A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{3\sqrt{2}}\]
D) \[\frac{\pi }{4\sqrt{2}}\]
Correct Answer: B
Solution :
\[\pi /6\] In a simple cube, no. of atoms/unit cell \[=8\times \frac{1}{8}=1\] \[\operatorname{Volume} of atom =\frac{4}{3}\pi {{r}^{3}}\] \[\operatorname{Volume} of cube = {{a}^{3}} = {{\left( 2r \right)}^{3}} = 8{{r}^{3}} \left( \because a = 2r \right)\] \[\therefore Fraction occupied = \frac{\frac{4}{3}\pi {{\operatorname{r}}^{3}}}{8{{\operatorname{r}}^{3}}}=\frac{\pi }{6}\]
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