Calculate tbe packing efficiency of a metal crystal for a simple cubic lattice.

Explanation

Packing efficiency of a metal crystal for a simple cubic lattice

Suppose the edge length of the unit cell = a
Radius of the sphere = r
In simple cubic unit cell as spheres are touching eath other a = 2r
No. of spheres per unit cell `=1/8xx8=1`
Volume of sphere =`4/3pir^3`
Volume of the cube = `a^3=(2r)^3=8r^3`
`therefore`Packing efficiency `=4/3pir^3//8r^3=pi/6=0.524`
Or % occupied `=0.524xx100=52.4%`