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A solid $A B$ has $\mathrm{NaCl}$ type structure. The radius of $A^{+}$is $100 \mathrm{pm}$. What is the radius of $B^{-}$?
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The correct answer is:
190.47
$\mathrm{NaCl}$ 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 .
$$
\begin{aligned}
\text { Radius ratio }=\frac{r_c}{r_a}= & \frac{\text { radius of cation }}{\text { radius of anion }} \\
\Rightarrow \quad \text { Radius of anion }\left(B^{-}\right) & =\frac{\text { radius of } A^{+}}{\text {radius ratio }} \\
& =\frac{100}{0.414} \text { to } \frac{100}{0.732} \\
& =241.5 \text { to } 136.6 .
\end{aligned}
$$
$$
\begin{aligned}
\text { Radius ratio }=\frac{r_c}{r_a}= & \frac{\text { radius of cation }}{\text { radius of anion }} \\
\Rightarrow \quad \text { Radius of anion }\left(B^{-}\right) & =\frac{\text { radius of } A^{+}}{\text {radius ratio }} \\
& =\frac{100}{0.414} \text { to } \frac{100}{0.732} \\
& =241.5 \text { to } 136.6 .
\end{aligned}
$$
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