What is the percentage of unoccupied volume i | vedclass

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(A) Packing efficiency $	ext{P.E.} = \frac{z 	imes \frac{4}{3} \pi r^3}{V} = \frac{2 	imes \frac{4}{3} 	imes \pi (\frac{\sqrt{3} a}{4})^3}{a^3} =

Vedclass · Accepted Answer

$32$

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(A) Packing efficiency $	ext{P.E.} = \frac{z 	imes \frac{4}{3} \pi r^3}{V} = \frac{2 	imes \frac{4}{3} 	imes \pi (\frac{\sqrt{3} a}{4})^3}{a^3} = \frac{\sqrt{3} \pi}{8} \approx 0.68$ or $68 \%$. Since $z = 2$,$r = \frac{\sqrt{3} a}{4}$,and $V = a^3$ for a $BCC$ unit cell. In $BCC$ structure,$68 \%$ of the total volume is occupied by atoms. Therefore,the percentage of unoccupied volume (void space) is $100 \% - 68 \% = 32 \%$.

What is the percentage of unoccupied volume in $BCC$ structure (in $\%$)?

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