This dissertation examines two areas of active research: 1) solution and aggregation behavior of uranyl peroxide nanosclusters, and 2) post-detonation nuclear forensic analysis of trinitite.  Over the past several years, the Burns group has reported more than 38 distinct uranyl peroxide nanoclusters utilizing the curvature induced by bridging uranyl ions through bidentate peroxo ligands. These nanoclusters self-assemble in aqueous solution. Mono-disperse distributions of clusters are achieved by dissolving cluster-bearing crystals in water. Subsequently, complementary dynamic light scattering (DLS), electrospray ionization mass spectrometry (ESI-MS), small angle X-ray scattering (SAXS), and ultra-small angle X-ray scattering (USAXS) studies have been conducted to examine the solution and aggregation behavior of the U60 nanocluster. Addition of alkali and alkali earth cations to cluster-bearing solution induces exchange of the counterions associated with the clusters, as well as triggering aggregation of clusters into larger entities. The world's first atomic bomb, the Trinity "gadget" was detonated on July 16, 1945. The explosion resulted in partial melting of the surrounding desert sand, which subsequently fused into blast-melt glass known as trinitite. Post-detonation nuclear forensic analysis was conducted on several trinitite samples, utilizing analytical techniques such as optical microscopy, alpha track and beta radiography, gamma spectroscopy, scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS), and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). This study examines the radionuclide distribution and Pu isotopes within trinitite. The results emphasize the importance of utilizing a combination of radiometric techniques and high spatial resolution mass spectrometry when characterizing post-detonation nuclear material.