Chemistry - Solid State Question with Solution | TestHub

Volume of the unit cell, $V=a^3=6.4\times 10^{-23}$ cm${}^3$

$a^3=64\times 10^{-24}$ cm${}^3$

$a=(64\times 10^{-24}{)}^{1/3}$ cm $=4\times 10^{-8}$ cm

Converting to picometers:

$a=4\times 10^{-8}\times 10^{10}$ pm $=400$ pm

For an fcc unit cell, the relation between edge length $a$ and radius $r$ is given by:

$4r=\sqrt{2}a$

$r=\frac{\sqrt{2}a}{4}=\frac{a}{2\sqrt{2}}$

$r=\frac{400}{2\sqrt{2}}=100\sqrt{2}$ pm

$r=100\times 1.414=141.4$ pm

Answer: $141.4$ pm