Question

. a) Calculate the packing efficiency in a body centred cubic (BCC) structure.

b) Metallic iron crystallizes in a particular type of cubic unit cell. The unit cell edge length is

287pm. The density of iron is 7.87gcm-3

. Calculate the number of iron atoms per unit cell.

[Given: Atomic mass of Fe is 56 & NA = 6.023 X 1023].​

Answer 1

Answer:

A. Solid State

The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

B. Given: Edge length of unit cell a  = 287 pm = 287 × 10−10 cm  = 2.87 x 10–8 cm  Density of iron d = 7.87 g/cm3  NA = 6.023 x 1023 atoms mol−1 Atomic mass of iron M = 55.845 To find: Number of iron atoms z = ? Formula: i. V = a3z = 2 atoms per unit cell. Hence it is Face centred cubic structure FCC

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