A metal crystallizes into two cubic systems-face centred cubic (fcc) and simple cubic (SC), whose unit cell lengths are 4 .5 and 1 .5 A o respectively. Calculate the ratio of densities of face centred cubic and Simple cubic.

Step-by-step solution

face centred cubic unit cell length = 4 .5 A o Simple cubic unit cell length = 1 .5 A o Density in face centred cubic = n 1 × a t o m i c w e i g h t V 1 × A v o g a d r o n u m b e r Density simple cubic (SC) = n 2 × a t o m i c m a s s V 2 × A v o g a r d r o n u m b e r D f c c D b c c = n 1 n 2 × V 2 V 1 n 1 for face centred cubic = 4; Also V 1 = a 3 = 4.5 × 10 - 8 3 n 2 for simple cubic = 1; Also V 2 = a 3 = 1.5 × 10 - 8 3 D f c c D s c = 4 × ( 1.5 × 1 0 - 8 ) 3 1 × ( 4.5 × 1 0 - 8 ) 3 = 0.15