4. [20 points] A silver (Ag) atom has only one valence electron. The Fermi surface of Ag is nearly a sphere (i.e., isotropic Fermi sphere for conduction electrons in Ag). It is known that the atomic mass of Ag is ~108, the density of Ag is 10.5x10' kg.m. From the resistivity measurements, the resistivities of Ag at 295K and 20K are p(295K) = 1.6x10- 2.m and p(20K) = 3.8x10- Q.m.(a) [10 points] Show in general that the total kinetic energy of the three-dimensional electron gas of N free electrons at 7= 0 K is = NEF, where EF is the Fermi energy. [Assume these electrons are confined in a cubic metal with each edge L. ] (b) [10 points] Calculate the Fermi energy EF, the Fermi temperature TF, and the radius of Fermi sphere in the k-space for electrons in Ag at 7= OK. [provide the number values.]