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