The vacant space in bec lattice cell is

Step-by-step solution

In a body-centered cubic (BCC) unit cell, the number of atoms per unit cell is Z = 2 . The relation between the edge length a and the atomic radius r is given by 4r = 3 a , which implies r = 3 a 4 . The volume occupied by the atoms is V_ atoms = Z 4 3 r³ = 2 4 3 ( 3 a 4 )³ . V_ atoms = 2 4 3 3 3 a³ 64 = 3 a³ 8 0.68 a³ . The packing efficiency is 68 % . The vacant space is 100 % - 68 % = 32 % . Answer: 32 %