I offer a slight re-phrasing, especially with (D), although I'm not sure about (E): (A) FALSE: Electrons have less degrees of freedom than free atoms, since electrons are bound to potential wells. (B) FALSE: My understanding of this is that it would mean that spontaneous heat may be given out by equilibration. Since metals don't just give off heat for no reason, I would say this is not true. (C) CORRECT ANSWER: A Fermi gas is an ideal gas of electrons, and, given that electrons are fairly free to move around, this would explain why they can be approximated as such a gas in a metal. (D) FALSE: Free electrons randomly bounce around inside the metal. They do this random motion at near-relativistic speeds. Since a metal can readily conduct (as opposed to a semiconductor), only a light perturbation or change in electric potential across a metal will induce the electrons to move toward the + side of the potential. That velocity is called the drift velocity and, although the electric field from the potential propagates at the speed of light, the drift velocity is surprisingly slow, as Yosun mentioned. However, while ''drifting'' at a slow speed, the electrons also practice their random motion at very high speeds. (E) : As a hand-waving explanation, what about the idea that regardless of how many sound waves (phonos) are generated by the electron, this has little to do with how fast the electron is moving? Since electrons are free in a metal, the phonons exciting electrons is much less plausible than electrons creating phonons.