A) \[9{{r}_{0}}\]
B) \[3{{r}_{0}}\]
C) \[{{r}_{0}}\]
D) \[\frac{{{r}_{0}}}{3}\]
Correct Answer: A
Solution :
Here: Radius of first orbit\[={{r}_{0}}\] The radius of \[n\]the orbit is given by, \[{{r}_{n}}=\frac{{{\varepsilon }_{0}}{{h}^{2}}}{\pi m{{Z}_{e}}^{2}}\times {{n}^{2}}\propto {{n}^{2}}\] Hence, \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{n}_{1}}}{{{n}_{2}}} \right)}^{2}}=\frac{1}{9}\] or \[{{r}_{3}}=9{{r}_{1}}=9{{r}_{0}}\](where \[{{r}_{3}}\] is the radius of 3rd orbit)
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