Question

The fraction of total volume occupied by the atoms present in a simple cube is :
AIPMT -2007

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

Answer 1

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

For simple cubic (SC):


$Z_{eff}\text{for SC = 1}$
So,
$\text{The total volume occupied by sphere}V=1\times \frac{4}{3}\times \pi r^3$
$\text{Volume of the cube}=a^3=(2r{)}^3$
$\text{Packing fraction (P.F.)}=\frac{1\times \frac{4}{3}\times \pi r^3}{(2r{)}^3}P.F.=\frac{\pi }{6}$