In simple cubic unit cell, two atoms touch along the edge of the unit cell.
For simple cubic cell, the relationship between the edge length a and the radius r is a=2r
The volume of the unit cell V=a3=(2r)3=8r3
Each simple cubic cell contains eight atoms present at eight corners. Each atom contributes one eight to the unit cell. Hence, number of atoms present in one unit cell =8×18=1
The volume occupied by one atom in unit cell =43πr3
Packing efficiency=Volume occupied by one atomvolume of unit cell×100
Packing efficiency=43πr38r3×100
Packing efficiency=52.4%.
Hence, the percentage efficiency of packing in case of simple cubic cell is 52.4 %.