$2-(20$ points$)$ The density of a metal is $10500k\frac{g}{m^3}$ and its atomic weight is $107\mathrm{.}9$ and it has one conduction electron per atom.

a$)$ Calculate the concentration of free electrons in the metal,

b$)$ Calculate the Fermi energy in eV for the metal at $0$ K $,$

c$)$ What is the energy for which the probability of occupancy at $300$ K is $0\mathrm{.}34?$