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(A) For a simple cubic unit cell,the number of atoms per unit cell $(Z)$ is $1$.The relationship between the edge length $(a)$ and the atomic radius $

Vedclass · Accepted Answer

$\frac{\pi}{6}$

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(A) For a simple cubic unit cell,the number of atoms per unit cell $(Z)$ is $1$.The relationship between the edge length $(a)$ and the atomic radius $(r)$ is $a = 2r$ or $r = \frac{a}{2}$.The volume of one atom is $V_{atom} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (\frac{a}{2})^3 = \frac{4}{3} \pi \frac{a^3}{8} = \frac{\pi a^3}{6}$.The packing fraction is defined as the ratio of the volume of atoms to the total volume of the unit cell $(a^3)$:$	ext{Packing Fraction} = \frac{Z 	imes V_{atom}}{a^3} = \frac{1 	imes \frac{\pi a^3}{6}}{a^3} = \frac{\pi}{6}$.

The fraction of total volume occupied by the atoms present in a simple cubic unit cell is

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