Another hint as to what is wrong comes from the heat capacity of metals and insulators. In both, we should see the heat capacity of the nuclei vibrating around their locations on the crystalline lattice (3R in gas law constant units) and in insulators, no more, if there are no free electrons to move around. This is observed. In metals, we should expect an additional ˝kT for motion in each direction (xyz). Not observed! There is an excess of only about 0.02R. Evidently, there are very few free electrons, but the conductivity at low temperatures is way greater than that given by our classical theory! Those few must be working very hard!
Another hint as to what is wrong comes from the heat capacity of metals and insulators. In both, we should see the heat capacity of the nuclei vibrating around their locations on the crystalline lattice (3R in gas law constant units) and in insulators, no more, if there are no free electrons to move around. This is observed. In metals, we should expect an additional ˝kT for motion in each direction (xyz). Not observed! There is an excess of only about 0.02R. Evidently, there are very few free electrons, but the conductivity at low temperatures is way greater than that given by our classical theory! Those few must be working very hard!