Question

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

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

Answer 1

Answer: (D)

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

Answer 2

Volume of an atom $=\frac{4}{3} \pi r^{3}$ In fcc, number of atoms per unit cell $=4$ $\therefore$ Volume of total atoms $=4 \times \frac{4}{3} \pi r^{3}$ $=\frac{16}{3} \pi^{3}$