Question

Suppose the energy liberated in the recombination of a hole-electron pair is converted into electromagnetic radiation. If the maximum wavelength emitted is 820 nm, what is the band gap?

Answer 1

Given:
Wavelength, $\lambda =820\mathrm{nm}$
The minimum energy released in the recombination of a conduction band electron with a valence band hole is equal to the band gap of the material.
Band gap, $E\mathit{=}\frac{hc}{\lambda }$

$$\begin{gathered} \Rightarrow E=\frac{1240}{820}\frac{\mathrm{eV}-\mathrm{nm}}{\mathrm{nm}} \\ \Rightarrow E=1.5\mathrm{eV} \end{gathered}$$