The packing effciency ofa simple cubic crystal is given by

Options

A. `sqrt(2)pi//6`
B. `sqrt(3)pi//8`
C. `pi//6`
D. `pi//8`

Answer

3

Explanation

In simple cubic unit cell ,the edge length (or side) of the cube `a` and the radius of atom, `r` are related as
`a=2r`
The volume of the cubic unit cell=`a^(3)`
`=(2r)^(3)=(8r)^(3)`
Since a simple cubic unit cell contains only `1`atom , the volume of the volume of the occupied space `=(4)(3)pir^(3)`
:.Packing efficiency
`=("volume of one atoms ")/("volume of cubic unit cell")xx100%`
`=(4//3pir^3)/(8r^(3))xx100`
`= (pi)/(6)xx100%`