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Explain why it makes sense that the rotation state of a diatomic molecule is determined by...

Explain why it makes sense that the rotation state of a diatomic molecule is determined by two quantum numbers, but its rotational energy only depends on one of the two quantum numbers? [angular momentum, vector, magnitude (length), orientation, energy, only depends on ...]

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Answer #1

In a diatomic molecule, two moments of inertia are same, and thus there are two distinct rotation axis. So a diatomic molecule can rotate in two different orientations and hence its rotation state is determined by two different quantum numbers.

But in every mode of rotation, the angular momentum remains constant in the sense that the angular momentum does not change and is fixed for a rotation state. Rotational energy depends upon the angular momentum, and so it has only one quantum number.

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