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If the radius and energy of the second Bohr orbit of hydrogen atom is $r_2$ and $E_2$, respectively. The radius and energy of the third Bohr orbit will be 
respectively.
Options:
respectively.
Solution:
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Verified Answer
The correct answer is:
$\frac{9}{4} \mathrm{r}_2, \frac{4}{9} \mathrm{E}_2$
$\begin{array}{ll} \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^2 & \varepsilon_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^2} \\ \frac{\mathrm{r}_3}{\mathrm{r}_2}=\frac{(3)^2}{(2)^2}=\frac{9}{4} & \frac{\varepsilon_3}{\varepsilon_2}=\frac{(2)^2}{(3)^2}=\frac{4}{9} \\ \mathrm{r}_3=\frac{9}{4} \mathrm{r}_2 & \varepsilon_3=\frac{4}{9} \varepsilon_2\end{array}$
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