A) \[{{r}_{n}}{{\alpha }_{n}}\]
B) \[{{r}_{n}}\alpha 1/n\]
C) \[{{r}_{n}}\alpha \,{{n}^{2}}\]
D) \[{{r}_{n}}\alpha \,1/{{n}^{2}}\]
Correct Answer: A
Solution :
| electric field, \[E=-\frac{dV}{dr}\]\[=-\frac{d}{dr}\left[ {{V}_{0}}\ln \frac{r}{{{r}_{0}}} \right]\]\[=-\frac{{{V}_{0}}}{r}\] |
| Centripetal force, \[E\,e=\frac{m{{v}^{2}}}{r}\] |
| \[\operatorname{or}\frac{{{V}_{0}}}{r}e\,\,\,=\frac{m{{v}^{2}}}{r}\] |
| \[\operatorname{or}\,\,\,\,\,\,\,\,\,v\,\,\,\,=\,\,\,cr{}^\circ \] |
| Now \[mvr=\frac{nh}{2\pi }\] |
| \[\therefore \,\,\,\,\,\,\,r\,\,\,\,\,\,\,=\frac{nh}{2\pi mv}\] |
| Or \[\,\,\,\,r\,\,\,\,\,\,\,\propto \,\,\,\,\,\,\,n\] |
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