Question

An element with cell edge of 288 pm has a density of 7.2 g cm^-3. What type of structure does the element have if it’s atomic mass M=51.8 g mol^-1?

(a) Body-Centred Cubic (BCC)

(b) Face-Centred Cubic (FCC)

(c) Simple Cubic

(d) Hexagonal Closed Packing (HCP)

The question was asked during an internship interview.

The doubt is from Solid State topic in portion Solid State of Chemistry – Class 12

Answer 1

Correct answer is (a) Body-Centred Cubic (BCC)

For explanation I would say: Given,

Edge length (a) = 288 pm

Density (ρ) =  7.2 g cm^-3

Atomic mass (M) = 51.8 g mol^-1

Avogadro’s number (N0) = 6.02 x 10^23

We know, (ρ) = (Z x M)/(a^3 x N0)

Or Z =(ρ x a^3 x N0)/M = (7.2 x (288 x 10^-10) ^3 x 6.02 x 10^23)/51.8

      Z = 2

Therefore, the element has Body-Centred Cubic (BCC) type of structure.