Find the minimum energy of electron-hole pair formation in an impurity-free semiconductor whose electric conductor increase `eta=5.0` times when the temperature increases from `T_(1)= 300K t o T_(2)= 400K`

Explanation

In a pure(intrinsic) semiconductor the conductivity is related to the temperature by the following formula very closely:
`sigma= sigma_(0)e^(-Delta epsilon//2kt)`
where `Delta epsilon` is the energy gap between the top of valence band and the bottom of conduction band, it is also the minimum enrgy required for the formation of electron-hole pair. The conductivity increases with temperature and we have
`eta=2^(+(DeltaE)/(2k)((1)/(T_(1))-(1)/(T_(2)))`
or In `eta=(Deltaepsilon)/(2k)(T_(2)-T_(1))/(T_(1)-T_(2))`
Hence `Delta epsilon=(2kT_(1)T_(2))/(T_(2)-T_(1)) In eta`
Substitution gives
delta epsilon= 0.333eV`=E_(mi n)`