Chemistry - Solid State Question with Solution | TestHub

For a body-centered cubic (bcc) unit cell, the relationship between the edge length $a$ and the atomic radius $r$ is:

$\sqrt{3}a=4r$

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

Substituting $r=1.86\times 10^{-8}\mathrm{cm}$ and $\sqrt{3}\approx 1.732$:

$a=\frac{4\times 1.86\times 10^{-8}}{1.732}\approx 4.30\times 10^{-8}\mathrm{cm}$

The volume of the unit cell is $V=a^3$:

$V=(4.30\times 10^{-8}{)}^3$

$V=79.507\times 10^{-24}{\mathrm{cm}}^3$

$V\approx 7.951\times 10^{-23}{\mathrm{cm}}^3$

Answer: $7.951\times 10^{-23}{\mathrm{cm}}^3$