Electrolytes for which one dissociation product is a negative ion formed by an oxygen and a hydrogen atom. BETA PARTICLE An electron which is ejected by the nucleus of a radio- active atom. BETA RAYS A stream of beta particles. CALORIE A unit of energy used in discussing heat. cf. p. 178. CARBOHYDRATE A chemical compound of a particular type which con- tains carbon, hydrogen and oxygen. Of this type the sugars are examples. CATHODE A plate or other terminal in a conducting gas (or liquid) at which positive ions are collected or electrons are emitted. The negative electrode. CATHODE RAYS A stream of electrons proceeding outward from the cathode of a tube (of gas) which is conducting elec- tricity. CENTIMETER Approximately 0.394 inch. CHARGE The excess of positive or negative electricity in a body. , GLOSSARY 209 CHEMICAL ELEMENT A substance all of whose atomic systems have the same atomic number. CONTACT ELECTROMOTIVE FORCE The potential difference which is set up by the contact of two dissimilar substances, i. e., substances with dif- ferent electronic structure. CONTINUOUS SPECTRUM A spectrum which includes all possible frequencies. COULOMB A unit of charge, cf. Appendix. DISSOCIATION A disruption of a molecular system which may or not, as the case may be, result in neutral systems. Elec- trolytes dissociate into charged systems, the ions. DISINTEGRATION A disruption of the nucleus of an atomic system. DISINTEGRATION PRODUCT The atomic system which results when alpha or beta particles are expelled from a nucleus. ELECTRICAL ELEMENTS The electron and the proton. ELECTRODE The metal plate which terminates the solid portion of an electrically conducting path, the other portion of which either is gaseous or liquid or is a vacuum. ELECTROLYTE A solution for which the solute partially dissociates into ions. ELECTROMAGNET A piece of magnetic material about which is wound a current-carrying loop of wire. ELECTROMAGNETIC THEORY The generally accepted -theory of electricity and mag- netism which was formulated by Maxwell. ELECTROMETER An instrument for measuring an electrical charge. ELECTRON The elementary corpuscule of negative electricity. It is complementary to the proton. 210 WITHIN THE ATOM ELECTRONEGATIVE A term applied to chemical elements whose atoms have a negative valence. ELECTROPOSITIVE The opposite of electronegative. ELECTROSCOPE An instrument for detecting an electrical charge. ELECTROSTATIC A term applied to an electrical charge which is fixed in position. EMANATION The name applied to the product formed by the ex- pulsion of alpha particles from the nucleus of radium or thorium atoms. In this book radium emanation is called "niton." EMISSION SPECTRUM The spectrum of the radiation from a body. ENERGY The name applied to the motive power in the physical ' universe. One of the two fundamental entities of modern physics ; the other is electricity. ENTROPY A numerical expression which increases as energy loses its availability. ERG A unit of energy, cf. Appendix. FLUORESCENT Giving rise to radiations of other frequencies than those which it absorbs. FREQUENCY Number of oscillations per second. GAMMA RAYS A radiation, similar in type to X-rays, which proceeds outward from some radioactive atoms when the sub- stance is emitting beta rays. GRAM A unit of mass approximately equal to 0.0353 ounce. GRATING A series of equally spaced reflecting surfaces which serve to analyse radiations into their component fre- quencies. GLOSSARY 211 INERTIA A characteristic unwillingness to change in state of motion which all bodies display. INFRA-RED Of lower frequency than the visible radiation. INTERFEROMETER An instrument for measuring distances very accurately in terms of wave lengths of visible . light. Used by Michelson to measure the international meter. ION An atomic or molecular system which is electrically charged by virtue of an inequality in the number of its protons and its electrons. IONIZATION A disruption of an atom or molecule into ions or into ions and electrons. IONIZATION POTENTIAL The amount of potential energy which must be con- verted into kinetic in order that an impact of the body with which the energy is associated shall ionize an atom or molecule. ISOTOPE A substance which occupies with another substance the same place in the periodic table of chemical ele- ments. The two substances then have the same atomic number but different atomic masses. JOULE A unit of energy, cf. Appendix. KINETIC ENERGY Energy associated with electricity in motion. LINE SPECTRUM A discontinuous spectrum formed by radiation of only certain definite frequencies. MASS The amount of matter in a body; more strictly, a measure of its ability to acquire kinetic energy. MOLE A number of grams of a given substance equal to the sum of the atomic weights of all the atoms in a molecule of the substance. 212 WITHIN THE ATOM MOLECULAR HEAT The heat required per molecule (strictly per mole) to raise the temperature of a substance 1 centigrade. MOLECULAR SYSTEM A union formed by two or more atomic systems. It may be either a normal molecule or an ion. MOLECULE A molecular system which is uncharged, having equal numbers of protons and electrons. NITON Radium emanation. An inert gas of atomic number 86. NUCLEUS One or more protons associated with electrons in a com- pact group central to an atomic system. OSCILLATOR An atomic or electronic system the parts of which vibrate or oscillate. PELLATE Move apart except as restrained. PERIODIC TABLE The arrangement of the chemical elements, in ascend- ing order of atomic numbers, in which elements of somewhat similar electronic structure, and hence chemical properties, appear periodically. PHOSPHORESCENT Emitting radiation as a result of radiation which is absorbed but after absorption has ceased. PHOTO-ELECTRIC Pertaining to the emission of electrons which occurs under the action of light. PLANCK'S CONSTANT The factor of proportionality by which the frequency of an electronic oscillator must be multiplied in order to express a quantum in ergs. PLANETARY ELECTRONS The electrons in an atom which are external to the nucleus. POLYMERIZATION The formation of aggregates of molecules which move about (in solution) as if they were single molecules. GLOSSARY 213 POSITIVE RAYS A stream of positive ions from a tube of conducting gas. POTENTIAL DIFFERENCE A measure of the potential energy which is available between two points. POTENTIAL (ELECTRICAL) The measure of the potential energy which is associated with a unit quantity of electricity. POTENTIAL ENERGY Energy which it is assumed, upon the basis of the conservation of energy, is associated with the con- figuration of electrical systems. POTENTIAL GRADIENT The rate at which the potential difference between two points changes as the position of one is varied. PROTON The elementary corpuscule of positive electricity. It is complementary to the electron. QUANTUM A variable amount of energy, directly proportional to the frequency of the radiation which is emitted by an electronic oscillator. RADIATION Energy, unassociated with matter, which is being trans- ferred through space. RADIOACTIVE A term applied to substances the nuclei of whose atoms spontaneously disintegrate. RADIUM The most famous radioactive substance, discovered by the Curies in 1897. RE-RADIATION Radiation emitted by a body which is absorbing radia- tion from a distant source. RESISTANCE (ELECTRICAL) The unwillingness of a body to transmit electricity, which is measured by the ratio of an electrical potential (the cause) to a current (the effect) . RESONANCE POTENTIAL The amount of potential energy which must be con- 214 WITHIN THE ATOM verted into kinetic in order that an impact shall excite the characteristic radiation from an atom. SALTS Electrolytes which are neither acids nor bases. SCINTILLATION A discrete speck of light produced in a screen by the impact of a high speed ion, usually of an alpha particle. SOLENOID A tubular winding of wire formed by spiralling a wire as in Fig. 4. SPECIFIC HEAT Energy required to raise the temperature of unit mass of a substance one degree. SPECTROMETER An instrument for the quantitative analysis of radia- tion into its component frequencies. SPECTROSCOPE An instrument for the qualitative investigation of the component frequencies of a given radiation. SPECTRUM A broad band of radiation in which the several com- ponent radiations are arranged side by side in the order of their frequencies. TEMPERATURE ENCLOSURE A region surrounded by walls which are maintained at a constant temperature. TEMPERATURE EQUILIBRIUM The condition of a system the parts of which undergo no relative changes in temperature. TEMPERATURE RADIATION Radiation emitted as the result of the thermal agitation in a body. THERMION An electron emitted from a body as a result of thermal agitation. THERMODYNAMIC EFFICIENCY c/. p. 186. THERMODYNAMIC PROBABILITY c/. p. 190. THERMODYNAMIC SCALE OF TEMPERATURE A temperature scale starting from the absolute zero. GLOSSARY 215 THRESHOLD FREQUENCY The minimum frequency of radiation which will pro- duce photo-electric effects. TRACTATE Move toward each other except as restrained. ULTRA-VIOLET Of higher frequency than visible radiation. VALENCE A numerical statement of the ability of atoms to com- bine, expressed in terms of the combining ability of hydrogen as unity, e.g., hydrogen, sodium, chlorine are monovalent; oxygen, sulphur and zinc are divalent; phosphorus and boron are trivalent and carbon and silicon are tetravalent. VELOCITY Rate of change of position, that is speed, measured in distance per unit of time. VOLT A unit of potential difference, cf. Appendix. WATT A unit of power, that is of the rate at which energy is expended, cf. Appendix. WAVE LENGTH The distance traversed by radiant energy in the period occupied by one complete oscillation of its source. Numerically equal to the velocity of light divided by the frequency. X-RAYS The radiation from the anode or target of a vacuum tube, when the anode is subjected to severe bombard- ment by a cathode stream. THE NEWER PHYSICS THE ATOM By A. C. CREHORE, Ph.D. 1920. 177 Pages. 5x7%. Ills. Postpaid, $2.00 THE MYSTERY OF MATTER AND ENERGY RECENT PROGRESS AS TO THE STRUCTURE OF MATTER By A. C. CREHORE, Ph.D. 1917. 172 Pages. 4^x6^. Cloth. 8 Plates and Folding Charts. Postpaid, $1.00 THE NATURE OF MATTER AND ELECTRICITY 4iV OUTLINE OF MODERN VIEWS By DANIEL F. COMSTOCK, S.B., Ph.D. Engineer and Associate Professor of Theoretical Physics in the Massachusetts Institute of Technology and LEONARD T. TROLAND, S.B., A.M., Ph.D. Instructor in Harvard University 1917. 225 Pages. 5^x8. Cloth. 22 Illustrations. 11 Plates Postpaid, $2.50 D. VAN NOSTRAND COMPANY Publishers and Booksellers 8 WARREN STREET NEW YORK LIGHT AND COLOR HTHREE authoritative, well illustrated books writ- ten by an investigator in the general field of color, who has the faculty of bringing forth scientific facts in such a manner as to be helpful not only to scientists but to those interested in the various arts. By M. LUCKIESH Director of Applied Science, Nela Research Laboratories, National Lamp Works of General Electric Company COLOR AND ITS APPLICATIONS Second Edition, Revised and Enlarged 431 Pages. 6x9. Cloth. Postpaid, $4.50 150 Illustrations. 4 Color Plates. 21 Tables LIGHT AND SHADE AND THEIR APPLICATIONS 277 Pages. 6x9. Cloth. Postpaid, $3.00 135 Illustrations. 10 Tables VISUAL ILLUSIONS AND THEIR APPLICATIONS 200 Pages. 6x9. Cloth. In Press Fully Illustrated D. VAN NOSTRAND COMPANY Publishers and Booksellers 8 WARREN STREET NEW YORK Eminent Chemists of Our Time By BENJAMIN HARROW, Ph.D. Associate in Physiological Chemistry, Columbia University Author of "From Newton to Einstein" A non-technical account of the more remarkable achievements in the realm of chemistry as exemplified by the life and work of the more modern chemists. There is hardly a chemist of note whose work is not men- tioned in connection with one or another of the eleven following : Perkin and Coal Tar Dyes; Mendeleeff and the Periodic Law; Richards and Atomic Weights; Ram- say and the Gases of the Atmosphere ; van't Hoff and Physical Chemistry; Arr- henius and the Theory of Electrolytic Dissociation; Moissan and the Electric Furnace; Curie and Radi- um; Victor Meyer and the Rise of Organic Chemistry; Remsen and the Rise of Chemistry in America; Fischer and the Chemistry of Foods. The book has all the interest of a work of fiction, the charm of a spark- ling biography and the romance of expanding life overcoming .obstacles and making conquests. It tells the story of the life, work, aspirations and successes of eleven men who have done the most to make the science of chemistry the important factor that it is today in every phase of our lives. Brooklyn Daily Eagle. Popular charm in Professor Har- row's work. . . . Decidedly non- technical, yet manages to convey a wealth of information ... an in- teresting and informative book. N. Y. Tribune. Dr. Harrow's sketches are intelli- gently sympathetic, critical enough, and interestingly interpretative. The book will appeal to the general reader as well as to the special student. N. Y. Evening Post. Chemical literature is enriched by such contributions, and it is by read- ing such works that inspiration for the struggle to attain is brought to the younger generation. It is well for the chemist to know his family tree. 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