Question

A metal X has a BCC structure with nearest neighbor distance 365.9 pm. What is metal X if its density is 1.0016 g cm^-3?

(a) Aluminum

(b) Magnesium

(c) Sodium

(d) Potassium

I had been asked this question in an interview for internship.

Question is taken from Solid State in portion Solid State of Chemistry – Class 12

Answer 1

The correct answer is (c) Sodium

The explanation: Given,

Nearest neighbor distance (d) = 365.9 pm

Density (ρ) = 1.51 g cm^-3

For the BCC structure, nearest neighbor distance (d) is related to the edge length (a) as d=\(\Big(\frac{\sqrt{3}}{2}\Big)\) x a

Or a=\(\Big(\frac{2}{\sqrt{3}}\Big)\) x d = 2/1.732 x 365.9 = 422.5 pm

For BCC structure, Z=2

We know, (ρ) = (Z x M)/(a^3 x N0)

Or M = (ρ x a^3 x N0)/Z

          = (1.0016 x 10^6 x (422.5 x 10^-12)^3 x 6.02 x 10^23)/2

          = 23 amu

Therefore, the given metal X is Sodium.