Q85 / 180 · AIIMS 2001 · Chemistry

A solid $A B$ has $\mathrm{NaCl}$ type structure. The radius of $A^{+}$is $100 \mathrm{pm}$. What is the radius of $B^{-}$?

  • Correct answer
    A
    190.47
  • B
    540.13
  • C
    525
  • D
    78.12

Solution

$\mathrm{NaCl}$ type structure is also called face centred cubic lattice. Here the radius ratio $\left(r_c / r_a\right)$ ranges from 0.414 to 0.732 . $$ \begin{aligned} \text { Radius ratio }=\frac{r_c}{r_a}= & \frac{\text { radius of cation }}{\text { radius of anion }} \\ \Rightarrow \quad \text { Radius of anion }\left(B^{-}\right) & =\frac{\text { radius of } A^{+}}{\text {radius ratio }} \\ & =\frac{100}{0.414} \text { to } \frac{100}{0.732} \\ & =241.5 \text { to } 136.6 . \end{aligned} $$

Hence, the correct answer is option: 'A'.

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