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← IIT-JEE 2010 · Paper 2
ChemistrySingle correct+5 / -2Question 5 of 57

IIT-JEE 2010 · Paper 2, Chemistry question 5

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

A square unit cell of edge L with a circle centred at each corner and one circle at the centre; the central circle touches the four corner circles along the diagonals.
Choose one option
Answer and worked solution

Official answer: D

Radius. The centre circle touches the corner circles along the diagonal: 4r=L24r=L\sqrt2, so r=2L4r=\dfrac{\sqrt2L}4.

Circles per cell. 4×14+1=24\times\frac14+1=2.

Efficiency.
2πr2L2=2π⋅2L216L2=π4=78.54%.\frac{2\pi r^2}{L^2}=\frac{2\pi\cdot\frac{2L^2}{16}}{L^2}=\frac\pi4=78.54\%.

(D)

Topics:Packing efficiency
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