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

Explanation

Let the side of the cube be a and the radius of each particle be r.

Then`" "a=2r`
Volume of the unit cell `=(2r)^(3)=8r^(3)`
Simple cubic unit cell contains only 1 atom
Volume of the occupied space `=(4)/(3)pir^(3)`
Volume of the occupied space `=(4)/(3)pir^(3)`
`therefore" Packing efficiency "=("Volume of one atom")/("Volume of cubic unit cell")xx100`
`=((4)/(3)pir^(3))/(8r^(3))xx100=(pi)/(6)xx100=52.4%`