What is the packing efficiency in simple cubic unit cell?

52.4%

The correct answer is option 2. 52.4%.

Simple cubic lattice

In a simple cubic lattice, the atoms are located only on the corners of the cube. The particles touch each other along the edge.

Thus, the edge length or side of the cube ‘a’, and the radius of each particle, 'r' are related as a = 2r

The volume of the cubic unit cell = a³ = (2r)³ = 8r³

Since a simple cubic unit cell contains only 1 atom.

The volume of the occupied space = \(\frac{4}{3}\)πr³

∴ Packing efficiency = \(\frac{\text{Volume of one atom}}{\text{Volume of cubic unit cell}}\) × 100%

P.E. = \(\frac{\frac{4}{3}πr^3}{8r^3}\) x 100 = \(\frac{π}{6}\) x 100 = 52.36% = 52.4 %