A) \[3a\]
B) \[9a\]
C) \[27a\]
D) \[81a\]
Correct Answer: B
Solution :
Radius of Bohr orbit is given by \[{{r}_{n}}=\left( \frac{{{\varepsilon }_{0}}{{h}^{2}}}{\pi m{{e}^{2}}} \right){{n}^{2}}\] The quantities in the bracket are constant. \[\therefore \] \[{{r}_{n}}\,\propto \,{{n}^{2}}\] The expression gives the radius of nth Bohr orbit \[\therefore \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{n_{1}^{2}}{n_{2}^{2}}\] \[\Rightarrow \] \[\frac{a}{{{r}_{2}}}=\frac{1}{{{3}^{2}}}\] \[{{r}_{2}}=9a\]
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