In the work, proceeding from the equations of compressible oscillating ether, deduced from laws of classical mechanics, ethereal mathematical models of nucleus and atoms of chemical elements of the first and second periods of the Mendeleyev’s periodic table, including nucleus of many isotopes are constructed. The formulas for their internal energies, masses, magnetic moments and binding energies are derived, the numerical values of which coincide, with an accuracy of tenths of a percent, with the "anomalous" values, which are in no way understandable from the point of view of modern physical science. In the absence of relativistic effects and the orbital motion of electrons in the ether model, formulas were obtained for calculating the radii of atoms, and the physical and chemical essence of the periodic law was clarified.

Keywords: ether equations, atom, atomic nucleus, binding energy, ionization energy, magnetic moment, atom radius, degree of oxidation, periodic law.