Question

calculate the packing efficiency of simple cubic structure

Answer 1

suppose the edge length of the unit cell =a.
radius of the sphere=r
As spheres are touching each other evidently
a=2r
number of spheres per unit cell=8·1/8=1
volume of the sphere=4/3(pi)r^3
volume of the cube=a^3
=(2r)^3=8r^3
therefore packing efficiency= volume of the sphere/ volume of the cube ·100=52.4%