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Abstract The Thomas-Fermi statistical model of the atom leads to the formula 20·92Z 7,3 ev for the total binding energy of an atom with atomic number Z, but this formula gives values which are too high by roughly 20%. The actual binding energies increase quite smoothly with increasing Z, which suggests the existence of a more appropriate formula. The reasons for the discrepancy are explained and a new theoretical formula derived. This is compared with spectroscopic and self-consistent field data and is found to agree within 1 or 2%. Some uncertainty remains about the relativistic correction for heavy atoms.
J.M.C. Scott (Fri,) studied this question.