In FCC unit cell, what fraction of edge is not covered by atoms? — Solid State Chemistry Question

💡 Solution & Explanation

In FCC, atoms touch along the face diagonal: 4r = a √2 => 2r = a / √2. Along any edge of length a, there are two corner atoms, so the covered distance along the edge is 2r. The fraction of edge covered is 2r / a = 1 / √2 ≈ 0.707. The fraction of edge NOT covered is 1 - 0.707 = 0.293.