Answer :

Originally the band gap was 1eV. After doping, the band gap will become =(1eV-1meV)

= (1-0.001) eV


=0.999 eV


It is given that the transition is almost forbidden at 1/50 of 0.999eV. Let the upper limit for temperature be T1 over which the transition becomes a forbidden transition.


kT1=0.999/50


T1=231.78K≈231.8K


Let the lower limit for temperature be T2 for which the transitions are most feasible or for which the upper levels have maximum population.


kT2=2(0.999)


T2=23.2K


Therefore, the required temperature range=(23.2K-231.8K)


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