Calculate the packing efficiency in simple cubic lattice.

Explanation

Packing efficiency of metal crystal for simple cubic lattice.
Let a be the edge length of the unit cell and r be radius of the sphere.
Volume of the sphere `= (4)/(3) pi r^(3)`

As the spheres at the corners are touching each other, the edge length a = 2r
Volume of the cube `= a^(3) = 8r^(3)`
% of the space occupied by spheres
`= ("Volume of sphere")/("Volume of cube") xx 100`
`= ((4)/(3) pi r^(3) xx 100)/(8r^(3)) = 52.4%`
Packing efficiency of simple cubic lattice is 52.4%
Example : Silicon and germanium (Any one).