Using Bohr's quantization condition, what is the rotational energy in the second orbit for a diatomic…

Using Bohr's quantization condition, what is the rotational energy in the second orbit for a diatomic molecule. (I = moment of inertia of diatomic molecule, $\mathrm{h}=$ Planck's constant)
  1. $\frac{n^{2}}{2 I^2 \pi^{2}}$
  2. $\frac{h}{2 I \pi^{2}}$
  3. $\frac{h}{2 \mathrm{I}^{2} \pi}$
  4. $\frac{n^{2}}{2 I^{2} \pi^{2}}$

Solution

According to Bohr's quantization condition $\mathrm{L}=\frac{\mathrm{nh}}{2 \pi}=\frac{2 \mathrm{~h}}{2 \pi}=\frac{\mathrm{h}}{\pi} \quad\left[\right.$ For $2^{\text {nd }}$ orbit $]$ Rotational $\mathrm{KE}=\frac{1}{2} \frac{\mathrm{L}^{2}}{\mathrm{I}}=\frac{1}{2} \frac{\mathrm{h}^{2}}{\mathrm{I} \pi^{2}}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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