In an intrinsic semiconductor, the band gap is so small that the Fermi-Dirac distribution results in some electrons populating the conduction band. It follows from the exponential form of the Fermi-Dirac distribution that the conductance G, the inverse of the resistance (with units of siemens, 1 S = 1 Q-I), of an intrinsic semiconductor should have an Arrhenius-like temperature dependence, shown in practice to have the form G = Goe-E/ZkT, where Eg is the band gap. The conductance of a sample of germanium varied with temperature as indicated below. Estimate the value of Eg.

T/K 312 354 420

G/S 0.0847 0.429 2.86