Caleulate the packing efficiency in a unit cell of Cubic Close Packing(CCP) structure. 

Explanation

a) Packing efficiency is a percentage of total space filled by the particles in a crystal. The unit cell of a simple cube is

A simple cubic unit cell consists of only one atom/ particle/sphere per unit cell. Let .a. be the edgelength of the unit cell and .r. be the radius of the sphere.
We know that volume of the spherer `=(4)/(3)pir^(3)`
The spheres/ lattice points at the corners in the simple cubic unit cell are touching each other. Therefore edge length `= a = 2r`
Similarly volume of the cube `=a= (2r) 3 = 8r^(3)`
Percentage of the space occupied by spheres
`=("Volume of the sphere")/("Volume of the cube")xx100=((4)/(3)pir^(3))/(8r^(3))xx100`
`=(4xx100xx22)/(8xx3xx7)`
`=52.38%~~52.4%` is the packing fraction in simple cubic lattice