Describing fermi-dirac distribution function

Question

1) What do you mean by a carrier concentration of metals?

2) Fermi temperature of the metal is 24600k. Compute the Fermi velocity.

3) Determine the value of f(E) for E-EF= 0.01eV at 200K by using Fermi function.

4) Thermal conductivity of copper at 20^oC is 390 wm^-1 k^-1 and 5.87x10⁷ mho/m respectively. Compute the Lorentz Number.

5) Derive the mathematical expressions for electrical conductivity and thermal conductivity of the material and therefore get widemann - franz law.

6) Deduce the expression for density of states and based on that compute carrier concentration in metals.

7) Write down Fermi-Dirac distribution function. Describe how Fermi function differes with temperature. Estimate the Fermi function for energy KT above the fermi energy.