= Solution
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
$$
\boxed{E_1-E_v=1.20176\ \mathrm{eV},\qquad
E_2-E_v=1.23044\ \mathrm{eV}.}
$$
Their positive <exciton binding energies> relative to the continuum are $38.24$ meV and $9.56$ meV, respectively.
\Image[/past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2024/paper-2-band-excitons.png]
{title=Original near-zone-centre band curvatures and hydrogenic exciton levels measured above the valence-band maximum}
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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