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MHT CET 2024 (4 May, Shift 1) · Transitions, Photon Emission & Excitation

Transitions, Photon Emission & Excitation question from MHT CET 2024 (4 May, Shift 1)

Q18MHT CET 2024 · 4 MAY · SHIFT 1Medium

Transitions, Photon Emission & Excitation

For hydrogen atom, ' λ1\lambda_{1} ' and ' λ2\lambda_{2} ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' λ1\lambda_{1} ' and ' λ2\lambda_{2} ' is x32\frac{x}{32}. The value of ' xx ' is

Figure

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Answer: (c)

  1. From the figure: transition 1 is n=3→1n=3\to1, transition 2 is n=2→1n=2\to1.
  2. 1λ1∝1−19=89\frac{1}{\lambda_1} \propto 1-\frac19 = \frac89; 1λ2∝1−14=34\frac{1}{\lambda_2} \propto 1-\frac14 = \frac34
  3. λ1λ2=3/48/9=2732\frac{\lambda_1}{\lambda_2} = \frac{3/4}{8/9} = \frac{27}{32}
  4. So x=27x = 27, answer (c) 2727.
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