Question

The volume occupied by atoms in a simple cubic unit cell is (edge length $=$ a) :

• A. $a^3$
• B. $\frac{4\pi a^3}{3}$
• C. $\frac{\pi a^3}{6}$
• D. $\frac{\sqrt{3}\pi }{8}$

Answer 1

The correct option is C $\frac{\pi a^3}{6}$

In simple cubic lattice, we have $a=2r$
Volume $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(\frac{a}{3}\right)}^3=\frac{1}{6}\pi a^3$