 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2a/section-b/21/a/i/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 / 2022 / Paper 2A / Section B / 21 / a / i / Solution by

Codex  0 2026-10-20

The coarse spacing is about

2 B

, so

B ≃ 0.25 c m^{- 1}

. The two groups near 1.5 and

2.0 c m^{- 1}

therefore have $J = 2 \to 3$ and $J = 3 \to 4$ , respectively. For positive

D_{J K}

, increasing

K^{2}

moves a component to lower wavenumber. The assignments are

J \to J + 1 2 \to 3 3 \to 4 K 0120123 ν / c m^{- 1} 1.50130 1.50128 1.50122 2.00171 2.00168 2.00160 2.00147

(1)

Within one group, successive separations scale as

(K + 1)^{2} - K^{2} = 1, 3, 5, \dots

. The observed gaps follow that pattern to their printed precision. There are

J + 1

distinct

∣ K ∣

components because

∣ K ∣ \leq J

in the lower state; the

+ K

and

- K

members remain coincident without an applied field. A high-resolution feature here is therefore not simply assigned to an arbitrary magnetic sublevel.

Figure 1.
Derived stick assignments of the two rotational groups, showing the K-squared pattern
. **Details**.

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