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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2a/section-b/21/d/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 21 / d / Solution by

Codex  0 2026-10-20

The inferred dipole moment is approximately $0.626 D$ . With the static field parallel to the radiation electric field, the microwave selection rule is

Δ M_{J} = 0

. A fully resolved three-component first-order rotational Stark effect pattern naturally identifies the

J = 1 \to 2

∣ K ∣ = 1

transition: the three initial

M_{J} = - 1, 0, 1

values give the three components.

K = 0

would have no first-order shift.

Subtract the lower-state field shift from the upper-state field shift, rather than equating a transition shift to one level's shift:

δ ν = \frac{μ E _{field} K M _{J}}{h} [\frac{1}{J ( J + 1 )} - \frac{1}{( J + 1 ) ( J + 2 )}] .

(1)

For

J = 1

and

∣ K ∣ = 1

, neighbouring components are separated by

μ E_{field} / (3 h)

. Hence

μ = \frac{3 h ( 21 \times 1 0 ^{6} s ^{- 1} )}{2.0 \times 1 0 ^{4} V m ^{- 1}} = 2.09 \times 1 0^{- 30} C m = 0.626 D .

(2)

This assignment assumes the stated splitting resolves all allowed first-order components, rather than three accidentally unresolved groups of a higher-

J

transition.

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