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(B) In a $BCC$ (Body-Centered Cubic) unit cell,the number of atoms per unit cell $(Z)$ is $2$. The radius $(r)$ of the atom is related to the edge len

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) In a $BCC$ (Body-Centered Cubic) unit cell,the number of atoms per unit cell $(Z)$ is $2$. The radius $(r)$ of the atom is related to the edge length $(a)$ by the formula $r = \frac{\sqrt{3}a}{4}$. The volume of one atom is $V_{atom} = \frac{4}{3} \pi r^3$. The total volume occupied by atoms $(V)$ is $Z 	imes V_{atom} = 2 	imes \frac{4}{3} \pi \left( \frac{\sqrt{3}a}{4} ight)^3$. $V = \frac{8}{3} \pi \left( \frac{3 \sqrt{3} a^3}{64} ight) = \frac{\sqrt{3} \pi a^3}{8}$. Thus,the correct option is $(B)$.

What is the relation between edge length $a$ and the total volume occupied by atoms in a $BCC$ unit cell?

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