Question

A metal crystallizes into two cubic phases BCC and FCC. The ratio of densities of FCC and BCC is equal to 1.5. Calculate the difference between the unit cell lengths of the FCC and BCC crystals if the edge length of the FCC crystal is equal to 4.0 Å.

(a) 0.5 Å

(b) 0.37 Å

(c) 0. 28 Å

(d) 0.73 Å

I have been asked this question in an interview.

This interesting question is from Solid State topic in portion Solid State of Chemistry – Class 12

Answer 1

Right answer is (b) 0.37 Å

Easy explanation: Given,

Edge length of FCC crystal (aFCC) = 4.0 Å

For FCC structure, Z = 4

For BCC structure, Z=2

Avogadro’s number (N0) = 6.02 x 10^23

The density of a crystal (ρ)=(Z x M)/(a^3 x N0)

 Therefore, the ratio of Densities= ρFCC/ρBCC = (ZFCC x a^3BCC) / (ZBCC x a^3FCC)

      1.5 = (4 x (aBCC)^3) / ( 2 x (4 x 10^-10)^3)

                            (aBCC)^3 = (1.5 x 2 x 64 x 10^-30)/ 4  = 48 x 10^-30

Therefore aBCC = 3.63 Å

Difference in Unit Cell Length = 4.0 – 3.63 = 0.37 Å.