The Radii of the Alkali and Halogen Ions and of the Atoms of Inert Gases

Abstract

Packing radii of the alkali and halogen ions in crystal lattices.---An analysis of recent results for the distances of closest approach of the ions in the lattices of all the alkali halides indicates (1) that these ions pack as though they were nearly spherical in shape; (2) that the heavier ions have packing radii which are nearly constant, i.e. independent of the ions with which they are combined; and (3) that the radii of ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, and ${\mathrm{Cs}}^{+}$ are approximately equal to those of the negative ions with the same number of electrons, ${\mathrm{Cl}}^{\ensuremath{-}}$, ${\mathrm{Br}}^{\ensuremath{-}}$, and ${\mathrm{I}}^{\ensuremath{-}}$, respectively, the approximation being closer the greater the atomic number. Assuming the radii of ${\mathrm{Cs}}^{+}$ and ${\mathrm{I}}^{\ensuremath{-}}$ to be equal, and that the first two conclusions above hold rigidly, the radii of the ions are computed to be as follows, in units of ${10}^{\ensuremath{-}8}$cm: for ${\mathrm{Cs}}^{+}$ and ${\mathrm{I}}^{\ensuremath{-}}$, 1.974; ${\mathrm{Rb}}^{+}$, 1.679; ${\mathrm{Br}}^{\ensuremath{-}}$, 1.737; ${\mathrm{K}}^{+}$, 1.548; ${\mathrm{Cl}}^{\ensuremath{-}}$, 1.589; ${\mathrm{Na}}^{+}$, 1.1 to 1.2; ${\mathrm{Fl}}^{\ensuremath{-}}$, 1.0 to 1.2. These values are in general agreement with the average of the ionic radii computed by Land\'e (from crystal data), Richards (from compressibility), and Saha (from ionization potentials), but differ considerably from Bragg's results from x-ray data. The above conclusions are shown to be in qualitative agreement with the Lewis-Langmuir theory.Packing radii of the inert gases computed from x-ray data on the assumption that for each gas the radius is the mean of those for the alkali and halogen ions with the same number of electrons, come out: for Xe, 1.97; Kr, 1.71; Ar, 1.57; Ne, 1.15. These are only from.0 to.27 units higher than the values obtained by Rankine from viscosity measurements. Assuming these radii, the atomic volume per electron comes out approximately constant for Xe, Kr and Ne, though somewhat low for Ar.