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MHT CET 2023 (13 May, Shift 2) · Transitions, Photon Emission & Excitation

Transitions, Photon Emission & Excitation question from MHT CET 2023 (13 May, Shift 2)

Q30MHT CET 2023 · 13 MAY · SHIFT 2Medium

Transitions, Photon Emission & Excitation

An excited hydrogen atom emits a photon of wavelength λ\lambda in returning to ground state. The quantum number nn of the excited state is (R=R = Rydberg's constant)

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Answer: (b)

  1. Return to ground state: 1λ=R(1−1n2)\frac{1}{\lambda} = R\left(1-\frac{1}{n^2}\right)
  2. 1n2=1−1λR=λR−1λR\frac{1}{n^2} = 1-\frac{1}{\lambda R} = \frac{\lambda R - 1}{\lambda R}
  3. n=λRλR−1n = \sqrt{\frac{\lambda R}{\lambda R - 1}}
  4. So the answer is (b).
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