Compare the Boltzmann distribution, the Bose-Einstein distribution, and the Fermi-Dirac distribution.
Estimate (e - µ)/kT using the average energy for:
A Nitrogen & Oxygen molecules in our atmosphere
B. Electrons in a metal
(Hint: In each case, you can make an estimate for µ based on your knowledge of either the max µ for the Bose-Einstein distribution, or the Fermi energy). Comment in each case on the validity of the Boltzmann distribution if it is used to describe these systems.