The Energies of Multiple X-Ray Ionization of Light Atoms

The assumption is made that the removal of a K electron has the same effect on the energies of the outer electrons of the atom as the increase of the nuclear charge by one unit. The energy for the successive removal of a K electron and an L electron is computed for elements Na to K on this basis. By means of Wentzel's theory and Hjalmar's measurements of the K spark lines ${\alpha }_3$, ${\alpha }_4$, ${\alpha }_5$, ${\alpha }_6$, other multiple ionization levels are computed for the elements Na to S. The square roots of the energies ($\sqrt{\frac{\nu }{R}}$) for the successive removal of the first, second, and third L electrons plotted against atomic numbers give three parallel straight lines indicating that the removal of the first L electron reduces the screening constant (7.27) for the remaining ones by 0.62, and that the removal of the second one causes a further reduction of 0.65. Similar lines are obtained for the two K electrons, the screening constant (1.5) being reduced 0.16 by the removal of the first one. The energies for the successive removal of two electrons from a helium-like ion made up of a nucleus of charge $Z$ and two electrons are computed for these atoms. The plot indicates that the experimental value of the $K$ absorption limit of phosphorus is in error.