Q.What are isoelectronic ions? Give examples.

Ionic radius is the distance from an ion's nucleus out to which it exerts influence over the surrounding electron cloud. Pauling's method finds the individual cation and anion radii of a uni-univalent ionic crystal from its measured inter-ionic distance $d = r_{C^+} + r_{A^-}$, using the assumption that for ions sharing a noble-gas electron configuration, radius is inversely proportional to effective nuclear charge: $r \propto 1/Z_{eff}$. Dividing the cation and anion proportionalities gives their radius ratio purely from Slater $Z_{eff}$ values, which combined with the measured $d$ solves for both radii (worked example: Na+ and F- in NaF, $d = 231$ pm, gives $r_{Na^+} = 95.9$ pm and $r_{F^-} = 135.1$ pm).

Comparing isoelectronic species (same electron count, different nuclear charge): the more positive the charge on a cation, the smaller its radius (more protons pulling on the same electron cloud); the more negative the charge on an anion, the larger its radius (more electron-electron repulsion swelling the same-shell electron cloud with the same nuclear pull). So for an isoelectronic series such as $N^{3-} > O^{2-} > F^- > Na^+ > Mg^{2+} > Al^{3+}$, radius shrinks steadily as the charge becomes more positive.

Comparing an atom to its own ion: a cation (fewer electrons than the parent atom, same nuclear charge) is always smaller than the neutral atom, and an anion (more electrons) is always larger -- so for the same element, $\text{cation} < \text{atom} < \text{anion}$.