Question

Lithium iodide crystal has a face-centred cubic unit cell. If the edge length of the unit cell a 620 pm, determine the ionic radius of $I^{-}$ ion.

Answer 1

Given that, $LiI$ crystallizes as face centered cubic unit cell. So, $I^{-}$ ions on the face diagonals will be touching each other. If $a$ is the edge of the cube and $r$ is the radius of the $I^{-}$ ions.

$\sqrt{2}a=4r$

$\Rightarrow r=\frac{\sqrt{2}}{4}a=\frac{a}{2\sqrt{2}}=\frac{620}{2\sqrt{2}}pm=219.20pm$