A Note on Atomic Binding Energies

By the use of Dickinson's recent calculations of the diamagnetic field for atoms based on Hartree calculations, and a theorem due to Feynman, an expression is obtained for the total binding energy of the electrons in an atom as a function of atomic number. The results are compared with predictions of the Fermi-Thomas statistical model. It is found that the binding energy for small $Z$ varies as $Z^{\frac{7}{3}}$ in accord with the statistical model but for high $Z$ the dependence on $Z$ becomes approximately $Z^{\frac{12}{5}}$. The equation for the binding energies is estimated to be correct to 5 percent or better.