Question

A diatomic molecules has a moment of inertia I. By Bohr’s quantisation condition, its rotational energy in the nth level (n ≠ 0) is

(1) \(\frac{h^2}{8\pi ^2 In^2}\)

(2) \(\frac{h^2}{8\pi ^2 In}\)

(3) \(\frac{nh^2}{8\pi ^2 I}\)

(4) \(\frac{n^2h^2}{8\pi ^2 I}\)

Answer 1

 (4) \(\frac{n^2h^2}{8\pi ^2 I}\)

Let ω_n be the angular speed of molecule in n^th allowed state. Its angular momentum is L_n = Iω_n . 

From Bohr’s postulate, we have

The rotational energy of the molecule