Density of states — UPSC Physics Optional CSE 2018 Paper I

Schematically, show the variation of density of states, D(\varepsilon) and distribution function, f(\varepsilon,T), of particles in a non-relativistic Fermi gas at high temperatures. At a temperature T, an electron occupies a state with energy 100\mathrm{meV} above the Fermi energy (\varepsilon_{\mathrm F}) with the probability of 1\%. Find the temperature T.