Chemistry - Solid State Question with Solution | TestHub

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

$\sqrt{3}a=4r$

$a=\frac{4r}{\sqrt{3}}$

Substituting $r=200\text{ pm}=2\times 10^{-8}\text{ cm}$:

$a=\frac{4\times 2\times 10^{-8}}{1.732}\approx 4.618\times 10^{-8}\text{ cm}$

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

$V=(4.618\times 10^{-8}{)}^3\approx 9.848\times 10^{-23}{\text{ cm}}^3$

Answer: $9.848\times 10^{-23}{\text{cm}}^3$