What is the packing efficiency of the two-dim | vedclass

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(D) The unit cell is a two-dimensional square with one atom at the center and four atoms at the corners.Number of atoms $(n)$ = $1 + (4 	imes \frac{1

Vedclass · Accepted Answer

$78.54$

Vedclass · Answer

(D) The unit cell is a two-dimensional square with one atom at the center and four atoms at the corners.Number of atoms $(n)$ = $1 + (4 	imes \frac{1}{4}) = 2$.The diagonal of the square $(d)$ is equal to $4r$,where $r$ is the radius of the atom.$d = \sqrt{2}a = 4r$,so $a = \frac{4r}{\sqrt{2}} = 2\sqrt{2}r$.Packing Efficiency $(P.E.)$ = $\frac{	ext{Area of atoms}}{	ext{Area of unit cell}} 	imes 100$.$P.E. = \frac{n 	imes \pi r^2}{a^2} 	imes 100 = \frac{2 	imes \pi r^2}{(2\sqrt{2}r)^2} 	imes 100$.$P.E. = \frac{2\pi r^2}{8r^2} 	imes 100 = \frac{\pi}{4} 	imes 100 \approx 78.54\%$.

What is the packing efficiency of the two-dimensional square unit cell shown below (in percentage) (in $\%$)?

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