= Solution
The emission energies are approximately
$$
E_{\rm core}=\frac{1240}{615}=2.02\,\mathrm{eV},\qquad E_{\rm shell}=\frac{1240}{690}=1.80\,\mathrm{eV}.
$$
Draw the Al-rich interface as a wider-gap barrier between these two emitting regions: a raised conduction-band edge impedes <electron> transfer, and a lowered valence-band edge impedes <hole> transfer. The following is a consistent straddling-barrier schematic, with the shell having the smaller optical gap.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-2-radial-bands.png]
{title=One consistent core–Al-rich-interface–shell alignment; absolute offsets are not fixed by the emission wavelengths}
{source=paper-2-radial-bands.py}
\b[The two emission wavelengths determine optical transition energies, not unique conduction- and valence-band offsets.] <Exciton> binding, confinement and <strain> can shift emission relative to the bulk <band gap>. The stated barrier supports inhibited <charge exchange>; its separate <electron> and <hole> barrier heights need additional band-alignment data.
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