Chemistry - CHEMICAL BONDING Question with Solution | TestHub

Pauling gave a method to calculate univalent ion radii by assuming that:

(i) In an ionic crystal (let M⁺ X⁻), cations and anions are in contact with each other, and the sum of their radii is equal to the interionic distance, $d({\mathrm{M}}^{+}-{\mathrm{X}}^{-})=r_{{\mathrm{M}}^{+}}+r_{{\mathrm{X}}^{-}}$.

(ii) The radius of an ion having a noble gas configuration is inversely proportional to the effective nuclear charge felt at the periphery of the ion, i.e., $r({\mathrm{M}}^{+})=\frac{C}{Z_{\mathrm{eff},{\mathrm{M}}^{+}}}$ and $r({\mathrm{X}}^{-})=\frac{C}{Z_{\mathrm{eff},{\mathrm{X}}^{-}}}$ pm.

Here, C is a constant of proportionality whose value depends on the electronic configuration of the ion. Thus, $d({\mathrm{M}}^{+}-{\mathrm{X}}^{-})=\frac{C}{Z_{\mathrm{eff},{\mathrm{M}}^{+}}}+\frac{C}{Z_{\mathrm{eff},{\mathrm{X}}^{-}}}$ pm.

Here, $Z_{\mathrm{eff}}$ is the effective nuclear charge, whose value can be calculated by the formula: $Z_{\mathrm{eff}}=Z-\sigma$. Here, $\sigma$ is the shielding constant, and for neon, the value of $\sigma$, when calculated by Slater's rule, is found to be 4.5.