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?

(Use Planck constant h = 4.14 × 10^-15 eV-s, Boltzmann constant k = 8·62 × 10^-5 eV/K.)

Answer 1

Given:
Wavelength, `lambda = 820  "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, \[E = \frac{hc}{\lambda}\]

\[\Rightarrow E = \frac{1240}{820}\frac{eV - \text{ nm}}{\text{ nm} }\] 

\[ \Rightarrow E = 1 . 5 \text{ eV }\]