A) \[{{e}^{2}}\]
B) \[{{e}^{3}}\]
C) \[{{e}^{5}}\]
D) \[{{e}^{6}}\]
Correct Answer: C
Solution :
Time period of electron, \[T=\frac{2\pi r}{v}\] \[=\frac{\frac{2\pi \times {{\varepsilon }_{0}}\,\,{{n}^{2}}{{h}^{2}}}{\pi m{{e}^{2}}}}{\frac{{{e}^{2}}}{2{{\varepsilon }_{0}}nh}}\] \[T=\frac{4\varepsilon _{0}^{2}{{n}^{2}}{{h}^{3}}}{m{{e}^{4}}}\] Current, \[i=\frac{e}{T}=\frac{e}{\frac{4\varepsilon _{0}^{2}{{n}^{2}}{{h}^{2}}}{m{{e}^{4}}}}\] \[i=\frac{m{{e}^{5}}}{4\varepsilon _{0}^{2}{{n}^{2}}{{h}^{5}}}\] i.e., \[i\propto {{e}^{5}}\]You need to login to perform this action.
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