JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Solid State

The packing efficiency of the two-dimensional square unit cell shown below is

(A)39.27%
(B)68.02%
(C)74.05%
(D)78.54%✓ Correct

Answer: (D)

Solution

For a 2D square unit cell with circles at corners, each circle contributes 1/4 to the unit cell, giving 4 × 1/4 = 1 circle per unit cell. If the circle radius is r, the square side length is 2r. Packing efficiency = (Area of circles)/(Area of unit cell) = (πr²)/(2r)² = π/4 ≈ 0.7854 = 78.54%.

JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Single correct option

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