Calculate the efficiency of packing in case of a metal crystal for

 In a simple cubic lattice the atoms are located only at the corners of the cube.

 Let us assume the edge length or the side of the cube = a

And the radius of each particle = r 

The relation between radius and edge a

Can be given as a = 2r

The volume of the cubic unit cell = side3 = a3

;     = (2r3)

;     = 8r3

Number of atoms in unit cell  =8×1/8=1

The volume of the occupied space =(4/3)πr^3

And we know that, the packing efficiency =(Volume of one atom×100)/(Volume of cubic unit cell)

=((4/3)πr^3×100)/(8r^3 )

    =π/6×100 

    = 52.36%