Calculate the packing efficiency in a simple cubic lattice. 

Explanation

In a simple cubic lattice, the atoms are located only on the corners of the cube.
The number of atoms per unit cell in simple cube is one. Each atom is considered as one sphere.
Let the edge length of the cube be `= a`
The radius of each atom `= r`
`a=2r`

Total volume of unit cell `=a^(3)=(2r)^(3)=8r^(3)`
So, the volume of one atom (one sphere) `=(4)/(3)pi^(3)`
`"Packing efficiency "=("Volume of one sphere (atom)")/("Total volume of the unit cell")xx100%`
`"Packing efficiency "=((4)/(3)pir^(3))/(8r^(3))xx100=(pi)/(6)xx100=52.4%`