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MHT CET 2020 (16 Oct, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from MHT CET 2020 (16 Oct, Shift 1)

Q99MHT CET 2020 · 16 OCT · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? (I=I = moment of inertia of diatomic molecule and, h=h = Planck's constant)

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Answer: (b)

  1. Quantisation: L=nh2πL = \frac{nh}{2\pi}, so E=L22I=n2h28π2IE = \frac{L^2}{2I} = \frac{n^2 h^2}{8\pi^2 I}.
  2. For n=2n = 2: E=4h28π2I=h22π2IE = \frac{4h^2}{8\pi^2 I} = \frac{h^2}{2\pi^2 I}
  3. So the answer is (b) h22Iπ2\frac{h^2}{2I\pi^2}.
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