[Olympiad] A metal crystallizes in a face-centered cubic (FCC) lattice. If the density is 10.5 g/cm³ and the atomic mass is 108 g/mol, calculate the unit cell edge length (a).
- 204 pm
- 312 pm
- 408 pm
- 520 pm
📝 Detailed explanation
Density = (Z * M) / (Na * a³). For FCC, Z=4.a³ = (4 * 108) / (6.022 × 10²³ * 10.5) = 432 / 6.323 × 10²⁴ = 6.83 × 10⁻²³ cm³.
a = ∛(6.83 × 10⁻²³) ≈ 4.08 × 10⁻⁸ cm = 408 pm.