Experimental data on the electronic binding energies in individual K, L, M, N, O, P shells for all atoms from hydrogen to uranium are analyzed using special reduced coordinates. The atomic number similarity law is found in every subshell and it is expressed through two smooth functions. The violation of smoothness usually indicates measurement errors and a change in slope indicates a filling subshell. The polynomial approximation of the functions allows restore missing or erroneous data with an accuracy of 1–2%.

periodic table of elements, orbital energy, electron binding energy, electron shell, atomic number self-similarity, semi-classical method

Mathematical modelling in actual problems of science and technics

Shpatakovskaya Galina Vasil’evna,  ,  orcid.org/0000-0002-8430-9114,  KIAM RAS