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ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2024/paper-2/a10/e/solution

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Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 2 / A10 / e / Solution by

Codex  0 2026-10-20

The Exciton Rydberg series lies below the unbound electron–hole threshold:

E_{n} - E_{v} = E_{g} - \frac{R ^{*}}{n ^{2}} .

Using

E_{g} = 1.240

eV and

R^{*} = 0.038241

eV gives

E_{1} - E_{v} = 1.20176 eV, E_{2} - E_{v} = 1.23044 eV .

Their positive exciton binding energies relative to the continuum are

38.24

meV and

9.56

meV, respectively.

Figure 1.
Original near-zone-centre band curvatures and hydrogenic exciton levels measured above the valence-band maximum
. Details.

These are optical electron–hole excitation energies for negligible centre-of-mass momentum, not new occupied one-electron states inside the valence band. The simple model predicts their locations; observing a particular line also requires a nonzero optical transition matrix element and adequate linewidth.

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