In crystalline silicon,Si atoms occupy all th | vedclass

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(D) The correct option is $D$.In a $ccp$ lattice,there are $4$ atoms per unit cell.Silicon atoms occupy all $ccp$ sites ($4$ atoms) and every alternat

Vedclass · Accepted Answer

$34$

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(D) The correct option is $D$.In a $ccp$ lattice,there are $4$ atoms per unit cell.Silicon atoms occupy all $ccp$ sites ($4$ atoms) and every alternate tetrahedral void ($4$ atoms).Total number of atoms per unit cell,$Z = 4 + 4 = 8$.The distance between a corner $Si$ atom and a $Si$ atom at the tetrahedral void is $\frac{\sqrt{3}a}{4}$,which is equal to $2r$.Thus,$2r = \frac{\sqrt{3}a}{4} \implies r = \frac{\sqrt{3}a}{8}$.Packing Efficiency $(PE)$ = $\frac{Z 	imes \frac{4}{3} \pi r^3}{a^3} 	imes 100$.Substituting the values: $PE = \frac{8 	imes \frac{4}{3} \pi (\frac{\sqrt{3}a}{8})^3}{a^3} 	imes 100$.$PE = \frac{8 	imes \frac{4}{3} \pi 	imes \frac{3\sqrt{3}a^3}{512}}{a^3} 	imes 100 = \frac{\pi \sqrt{3}}{16} 	imes 100 \approx 34\%$.

In crystalline silicon,$Si$ atoms occupy all the $ccp$ sites and every alternate tetrahedral void. The value of packing efficiency is closest to $....\%$

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