題組內容

5.[20 points] There are N free electrons in a metal of volume V and the temperature is at absolute zero. It is also known that the distribution of the frce electron energy can be described by the density of the electron energy levels6177a9e82a641.jpg, where e is the (kinetio) cnergy of the frce electron and6177aa14b5a54.jpg is the number of electronic energy levels (including both spins) between e and 6177aa3e307ff.jpg m the mass of electron, and h the Planck' s constant.

5.2 [10 points] What is the total energy of all the N electrons in the metal as expressed in terms of N and6177aa8720688.jpg? What is the average electron energy?