Question

Packing fraction is simple cubic lattice is

• A. $\frac{1}{6}\pi$
• B. $\frac{\sqrt{2}}{6}\pi$
• C. $\frac{\sqrt{3}}{8}\pi$
• D. $\frac{1}{2}\pi$

Answer 1

The correct option is A $\frac{1}{6}\pi$

As we know ,

Radius of atom in simple unit cell = $\frac{a}{2}$

Packing fraction = $\frac{1\times volume-of-atom}{volume-of-unit-cell}$

Volume of atom = $\frac{4}{3}\times \pi \times r^3$

Volume of unit cell = $a^3=(2r{)}^3$

Putting the value of above two in the main equation, we get

Packing fraction = $\frac{\frac{4}{3}\times \pi \times r^3}{(2r{)}^3}$

Hence , Packing fraction = $\frac{\pi }{6}$