Fermi–Dirac distribution — UPSC Physics Optional CSE 2004 Paper I

Show that for Fermi-Dirac distribution of electrons, the number of electrons N_i in the energy state \varepsilon_i are given by N_i = \frac{g_i}{A \exp(\varepsilon_i / kT) + 1} where g_i represents the number of quantum states in the energy level \varepsilon_i. Further state under what conditions this distribution law goes over to Maxwell-Boltzmann statistics. Show by drawing curves how the Fermi-Dirac distribution function varies with the energy at T = 0 and also at the other finite temperatures.