A hexagonal closed packed solid in 2D is made up of cylindrical atoms. Calculate the packing efficiency of this solid, in 2 D (area wise). (Answer to nearest integer)

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TestHub · Accepted Answer

To calculate the packing efficiency, consider a unit cell of the 2D hexagonal close-packed structure. This unit cell is a rhombus containing two atoms.

Area of atoms = $2 \times π r^{2}$

Area of rhombus = $2 \times \frac{3}{2} (2 r)^{2} = 23 r^{2}$

Packing efficiency = $\frac{2 π r ^{2}}{2 3 r ^{2}} \times 100 = \frac{π}{3} \times 100 \approx 90.69% \approx 91%$

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