Question

The packing fraction of the element that crystallises in simple cubic arrangement is :

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

Answer 1

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

In simple unit cell $a=2r$
$Z=1$

$\therefore \text{Packing fraction}=\frac{\text{Volume occupied by all the spheres in the unit cell}}{\text{Total volume of the unit cell}}$
$\Rightarrow \frac{\frac{4}{3}\pi r^3}{a^3}=\frac{\frac{4}{3}\pi r^3}{(2r{)}^3}=\frac{\pi }{6}$