Solid StateHard
Question
Packing fraction in 2D-hexagonal arrangement of identical spheres is
Options
A.$\frac{\pi}{3\sqrt{2}}$
B.$\frac{\pi}{3\sqrt{3}}$
C.$\frac{\pi}{2\sqrt{3}}$
D.$\frac{\pi}{6}$
Solution
$P.F. = \frac{V_{\text{particle}}}{V_{\text{Unitcell}}} = \frac{3 \times \frac{4}{3}\pi r^{3}}{\left\{ 6 \times \frac{\sqrt{3}}{4} \times (2r)^{2} \right\} \times 2r} = \frac{\pi}{3\sqrt{3}}$
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