The packing fraction of the primitive cubic unit cell is

Options

A. `0.283`
B. `0.321`
C. `0.523`
D. `0.685`

Answer

C

Explanation

No. of spheres per unit cell `=(1)/(8)xx8=1`
Volume of the sphere `=(4)/(3) pi r^(3)`
Volume of the cube `=a^(3)=(2r)^(3)=8r^(2)`
Packing fraction `=((4)/(3) pi r^(3))/( 8r^(3))=(pi)/(6)=0.523`