Ionic radius

Definition. The ionic radius of an ion is the distance from the centre of its nucleus out to which it exerts influence on the surrounding electron cloud.

Pauling's method. For a uni-univalent ionic crystal, Pauling calculated the individual cation and anion radii from the experimentally measured inter-ionic distance $d$, starting from two assumptions: the ions are perfect touching spheres, so

and, for ions that have a noble-gas electronic configuration, the ionic radius is inversely proportional to the effective nuclear charge felt at the ion's periphery:

Dividing (2) by (3) gives the ratio of the two radii purely in terms of their effective nuclear charges (found via Slater's rules, Section 3.5.1), and combining that ratio with equation (1) lets both individual radii be solved for.

Worked example: Na+ and F- in NaF, given the inter-ionic distance $d_{Na-F} = 231$ pm. Both ions have the neon (Ne) electron configuration $1s^2\,2s^2\,2p^6$, so Slater's rules give the same screening constant for both: for a 2p electron in this configuration, $S = (7 \times 0.35) + (2 \times 0.85) = 2.45 + 1.70 = 4.15$. Then:

$(Z_{eff})_{Na^+} = 11 - 4.15 = 6.85 \qquad\qquad (Z_{eff})_{F^-} = 9 - 4.15 = 4.85$ …