Calculate packing efficiency in simple cubic unit cell.

Explanation

In simple cubic lattice the atoms are located only on the corners of the cube.
(a) The atoms touch each other along the edge.
(b) Edge length of the cube is 'a' and radius of the each atom is r. `therefore a=2r`.
( c) The volume of unit cell is `a^(3) = (2r)^(3) =8r^(3)`
( d) Simple cubic unit cell contain only one atom.
( e) The volume of the one atom `=4/3 pi r^(3)`
Packing efficiency `=("volume of one atom")/("volume of the cubic unit cell") xx 100`
`(4//3 pi r^(3))/(8r^(3)) xx 100`
`= pi//6 xx 100 = 52.4`%