Question

Total volume of atoms present in a face centred cubic unit cell of a metal is ($r$ is atomic radius)

• A. $\frac{16}{3} \pi r^3$
• B. $\frac{20}{3} \pi r^3$
• C. $\frac{24}{3} \pi r^3$
• D. $\frac{12}{3} \pi r^3$

Answer 1

Answer: (A)

$\frac{16}{3} \pi r^3$

Answer 2

In $fcc$, no. of spheres in the unit cell
$= 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$
Volume of 4 spheres = $4 \times \frac{4}{3} \pi r^3 = \frac{16}{3} \pi r^3$