A) \[\frac{2{{E}_{1}}}{{{n}^{3}}h}\]
B) \[\frac{2{{E}_{1}}{{n}^{3}}}{h}\]
C) \[\sqrt{\frac{2m{{E}_{1}}}{{{n}^{2}}h}}\]
D) \[\frac{{{E}_{1}}{{n}^{2}}}{h}\]
Correct Answer: A
Solution :
\[{{E}_{n}}\,=\frac{{{E}_{1}}}{{{n}^{2}}}\] \[\frac{1}{2}m{{v}^{2}}\,=\,\left( \frac{{{E}_{1}}}{{{n}^{2}}} \right)\] \[mvr\,=\,\frac{nh}{2\pi }\] \[\omega =\frac{v}{r}\,=\frac{{{E}_{1}}4\pi }{{{n}^{3}}h}\] \[\frac{\omega }{2\pi }=f\,=\frac{2{{E}_{1}}}{{{n}^{3}}h}\]
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