Problem 11.4. The electrons in a cubic sample of metallic solid of volume 23 and temperature 7 may be considered to be a highly degenerate ideal Fermi-Dirac gas. Assume the surface of the cube forms a potential energy barrier which is infinitely high.

and assume that the electrons have spins, mass m, and charge

e.

(a) What is the number of electrons in the velocity interval, vv+dv?

(b) Assume that an electrode is attached to the surface which lowers the potential energy to a large but finite value, W, in a small area, A, of the surface. Those electrons which have enough kinetic energy to overcome the barrier can escape the solid. How many electrons per second escape through the area, A? Assume that W>0 and use this fact to make simplifying approximations to any integrals you might need to do.