A solid element (monoatomic) exists in cubic crystal. If its atomic radius is Å and the ratio of pac — Solid State Chemistry Question

💡 Solution & Explanation

Packing fraction (PF) = $\frac{Z \times \frac{4}{3}\pi r^3}{a^3}$. Density ($d$) = $\frac{Z \times M}{N_A \times a^3}$. $\frac{\text{PF}}{d} = \frac{4\pi r^3 N_A}{3M}$. Given $\frac{\text{PF}}{d} = 0.1 \text{ cm}^3\text{/g}$ and $r = 10^{-8} \text{ cm}$. $0.1 = \frac{4\pi \times (10^{-8})^3 \times 6 \times 10^{23}}{3M} = \frac{8\pi \times 10^{-1}}{M} \implies M = 8\pi$. Therefore, correct answer is A.