Packing Efficiency in Simple Cubic Structures

Let 'a' be the cube edge and 'r' the atomic radius.
As the particles touch each other along the edge,
therefore, a = 2r
Volume of the unit cell (V) = a³
Since one atom is present in a unit cell, so, its volume
v = 4/3 πr³
or, v = 4/3 π(a/2)³
or, v = πa³/6

So, packing efficiency = (100 × v)/V
= (πa³ × 100)/6 × a³
= 314/6 = 52.4%

Therefore, 52.4% of unit cell is occupied by atoms and the rest 47.6% is empty space.