The questions of natural science knowledge of the laws of Nature, actualizing the problem of positioning atoms of chemical elements. Using the known physical concepts and methodology of information retrieval of significant indicators of the event, an endogenous model of the atom is formed. A set of mathematical procedures characterizing the systemic nature of changes in the properties of atomic structures is proposed. A series of computational procedures for estimating the mass of atoms over the entire natural numerical series is implemented. The presence of an un-countable set of atomic constructions possessing the fundamental property of exponential reduction of the lifetime is established.