With Goudsmit's extension of Landé's formula for ($\overline{\frac{1}{r^3}}$) it is possible to explain the order of magnitude of the isotope displacements in Hg, Tl, Pb arc and spark spectra on the hypothesis of small changes in nuclear radii. The nuclear radius is supposed to be proportional to the $\frac{1}{3}$ power of the atomic weight. The effective nuclear charge is supposed to be distributed with a roughly uniform density through the interior of the nucleus. The spectra Hg I, Hg II, Tl I, Tl II, Pb II, are in agreement with the above theory. The larger displacements are due to the addition or removal of a $6s$ or $7s$ electron to the electron configuration. The direction of the shift is in agreement with the supposition that the nuclear radius increases with atomic weight, the heavier isotope having the looser binding for the $s$ and $p_{\frac{1}{2}}$ electrons. In order to explain the shifts of the $6p^2$, $6p7s$, $6p8s$, $d6p$, $6p8p$ configurations of PbI it is supposed that in this case the displacements are due principally to changes in the penetration to the nucleus of the $6s^2$ subgroup. These changes are presumably caused by differences in screening of the two $6s$ electrons from the nucleus as the valence electron is excited from the $6p$ state to the ionization limit.

• Received 12 September 1932

DOI:https://doi.org/10.1103/PhysRev.42.348