A) \[\frac{{{n}^{2}}{{h}^{2}}}{4{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
B) \[\frac{{{n}^{2}}{{h}^{2}}}{2{{n}^{2}}{{r}^{3}}}\]
C) \[\frac{4{{n}^{2}}{{h}^{2}}}{{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
D) \[\frac{4{{n}^{2}}{{h}^{2}}}{4{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
Correct Answer: A
Solution :
\[mvr=\frac{nh}{2\pi }\] Þ \[v=\frac{nh}{2\pi mr}\] Þ \[\frac{{{v}^{2}}}{r}=\frac{{{n}^{2}}{{h}^{2}}}{4{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\].
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