Q. A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass about 50 g ${mol}^{- 1}.$ What would be the density of the metal$\left( in\ g\ {cm}^{- 3} \right)?$

A) 3.1
B) 6.2
C) 9.3
D) 12.4
Explanation

(b)
Given,
Molar mass, $M =$50g/mol
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ N_{A} = 6.02 \times 10^{23}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z = 2$ (for bcc crystal)
Edge length $a = 300\ pm$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3 \times 10^{- 8}cm$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d = \frac{Z \times M}{N_{A} \times a^{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{2 \times 50}{6.02 \times 10^{23} \times \left( 3 \times 10^{- 8} \right)^{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 6.15$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \approx 6.2$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.