The percentage of unoccupied volume in a simp | vedclass

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Question

(C) Key Idea: Percentage of unoccupied volume $= 100 - 	ext{Packing efficiency}.$Packing efficiency $= \frac{	ext{Volume of one atom}}{	ext{Volume

Vedclass · Accepted Answer

$47.60$

Vedclass · Answer

(C) Key Idea: Percentage of unoccupied volume $= 100 - 	ext{Packing efficiency}.$Packing efficiency $= \frac{	ext{Volume of one atom}}{	ext{Volume of cubic unit cell}} 	imes 100\%.$For a simple cubic cell,the number of atoms per unit cell is $1$ and the relation between edge length $a$ and radius $r$ is $a = 2r.$Packing efficiency $= \frac{\frac{4}{3} \pi r^3}{(2r)^3} 	imes 100 = \frac{\frac{4}{3} \pi r^3}{8 r^3} 	imes 100 = \frac{\pi}{6} 	imes 100 \approx 52.4\%.$$	herefore$ Percentage of unoccupied volume in $SCC = 100 - 52.4 = 47.6\%.$

The percentage of unoccupied volume in a simple cubic cell is (in $\%$)

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