Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2B / Section B / 35 / c / i

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- Solution i

Solution

For a linear rigid rotor, dividing the angular momentum squared eigenvalue by twice the moment of inertia gives

E_{J} = \frac{ℏ ^{2}}{2 I} J (J + 1), g_{J} = 2 J + 1.

The quantum degeneracy counts the values

M = - J, \dots, J

with the same energy. It excludes nuclear-spin multiplicity and any fine or hyperfine splitting absent from this model.

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