A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius of A is half of radius of B. What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?

Effective no. of atoms of  B present in unit cell = 2 Total volume of B unoccupied by A in a unit cell= 2×43(R3-r3)×π = 7πR33                                           ∵ r = R2Volume of unit cell =  a3⇒4R33=6433R3                        ∵ 3a = 4R Desired ratio ⇒7πR336433R3=7π364