Question

To determine the radii of a univalent ion, Pauling gave a method as follows:
i. In an ionic crystal of the type $M^{+}{X}^{-}$, cations and anions are in contact with each other. Therefore, the sum of their ionic radius is equal to the interionic distance.
ii. $r_M^{+}+r_X^{-}=\frac{c}{Z_{eff}\left(M^{+}\right)}+\frac{c}{Z_{eff}\left(X^{-}\right)}$ pm $Z_{eff}$ is the effective nuclear charge $Z_{eff}=Z-\sigma$ ; where $\sigma$is the screening constant. For $\text{Ne},\sigma =4.5$
$\therefore r_{\text{M}}^{+}=\frac{c}{Z_{\text{eff}}\left(M^{+}\right)}$ and $r_X^{-}=\frac{c}{Zeff\left(X^{-}\right)}$

The actual interionic distance in $MgO$ should be:

• A. 256 pm
• B. 276 pm
• C. Lesser than 256 pm
• D. 372 pm

Answer 1

The correct option is C Lesser than 256 pm

$c=\frac{6.5\times 4.5\times 230}{11}pm$
$r_M^{+}+r_X^{-}=d_{MgO}=c[\frac{1}{(12-4.5)}+\frac{1}{(8-4.5)}]$
$d_{MgO}=[\frac{6.5\times 4.5\times 230}{11}\times \frac{11}{(7.5\times 3.5)}]=256pm$
Since $M{g}^{2+}$ and $O^{2-}$ are bivalent ions, force of attraction between them are greater than the monovalent ions.
Actual $d_{MgO}<256pm$