A) \[\frac{\pi }{2}\]
B) \[\frac{\sqrt{3\pi }}{8}\]
C) \[\frac{\sqrt{2\pi }}{6}\]
D) \[\frac{\pi }{6}\]
Correct Answer: D
Solution :
In simple cubic arrangement, no. of atoms = 1 \[a=2r\] \[\therefore \,\,\,\,\,~Packing\text{ }fraction\] \[=\,\,\frac{Volume\,\,occupied\,\,by\,\,one\,\,atom}{Volume\,\,of\,\,unit\,\,cell}\] \[=\,\,\,\frac{\frac{4}{3}\pi {{r}^{3}}}{{{a}^{3}}}=\frac{\frac{4}{3}\pi {{r}^{3}}}{{{(2r)}^{3}}}=\frac{\pi }{6}\]
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