Question

The fraction of total volume occupied by the atoms present in a simple cubic lattice is:

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{3\sqrt{2}}$
• D. $\frac{\pi }{4\sqrt{2}}$

Answer 1

The correct option is B $\frac{\pi }{6}$

For simple cubic lattice,

Radius (r) = $\frac{a}{2}$

Volume of the atom = $\frac{4}{3}\times \pi \times {\left(\frac{a}{2}\right)}^3$

Packing fraction = $\frac{\frac{4}{3}\times \pi \times {\left(\frac{a}{2}\right)}^3}{a^3}=\frac{\pi }{6}$

Hence, the correct answer is option $\text{B}$.