An element (atomic mass = 125) crystallizes in simple cubic structure. If the diameter of the larges — Solid State Chemistry Question

💡 Solution & Explanation

In simple cubic, the largest sphere fits in the body-centred cubic void, with diameter $d_{void} = (\sqrt{3} - 1)a$. Given $d_{void} = 366 \text{ pm} \implies a(0.732) = 366 \implies a = 500 \text{ pm} = 5 \times 10^{-8} \text{ cm}$. Density $d = \frac{1 \times 125}{6 \times 10^{23} \times (5 \times 10^{-8})^3} = \frac{125}{75} = \frac{5}{3} \text{ g/cm}^3$. Thus, $300 d = 300 \times \frac{5}{3} = 500$. Therefore, correct answer is 0500.