Question

What is the radius of a metal atom if it crystallizes with body-centered lattice having a unit cell edge of 333 Pico meter?

(a) 1538.06 pm

(b) 769.03 pm

(c) 288.38 pm

(d) 144.19 pm

The question was asked in a national level competition.

My question is based upon Solid State topic in section Solid State of Chemistry – Class 12

Answer 1

Right option is (d) 144.19 pm

Easiest explanation: For body-centered unit cells, the relation between radius of a particle ‘r’ and edge length of unit cell ‘a’ is given as \(\frac{\sqrt{3}}{4}\)a=r

On substituting the values we get r = \(\frac{\sqrt{3}}{4}\) x 333 pm = 144.19 pm is the radius of the metal atom.