Electron in hydrogen atom first jumps from third excited state to… | NEET 2012 (AIPMT, Prelims)

Q69NEET 2012 · AIPMT · PRELIMSMedium

Transitions, Photon Emission & Excitation

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths $\lambda$ 1: $\lambda$ 2 emitted in the two cases is

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Answer: (d)

Third excited state is $n=4$ , second excited is $n=3$ , first excited is $n=2$ .
$\frac{1}{\lambda_1} = R\left(\frac{1}{9} - \frac{1}{16}\right) = \frac{7R}{144}$
$\frac{1}{\lambda_2} = R\left(\frac{1}{4} - \frac{1}{9}\right) = \frac{5R}{36} = \frac{20R}{144}$
$\frac{\lambda_1}{\lambda_2} = \frac{20}{7}$ , so the answer is (d).

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