Chemistry - Solid State Question with Solution | TestHub

For a body-centered cubic (bcc) unit cell, the relation between the atomic radius $r$ and the edge length $a$ is $4r=\sqrt{3}a$.

The number of atoms per unit cell in a bcc structure is $Z=2$.

The packing fraction is the ratio of the volume occupied by the atoms to the total volume of the unit cell:

$\text{Packing fraction}=\frac{2\times \frac{4}{3}\pi r^3}{a^3}=\frac{\sqrt{3}\pi }{8}\approx 0.68$

Given the total volume of the unit cell $V=1.5\times 10^{-22}{\mathrm{cm}}^3$.

The volume occupied by all atoms is:

$V_{\text{atoms}}=0.68\times 1.5\times 10^{-22}{\mathrm{cm}}^3=1.02\times 10^{-22}{\mathrm{cm}}^3$

Answer: $1.02\times 10^{-22}{\mathrm{cm}}^3$