# Rotation Spectrum of a diatomic molecule (QM)

#### joker_900

1. The problem statement, all variables and given/known data
In the rotation spectrum of 12C16O the line arising from the transition l = 4 -> 3 is at 461.04077GHz, while that arising from l = 36 -> 35 is at 4115.6055GHz. Show from these data that in a non-rotating CO molecule the intra-nuclear distance is s ~ 0.113 nm, and that the electrons provide a spring between the nuclei that has force constant ~1904Nm−1. Hence show that the vibrational frequency of CO should lie near 6.47×10^13Hz (measured value 6.43 × 1013 Hz). Hint: show from classical mechanics that the distance of O from the centre of mass is (3/7) s and that the molecule’s moment of inertia is (48/7) ms^2. Recall also the classical relation L = Iw.

2. Relevant equations
f = j h/((2pi)^2*I)

Where f is the frequency of the emitted photon and j(j+1) is the eigenvalue of J^2 (I think j is the same as l in this question?)

3. The attempt at a solution
I can derive the two classical bits in the hint and the above formula. I then tried taking one of the frequencies given, working out I using the above formula, and plugging it into the second classical expression to get s. It didn't work!

Thanks

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#### TheBaker

It's not (2pi)^2 on the bottom, it's just 2pi. Plugging in the numbers with the modified formula gives the correct value.

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