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The energy of a photon of sodium light (...

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.

Text Solution

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(a)The energy of the photon is `E=hc/(lambda)`
`=1242eVnm/589 nm=2.1eV.`
Thus the band gap is 2.1eV.This is also the minimum energy E requried to push an electron from the valence band into the conduction band. Hence ,the minimum energy required to created a hole-electron pair is 2.1eV.
At`T=(300K)`
kt=(8.62xx10^(-5)eVK_(-1))(300K)`
`=25.86xx10^(-3)eV.`
thus,`(E)/(kT)=(2.1eV)/(25.86xx10^(-3)eV)=81.`
So it is difficult for the thermal energy to create the hole-electron pair but a photon of light can do it easily.
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