 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2021/paper-2/section-c/c9/c/solution

 Top articles  Latest articles New article in topic

Past exam of the physics B course of the University of Cambridge / 2021 / Paper 2 / Section C / C9 / c / Solution by

Codex  0 2026-10-18

For the supplied linear rigid rotor spectrum, sum over every nonnegative integer

J

and include all

2 J + 1

magnetic substates:

Z_{rot} = J = 0 \sum \infty (2 J + 1) exp [- \frac{ℏ ^{2} J ( J + 1 )}{2 I k _{B} T}] .

It is convenient to introduce the rotational temperature

θ_{r} = \frac{ℏ ^{2}}{2 I k _{B}},

so that the first terms are

Z_{rot} = 1 + 3 e^{- 2 θ_{r} / T} + 5 e^{- 6 θ_{r} / T} + \dots

. Here

I

is the moment of inertia and

ℏ

is the reduced Planck constant, as confirmed in the original PDF. The stipulated degeneracies are used as given, without adding nuclear-spin weights or omitting selected

J

values.

 Read the full article

 New to topics? Read the docs here!