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JEE Main 2023 (31 Jan, Shift 1) · Transitions, Photon Emission & Excitation

Transitions, Photon Emission & Excitation question from JEE Main 2023 (31 Jan, Shift 1)

Q35JEE Main 2023 · 31 JAN · 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

Numerical answer type. Work it out, then open the answer.

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Answer: 27

  1. From the figure, transition 1 is 3→13\to1 and transition 2 is 2→12\to1.
  2. 1λ1=R(1−19)=8R9\frac{1}{\lambda_1} = R\left(1 - \frac{1}{9}\right) = \frac{8R}{9}, 1λ2=R(1−14)=3R4\frac{1}{\lambda_2} = R\left(1 - \frac{1}{4}\right) = \frac{3R}{4}
  3. λ1λ2=3/48/9=2732\frac{\lambda_1}{\lambda_2} = \frac{3/4}{8/9} = \frac{27}{32}
  4. So x=27x = 27.
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