What is the volume occupied by particles in B | vedclass

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(A) In a $BCC$ unit cell,the number of particles $(Z) = 2$. The relation between edge length '$a$' and radius '$r$' is $\sqrt{3} a = 4 r$,which gives

Vedclass · Accepted Answer

$\frac{\sqrt{3} \pi a^3}{8}$

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(A) In a $BCC$ unit cell,the number of particles $(Z) = 2$. The relation between edge length '$a$' and radius '$r$' is $\sqrt{3} a = 4 r$,which gives $r = \frac{\sqrt{3} a}{4}$. The volume occupied by particles is calculated as $Z 	imes 	ext{Volume of one sphere}$. $	ext{Volume} = 2 	imes \frac{4}{3} \pi r^3$. Substituting $r$: $	ext{Volume} = 2 	imes \frac{4}{3} \pi (\frac{\sqrt{3} a}{4})^3$. $	ext{Volume} = \frac{8}{3} \pi 	imes \frac{3 \sqrt{3} a^3}{64}$. $	ext{Volume} = \frac{\sqrt{3} \pi a^3}{8}$.

What is the volume occupied by particles in $BCC$ structure if '$a$' is the edge length of the unit cell?

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