A) \[{{r}_{n}}\propto n\]
B) \[{{r}_{n}}\propto 1/n\]
C) \[{{r}_{n}}\propto {{n}^{2}}\]
D) \[{{r}_{n}}\propto 1/{{n}^{2}}\]
Correct Answer: A
Solution :
Potential energy \[U=eV=e{{V}_{0}}\ln \frac{r}{{{r}_{0}}}\] Force \[F=-\left| \frac{dU}{dr} \right|=\frac{e{{V}_{0}}}{r}\]. The force will provide the necessary centripetal force. Hence \[\frac{m{{v}^{2}}}{r}=\frac{e{{V}_{0}}}{r}\] Þ \[v=\sqrt{\frac{e{{V}_{0}}}{m}}\] ?..(i) and \[mvr=\frac{nh}{2\pi }\] ?..(ii) From equation (i) and(ii) \[mr=\left( \frac{nh}{2\pi } \right)\sqrt{\frac{m}{e{{V}_{0}}}}\] or r µ nYou need to login to perform this action.
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