A metal having atomic mass crystallizes in ABCABC... type packing. The density of each metal atom if — Solid State Chemistry Question

💡 Solution & Explanation

Mass of 1 atom = $\frac{60.22}{6.022 \times 10^{23}} = 10^{-22} \text{ g}$. For ABCABC (FCC), $r = \frac{a}{2\sqrt{2}} = \frac{10}{2\sqrt{2}} = \frac{5}{\sqrt{2}}$ Å. Volume of one atom = $\frac{4}{3}\pi r^3 = \frac{4}{3} \pi (\frac{5}{\sqrt{2}} \times 10^{-8})^3 \approx 1.85 \times 10^{-22} \text{ cm}^3$. Density of one atom = $\frac{10^{-22}}{1.85 \times 10^{-22}} \approx 0.54 \text{ g/cm}^3$. Therefore, correct answer is C.