Blue LED and semiconductor gap

Problem

A blue LED consists of a semiconductor with gap $E_\text{gap} \approx 2{,}75\;\text{eV}$. Estimate the wavelength of the light emitted when an electron falls back from the conduction band to the valence band, and identify the colour.

Solution

When the electron falls back across the gap it emits a photon of energy $E \approx E_\text{gap}$. So

$\ev{\lambda = \frac{hc}{E_\text{gap}} = \frac{1240\;\text{eV·nm}}{2{,}75\;\text{eV}} \approx 450\;\text{nm}}$

A wavelength of $\approx 450\;\text{nm}$ corresponds to blue light, consistent with the name of the device. This is the same principle behind gallium-nitride blue LEDs (2014 Nobel Prize), which made white LED light possible.

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Topics: Fisica quantistica Concepts: Fotone