Question

2. Free Electron Gas

a. Consider a free electron gas of valence 4s-electrons in potassium (atomic mass M=39.1 and density 856 kg/m3). What is the energy (in electron volts, eV) of the highest filled level in the ground state (i.e., the Fermi energy at zero temperature)?

b. Calculate the corresponding electron velocities.

c. Calculate the density of states at the Fermi energy. How large is the number of electrons in so- called “soft zone” or “Fermi window” of about 4kBT around the Fermi energy at room temperature relative to the total number of electrons?

d. In a classical monatomics ideal gas, the average kinetic energy per particle is 3/2kBT, where kB is the Boltzmann constant and T is the temperature. Compare the average kinetic energy per particle at room temperature (300K) to your answer in (a).

Answer 1

in part c second part is missing .i could not solve that for you .i am sorry.thank you