A) \[\frac{{{h}^{2}}}{4\pi {{m}^{2}}{{r}^{3}}}\]
B) \[\frac{{{h}^{2}}}{{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
C) \[\frac{{{h}^{2}}}{8{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
D) \[\frac{{{h}^{2}}}{4{{\pi }^{2}}{{m}^{2}}{{r}^{3}}}\]
Correct Answer: D
Solution :
\[v=\frac{{{l}^{2}}}{2h{{\varepsilon }_{0}}}\] \[r=\frac{{{h}^{2}}{{\varepsilon }_{0}}}{\pi m{{e}^{2}}}\,\Rightarrow \,{{\varepsilon }_{0}}=\frac{r\pi m{{e}^{2}}}{{{h}^{2}}}\] \[\frac{{{v}^{2}}}{r}\,=\frac{{{l}^{6}}\pi m}{4{{h}^{4}}\varepsilon _{0}^{3}}\,=\frac{{{h}^{2}}}{4{{r}^{3}}{{\pi }^{2}}{{m}^{2}}}\]
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