Chemistry - Solid State Question with Solution | TestHub

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

$a=2\sqrt{2}r$

Given $r=180$ pm $=180\times 10^{-10}$ cm.

$a=2\sqrt{2}\times 180\times 10^{-10}$ cm $=360\sqrt{2}\times 10^{-10}$ cm

Volume of the unit cell $V=a^3$

$V=(360\sqrt{2}\times 10^{-10}{)}^3$ cm${}^3$

$V=46656000\times 2\sqrt{2}\times 10^{-30}$ cm${}^3$

$V=131964271\times 10^{-30}$ cm${}^3\approx 1.32\times 10^{-22}$ cm${}^3$

Answer: $1.32\times 10^{-22}c{m}^3$