Question

A crystalline solid $AB$ has $NaCl$ type structure with radius of $B^{-}$ ion is $250pm$. Which of the following cation can be made to slip into tetrahedral site of crystals of $A^{+}{B}^{-}$?

• A. $P^{+}(radius=180pm)$
• B. $Q^{+}(radius=56pm)$
• C. $R^{+}(radius=200pm)$
• D. $S^{+}(radius=150pm)$

Answer 1

The correct option is B $Q^{+}(radius=56pm)$

$\begin{array}{c}AB\text{as Nacl type structure}\to FCC\\ \text{Radius of}B,RB=250pm\\ \text{radius ratio}\end{array}$

$\begin{array}{cc}\Rightarrow \frac{R_{A^{+}}}{R_{B^{-}}}& =0.414\\ \Rightarrow R_{A^{+}}& =0.414\times 250\\ & =103.5Pm\end{array}$

$\begin{array}{c}{P}^{+},R^{+}\text{and}{S}^{+}\text{have greater radius then}103.5pm\\ \text{these are not able to slip.}\\ \text{only}{Q}^{+}(R=56pm)\text{can made to slip into tetrahedral}\\ \text{site.}\end{array}$