Question

In $CsCl$ structure, cesium and chloride ions are in contact along the body diagonal of the unit cell. The length of the side of the unit cell is $412$ pm and chloride ion has a radius of $181$ pm. Calculate the radius (in pm) of caesium ion.

• A. $35.24$
• B. $89.2$
• C. $134.4$
• D. $175.8$

Answer 1

The correct option is D $175.8$

The edge length $\left(a\right)$ is $412$ pm and the radius of chloride ion is $181$ pm.
The length of body diagonal is $\sqrt{3}\times a=\sqrt{3}\times 412=713.6$ pm $....\left(1\right)$
The length of the body diagonal is also equal to $2(r_{C{s}^{+}}+r_{C{l}^{-}})=2(r_{C{s}^{+}}+181)$ $....\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, we get
$713.6=2(r_{C{s}^{+}}+181)$
$351.6=2r_{C{s}^{+}}$
$r_{C{s}^{+}}=175.8$ pm