Methane crystallizes in a cubic unit cell with edge length 0.6 nm. The density of solid is only slig — Solid State Chemistry Question

💡 Solution & Explanation

Edge length $a = 0.6 \text{ nm} = 6 \times 10^{-8} \text{ cm}$. Volume $a^3 = 216 \times 10^{-24} \text{ cm}^3$. Molar mass of $\text{CH}_4 = 16 \text{ g/mol}$. Number of molecules $Z = \frac{d \times N_A \times a^3}{M} \approx \frac{0.5 \times 6.022 \times 10^{23} \times 216 \times 10^{-24}}{16} \approx \frac{65}{16} \approx 4.06$. The integer number of molecules is 4. Therefore, correct answer is 4.