1) Derive the Maxwell-Boltzmann velocity distribution. Generate a plot by implementing the final equation in MATLAB.
2) Using the velocity distribution, convert it to (a) speed distribution, (b) energy distribution. Again, generate plots for both of these.
3) Derive the Boltzmann distribution in the following form:
ni = gi * exp(-Ei / kT)
Q = Σ(gi * exp(-Ei / kT))
Qrot = Qvib * Qele