The energy of a photon of sodium light `(lambda=589 nm)`equal the band gap of a semiconducting material.(a)Find the minimum energy E requried to create a hole-electron pair.(b)Find the value of `E//kT`at a temperature of 300K.

Explanation

(a). The energy of the photon is `E=(hc)/(lamda)`
`=(1242eV-nm)/(589nm)=2.1eV`.
Thus the band gap is 2.1 eV. This is also the minimum energy E required to push an electron from the valence bank into the conduction band. Hence the minimum energy required to create a hole-electron pair is 2.1 eV.
So it is difficult for the thermal energy to create the hole-electron pair but a photon of light can do it easily.
(b). At `T=300K`
`kT=(8.62xx10^(-5) eV//K)(300K)`
`=25.86xx10^(-3)eV`.
Thus, `(E)/(kT)=(2.1eV)/(25.86xx10^(-3)eV)=81`.