A metal exists as FCC crystal. If the atomic radius is and the density of metal is , the metal is (A — Solid State Chemistry Question

💡 Solution & Explanation

For FCC, $a = 2\sqrt{2} r = 2\sqrt{2} \times 100\sqrt{2} = 400 \text{ pm} = 4 \times 10^{-8} \text{ cm}$. Density = $12,500 \text{ kg/m}^3 = 12.5 \text{ g/cm}^3$. Molar mass $M = \frac{d \times N_A \times a^3}{Z} = \frac{12.5 \times 6 \times 10^{23} \times (4 \times 10^{-8})^3}{4} = \frac{75 \times 10^{23} \times 64 \times 10^{-24}}{4} = 120$. Sn has an atomic mass of 119.8. Therefore, correct answer is C.