A) \[\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{2}}}\]
B) \[\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{3}}}\]
C) \[\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{5}}}{{{h}^{3}}}\]
D) \[\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{2}}}{{{h}^{3}}}\]
Correct Answer: B
Solution :
Current, \[i=\frac{e}{t}=\frac{e}{2\pi r/v}=\frac{ev}{2\pi r}\] Here, \[v={{e}^{2}}/h\] and \[r={{h}^{2}}/m{{e}^{2}}\] \[\therefore \] \[i=\frac{e({{e}^{2}}/h)}{2\pi ({{h}^{2}}/m{{e}^{2}})}=\frac{{{e}^{3}}\times m{{e}^{2}}}{2\pi {{h}^{3}}}=\frac{m{{e}^{5}}}{2\pi {{h}^{3}}}\] \[\because \] \[h=h/2\pi \] (given) \[\therefore \] \[i=\frac{m{{e}^{5}}}{2\pi {{\left( \frac{h}{2\pi } \right)}^{3}}}=\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{3}}}\]
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