6. In a metal conduction electrons are not attached to any one atom, but are relatively free to move through the entire metal. Consider a 1 µm x 1 µm × 1 µm piece of copper at room temperature. (a) What is the uncertainty in the x-momentum, Pr, of each electron confined to the metal? (b) What is the resulting estimate of the typical kinetic energy of an electron in the metal? [Assume Ap=√ Ap² + Ap² + Ap².] (c) Is the quantum contribution to the average internal thermal energy of the metal, K = kBT, significant? (d) Does the conclusion of (c) change for a smaller piece of copper, 1 nm x 1 nm × 1 nm?

6. In a metal conduction electrons are not attached to any one atom, but are relatively free to move through the entire metal. Consider a 1 µm x 1 µm × 1 µm piece of copper at room temperature. (a) What is the uncertainty in the x-momentum, Pr, of each electron confined to the metal? (b) What is the resulting estimate of the typical kinetic energy of an electron in the metal? [Assume Ap=√ Ap² + Ap² + Ap².] (c) Is the quantum contribution to the average internal thermal energy of the metal, K = kBT, significant? (d) Does the conclusion of (c) change for a smaller piece of copper, 1 nm x 1 nm × 1 nm?