A) \[\frac{\pi }{3\sqrt{2}}\]
B) \[\frac{\pi }{4\sqrt{2}}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
Correct Answer: D
Solution :
Volume of cube \[={{a}^{3}}\] Volume of unit cell \[=1\times \frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi {{\left( \frac{a}{2} \right)}^{3}}=\frac{\pi {{a}^{3}}}{6}\] \[\therefore \]Packing fraction \[=\frac{\pi {{a}^{3}}}{6/C{{l}^{3}}}=\frac{\pi }{6}\]
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