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Energy of the Electron & Energy Levels question from JEE Main 2017

Q44JEE Main 2017Medium

Energy of the Electron & Energy Levels

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $\lambda_{1}/\lambda_{2}$ , is given by:

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Answer: (a)

$\lambda = \frac{hc}{\Delta E}$ , so $\lambda \propto \frac{1}{\Delta E}$ .
$\lambda_1$ : $-E \to -2E$ , $\Delta E_1 = E$ . $\lambda_2$ : $-E \to -\frac{4}{3}E$ , $\Delta E_2 = \frac{E}{3}$ .
$r = \frac{\lambda_1}{\lambda_2} = \frac{\Delta E_2}{\Delta E_1} = \frac{1}{3}$
So the answer is (a) $r = 1/3$ .

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