Question

$\text{CsCl}$ crystallises in body centred cubic lattice. If 'a' is its edge length then which of the following expressions is correct?

• A. $\text{r}_{\text{Cs}^{+}} + \text{r}_{\text{Cl}^{-}} = 3 \text{a}$
• B. $\text{r}_{\text{Cs}^{+}} + \text{r}_{\text{Cl}^{-}} = \frac{3 \text{a}}{2}$
• C. $\text{r}_{\text{Cs}^{+}} + \text{r}_{\text{Cl}^{-}} = \frac{\sqrt{3}}{2} a$
• D. $\text{r}_{\text{Cs}^{+}} + \text{r}_{\text{Cl}^{-}} = \sqrt{3} \text{a}$

Answer 1

Answer: (C)

$\text{8}$ chloride ions at $\text{8}$ corners $\text{Cs}^{\text{+}}$ cation at body centre along body diagonal there will be one $\text{Cs}^{\text{+}}$ cation and $\text{2} \, \text{Cl}^{-}$ ions at ends of body diagonal.
$2 \text{r}_{\text{Cs}^{+}} + 2 \text{r}_{\text{Cl}^{-}} = \sqrt{3} a$
$\text{a}$ is edge length