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

The Correct Option is D

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