Question

Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is 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

Total number of atoms in face centred cubic unit cell = 4 At comer $= 8\times\frac{1}{8} = 1$ On faces $= 6\times\frac{1}{2} = 3$ Total $= 4$ Total volume $= 4 \times \frac{4\pi r^{3}}{3}$ $= \frac{16}{3}\pi r^{3}$