A metal crystallizes in such a lattice in which only 70% of the total space of the crystal is occupi — Solid State Chemistry Question

💡 Solution & Explanation

Packing fraction = $\frac{Z \times \frac{4}{3}\pi r^3}{V} = 0.70 \implies \frac{Z}{V} = \frac{2.10}{4\pi r^3}$. Density $d = \frac{Z \times M}{N_A \times V} = \frac{2.10}{4\pi r^3} \times \frac{32\pi}{N_A} = \frac{16.8}{r^3 N_A} = \frac{16.8}{(2 \times 10^{-8})^3 \times 6 \times 10^{23}} = 3.5 \text{ g/cm}^3$. Therefore, correct answer is B.