Question

The packing fraction of the element that crystallizes 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 cubic unit cell a = 2r, Z = 1.
Packing fraction $=\frac{\frac{4}{3}\pi r^3}{a^3}=\frac{\frac{4}{3}\pi r^3}{(2r{)}^3}=\frac{\pi }{6}$