In face centred cubic (fcc) crystal lattice, edge length is $400$ pm. Find the diameter (in pm) of a greatest sphere which can be fit into the interstitial void without distortion of a lattice.

(Give your answer to the nearest integer)

In fcc lattice, the largest void present is octahedral void.

If the radius of void sphere is $R$ and of lattice sphere is $r$, then
$r=\frac{\sqrt{2}\times 400}{4}=141.42$ pm

Applying condition for octahedral void

$2(r+R)=$ edge length, $a$

$\therefore 2R=a-2r$

$2R=400-(2\times 141.42)=117.16$

Hence, the diameter of greatest sphere is $117.16$ pm.