Consider a density of states N(E) of a conductor. (a) Obtain an analytical expression for the density of states at Fermi energy N(E_F) as a function of m and n, where m is the electron mass and n is the number of conduction electrons per unit volume. This expression should be in units of m^{ -2}eV^{-1} (mass^{-2}. electron-Volt^{-1}). (b) Calculation or numerical value of N(E_F) for Copper. To estimate the value of n, consider the following data for copper: molar mass 64.54 g/mol and density 8.96 g/cm^{3}. (c) Compare the result of item (b) with the result obtained from the N(E) x E curve and analytical expression for N(E). Do the values agree?

Consider a density of states N(E) of a conductor. (a) Obtain an analytical expression for the density of states at Fermi energy N(E_F) as a function of m and n, where m is the electron mass and n is the number of conduction electrons per unit volume. This expression should be in units of m^{ -2}eV^{-1} (mass^{-2}. electron-Volt^{-1}). (b) Calculation or numerical value of N(E_F) for Copper. To estimate the value of n, consider the following data for copper: molar mass 64.54 g/mol and density 8.96 g/cm^{3}. (c) Compare the result of item (b) with the result obtained from the N(E) x E curve and analytical expression for N(E). Do the values agree?