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

Minimum energy will produce maximum wavelength and ∴ we consider the energy lost by the electrons is only due to it moving from the conduction to valence band, which is the energy band gap

The energy lost is in the form of electromagnetic radiation, for which the energy is given as following,

where,

,

is the wavelength

∴

∴ Energy band gap = 1.514eV

Answer 2

The band gap is 1.5 eV when the emitted maximum wavelength is 820 nm.

Explanation:

It is given that,

Wavelength, λ = 820 nm

The minimum energy unconfined in the recombination of electron in the conduction band with a valence band hole is equal to the material’s band gap.

Band gap, $\lambda=820 \mathrm{nm}$

$\Rightarrow \mathrm{E}=1240820 \mathrm{eV}-\mathrm{nm}$

$\Rightarrow E=1.5 \mathrm{eV}$

So, in the hole-electron pair recombination, there is a conversion of the liberated energy into the electromagnetic radiation. The band gap is measured as $1.5 \mathrm{eV}$.