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 \[\,\,\,\,r\,\,\,\,\,\,\,\propto \,\,\,\,\,\,\,n\] |
You need to login to perform this action.
You will be redirected in
3 sec