Explain the following variations in atomic or ionic radii: (a) \(\mathrm{I}^{-}>\mathrm{I}>\mathrm{I}^{+}\) (b) \(\mathrm{Ca}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (c) \(\mathrm{Fe}>\mathrm{Fe}^{2+}>\mathrm{Fe}^{3+}\)

The three cases demonstrate different trends in atomic and ionic radii: (a) \(\mathrm{I}^{-} > \mathrm{I} > \mathrm{I}^{+}\): The iodine anion has gained an electron, causing repulsion between electrons and resulting in an increased atomic radius. The iodine cation has lost an electron, reducing electron-electron repulsion and decreasing its radius. (b) \(\mathrm{Ca}^{2+} > \mathrm{Mg}^{2+} > \mathrm{Be}^{2+}\): As we move down Group 2 elements in the Periodic Table, the atomic radius increases due to the addition of electron shells. All three ions have divalent charges but differ in electron shells. (c) \(\mathrm{Fe} > \mathrm{Fe}^{2+} > \mathrm{Fe}^{3+}\): As neutral iron loses electrons to form cations, electron-electron repulsion decreases and effective nuclear charge felt by the remaining electrons increases, causing the cations to have smaller radii.