Question

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

• A. 3.1
• B. 6.2
• C. 9.3
• D. 12.4

Answer 1

Answer: (B)

$a = 300\, pm,\, Z = 2$ (for bcc unit cell)
$M = 50 \,g\,mol^{-1}$
Density, $\rho = \frac{Z\times M}{N_{A} \times a^{3}\times 10^{-30}} g \,cm^{-3}$
$= \frac{2\times 50}{N_{A}\times 10^{23}\times \left(300\right)^{3}\times 10^{-30}} =\frac{100}{6.02\times 27\times 10^{-1}}$
$= \frac{1000}{6.02\times 27} = 6.15\,g\,cm^{-3} \approx 6.2\,g \,cm^{-3}$