The theoretical packing efficiency of a two-dimensional square unit cell (atoms at corners touching — Solid State Chemistry Question

💡 Solution & Explanation

In a 2D square unit cell, four corner circles contribute one full circle. If the edge length is $a$, then $a=2r$. Packing efficiency $=\frac{\pi r^2}{a^2}=\frac{\pi r^2}{4r^2}=\frac{\pi}{4}=0.785\approx78.5\%$.