# CsCI crystallizes in body centred cubic lattice. If 'a' its edge length then which of the following expressions is correct

1. A

${\mathrm{r}}_{{\mathrm{Cs}}^{+}}+{\mathrm{r}}_{{\mathrm{CI}}^{-}}=3\mathrm{a}$

2. B

${\mathrm{r}}_{{\mathrm{Cs}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}}=\frac{3\mathrm{a}}{2}$

3. C

${\mathrm{r}}_{{\mathrm{Cs}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}}=\frac{\sqrt{3}}{2}\mathrm{a}$

4. D

${r}_{{\mathrm{Cs}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}}=\sqrt{3}\mathrm{a}$

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### Solution:

In $\mathrm{CsCl},{\mathrm{Cl}}^{-}$ lie at corners of simple cube and ${\mathrm{Cs}}^{+}$ at the body centre. Hence. Along the body diagonal, ${\mathrm{Cs}}^{+}$ and $C{I}^{-}$ touch each other so.

$\frac{\sqrt{3}\mathrm{a}}{2}={\mathrm{r}}_{{\mathrm{Cs}}^{4}}+{\mathrm{r}}_{{\mathrm{CI}}^{-}}$

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