polonium crystallizes in a simple cubic unit cell

Question

polonium crystallizes in a simple cubic unit cell with an edge length of 3.36A.

1. what is the volume of the unit cell?

2. what is the volume of atom in the unit cell?

3. what is the packing efficiency of polonium?

Ans) Volume of unit cell = a³  = (3.36)³  = 37.93 cu Å

r = a/2 = 3.36/2 = 1.68

Vol of atom = 4/3*pi*r³ = {4*3.14*(1.68)³ }/3 = {4*3.14*4.74}/3 = 19.84 cu Å

Packing efficiency = Vol of atom * no. of atoms / vol of unit cell

For simple cubic, Packing efficiency = 19.84*1/37.93 = 0.52 = 52%