The Atomic Diameters of Hydrogen and the Inert Gases with respect to Electrons of Very Low Velocity

Abstract

THE wave-mechanical treatment of the problem of the scattering of α-particles by neutral atoms has been given by Sommerfeld (“Wave-Mechanics”, pp. 192–199). To simplify the calculations he assumes that all the electrons in the atom under consideration are concentrated in the K-shell and have no influence on one another. With similar assumptions, but by a somewhat different procedure, we have made an approximate calculation of the scattering of very slow electrons by neutral atoms. This has enabled us to calculate the atomic diameters of hydrogen, helium, neon, and argon with respect to electrons of vanishingly small velocity (0-volt electrons). We obtain the surprising result that the atomic diameters of these gases should vary inversely with respect to their atomic numbers. It is obvious that this result should come out most correctly by experiment in the relative magnitudes of the atomic diameters of hydrogen and helium, as only the K-shell exists in their case, and that the error introduced by the above assumptions as applied to the present problem will become much greater as we pass to the higher atomic numbers owing to the greater number of electrons far outside the K-shell.