Packing fraction in 2D - hexagonal arrangement of identical spheres is — Solid State Chemistry Question

💡 Solution & Explanation

In a 2D hexagonal close-packed layer, a regular hexagon of side 2r contains an effective number of 3 spheres. Area of hexagon = 6 × √3/4 × (2r)² = 6√3r². Area of 3 spheres = 3πr². Packing fraction = 3πr² / (6√3r²) = π / (2√3) ≈ 90.7%.