Question

Total volume of atoms present in a fcc cell of a metal with radius r is

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

Answer 1

Answer: (B)

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

Answer 2

$a = 2\sqrt{2}r$

Volume of the cell

$a^{3} = (2\sqrt{2}r)^{3} = 16\sqrt{2}r^{3}$

No. of spheres in fcc

$= 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$

Volume of 4 spheres

$= 4 \times \frac{4}{3}\pi r^{3} = \frac{16}{3}\pi r^{3}$