The measured thermal conductivity of germanium at 300k is 0.63w/k, in a range where acoustic phonon scattering dominates. (a) what fraction of this thermal conductivity is caused by free electrons if the free-electron density is 1017 cm-3 and the electron mobility is 4 * 103cm2/v-s? (b) what must the concentration of free electrons in germanium at 300k be in order for the electronic contribution to the thermal conductivity to be equal to the lattice contribution? (c) the thermoelectric power corresponding to (a) is measured to be 0.46mv/k. how far below the conduction band edge does the fermi level lie?