Discussion
Of the following materials, which is the most suitable for an LED emitting at around 380 nm?
Answer: C
The most suitable is a direct bandgap material with a large bandgap.
The photon energy at 380 nm is
\[ \begin{aligned} E &= \frac{hc}{\lambda} = \frac{1240\ \text{eV nm}}{380\ \text{nm}} \\ &\approx 3.26\ \text{eV} \end{aligned} \]
so the bandgap must be about 3.3 eV, which is large; materials such as GaN and InGaN are used for near-ultraviolet and violet LEDs.
The gap must also be direct, so that an electron and hole can recombine and emit a photon without needing a phonon to supply momentum; indirect materials such as silicon emit light very inefficiently. A small bandgap would emit in the infrared, not at 380 nm.
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