A) \[\frac{1}{2\pi n}\]
B) \[\frac{1}{2\pi {{n}^{2}}}\]
C) \[\frac{n}{2\pi }\]
D) \[\frac{{{n}^{2}}}{2\pi }\]
Correct Answer: C
Solution :
The velocity of electron in nth orbit is given by \[\upsilon =\frac{nh}{2\pi m{{r}_{n}}}\] ?.(1) Also, \[\lambda =\frac{h}{p}=\frac{h}{m\upsilon }\] ...(2) From eqs. (1) and (2), we have \[\lambda =\frac{h}{m\frac{nh}{2\pi m{{r}_{n}}}}\] \[=\frac{2\pi {{r}_{n}}}{n}\] \[\therefore \] \[\frac{{{r}_{n}}}{\lambda }=\frac{n}{2\pi }\]
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