Question

If the length of body diagonal for $\text{CsCl}$, which crystallises into a cubic structure with ${\text{Cl}}^{-}$ ions at the corners and ${\text{Cs}}^{+}$ ions at the centre of unit cell is $7\mathring{A}$ and the radius of ${\text{Cs}}^{+}$ ion is $1.69\mathring{A}$. The radius of ${\text{Cl}}^{-}$ ion?

Answer 1

$\text{CsCl}$ is BCC structure.

So, in $\text{BCC}$ structure atoms touch along the body diagonal i.e.,

$2(r_{{\text{Cl}}^{-}}+r_{{\text{Cs}}^{+}})=7$

$2r_{{\text{Cl}}^{-}}=7-2r_{{\text{Cs}}^{+}}=7-\left(3.38\right)=3.62A°$

$r_{{\text{Cl}}^{-}}=\frac{3.62}{2}=1.81A°$