Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A . The unit cell edge length is 50 % more in solid 2 than in 1 . What is the approximate packing efficiency in solid 2 ?

Step-by-step solution

If radius of A is r radius of B will be 2 r . Atoms in the body diagonal touch. Therefore: r + 2 r + 2 r + r = 3   a 6   r = 3   a or a = 6 r 3 Packing Efficiency = 1 × 4 3 π r 3 + 1 × 4 3 π ( 2 r ) 3 a 3 = 4 3 π r 3 × 9 ( 6 r / 3 ) 3 = 4 × 9 × π × r 3 × 3 3 3 × 216 × r 3 = 90.5   %