The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelength, λ1/ λ2 of the photons emitted in this process is :

Engineering

Physics

Spectrum of Hydrogen and Hydrogen Like Atoms

Question

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelength, λ₁/ λ₂ of the photons emitted in this process is :

22/5

9/7

20/7

7/5

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$\frac{hc}{λ_{1}} = 13 .6 (\frac{1}{9} - \frac{1}{16})$

$\frac{hc}{λ_{1}} = 13 .6 (\frac{1}{4} - \frac{1}{9})$

$\frac{λ_{2}}{λ_{1}} = \frac{(\frac{7}{9 \times 16})}{(\frac{5}{9 \times 4})}$

$\frac{λ_{2}}{λ_{1}} = \frac{7}{9 \times 16} \times \frac{9 \times 4}{5} = \frac{λ_{2}}{λ_{1}} = \frac{7}{20}$

$\frac{λ_{1}}{λ_{2}} = \frac{20}{7}$