Let △E denotes the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to  e−△E/2kT . Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature 300 K . △E  for silicon is 1.1 eV and for diamond is 6.0 eV.

Given  η=e−△E/2kT    △E  (diamond) = 6 eV             △E  (Si)  = 1.1 eV Now, η1 (Diamond)=e−△E12kT     =e−6 eV2×1.38×10−23×300 =e−6×1.6×10−192×1.38×10−23×300,η1=e−62×300×8.62×10−5 = e−116=4.14722×10−51                                     Similarly , η2  (Silicon)=e−△E22kT=e−1.12×1.38×10−23×300 =e−1.1×1.6×10−192×1.38×10−23×300 =e−1.12×8.62×10−5×300 = e−21.2683= 5.7979×10−10∴ratio = η1η2=4.14722×10−515.7979×10−10=7.15×10−42