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(C) In a $bcc$ (body-centered cubic) unit cell,the number of atoms per unit cell $(n)$ is $2$.The packing efficiency $(P.E.)$ is calculated using the

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$68$

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(C) In a $bcc$ (body-centered cubic) unit cell,the number of atoms per unit cell $(n)$ is $2$.The packing efficiency $(P.E.)$ is calculated using the formula:$P.E. = \frac{n 	imes \frac{4}{3}\pi r^3}{a^3}$For $bcc$,the relation between edge length $(a)$ and radius $(r)$ is $r = \frac{\sqrt{3}a}{4}$,which implies $a = \frac{4r}{\sqrt{3}}$.Substituting the values:$P.E. = \frac{2 	imes \frac{4}{3}\pi r^3}{(\frac{4r}{\sqrt{3}})^3} = \frac{\frac{8}{3}\pi r^3}{\frac{64r^3}{3\sqrt{3}}} = \frac{8\pi}{3} 	imes \frac{3\sqrt{3}}{64} = \frac{\sqrt{3}\pi}{8}$$P.E. \approx 0.68$ or $68\%$.

What is the percentage of space occupied in a $bcc$ arrangement (in $\%$)?

Similar Questions

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