The Solid State - Result Question 24
####24. The fraction of total volume occupied by the atoms present in a simple cube is
[2007]
(a) $\frac{\pi}{3 \sqrt{2}}$
(b) $\frac{\pi}{4 \sqrt{2}}$
(c) $\frac{\pi}{4}$
(d) $\frac{\pi}{6}$
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Solution:
- (d) Number of atoms per unit cell $=1$
Atoms touch each other along edges. Hence $r=\frac{a}{2}$
( $r=$ radius of atom and $a=$ edge length)
Therefore $%$ fraction $=\frac{\frac{4}{3} \pi r^{3}}{(2 r)^{3}}=\frac{\pi}{6}=0.52$
