Q1 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Chemistry

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 Figure
respectively.

  • A
    $\frac{4}{9} r_2, \frac{9}{4} E_2$
  • B
    $\frac{4}{9} r_2, \frac{4}{9} E_2$
  • Correct answer
    C
    $\frac{9}{4} \mathrm{r}_2, \frac{4}{9} \mathrm{E}_2$
  • D
    $\frac{9}{4} r_2, \frac{9}{4} E_2$

Solution

$\begin{array}{ll} \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^2 & \varepsilon_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^2} \\ \frac{\mathrm{r}_3}{\mathrm{r}_2}=\frac{(3)^2}{(2)^2}=\frac{9}{4} & \frac{\varepsilon_3}{\varepsilon_2}=\frac{(2)^2}{(3)^2}=\frac{4}{9} \\ \mathrm{r}_3=\frac{9}{4} \mathrm{r}_2 & \varepsilon_3=\frac{4}{9} \varepsilon_2\end{array}$

Hence, the correct answer is option: 'C'.

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