Aluminium crystallizes in cubic system with unit cell edge length equal to 4.0 Å. If its density is — Solid State Chemistry Question

💡 Solution & Explanation

Density ρ = (Z × M) / (Na × a³) => 45/16 = (Z × 27) / (6 × 10^23 × (4 × 10^-8)³) = (Z × 27) / 38.4 => Z = 4. Since Z = 4, Aluminium forms a Face-Centred Cubic (FCC) lattice. In an FCC unit cell, the relation between edge length (a) and atomic radius (r) is 4r = a × √2 => r = a × √2 / 4 = 4.0 × √2 / 4 = √2 = 1.414 Å.