A metal exists as FCC crystal. If the atomic radius is 100 √2 pm and the density of metal is 12,500 — Solid State Chemistry Question

💡 Solution & Explanation

In FCC, Z = 4. Edge length a = 2 √2 r = 2 √2 × 100 √2 pm = 400 pm = 4 × 10^-8 cm. Volume V = a³ = 6.4 × 10^-23 cm³. Density ρ = 12,500 kg/m³ = 12.5 g/cm³. Using the density formula ρ = (Z × M) / (Na × a³) => M = (ρ × Na × a³) / Z = (12.5 × 6 × 10^23 × 6.4 × 10^-23) / 4 = 480 / 4 = 120 g/mol, which is extremely close to Sn (atomic mass = 119.8).