A metal crystallises in a body-centred cubic lattice with unit cell edge 330 pm. Using sqrt3 = 1.732, calculate the atomic radius in pm (nearest integer).

JEE Main levelNumerical answerDifficulty 2 of 3ss013

A metal crystallises in a body-centred cubic lattice with unit cell edge $330 pm$ . Using $3 = 1.732$ , calculate the atomic radius in pm (nearest integer).

Numerical answer type, answer in pm, tolerance 0.5.

In bcc the atoms touch along the body diagonal of length

3 a = 4 r

. So

r = \frac{3 a}{4} = \frac{1.732 \times 330}{4} = 142.89 pm \approx 143 pm