b) Later this semester, we will derive the Maxwell-Boltzmann speed distribution P(v) for molecules with 2 m mass m at temperature T, P(v) = 4 exp 2kBT my 2kRT B where kB is Boltzmann's constant. Show explicitly that this distribution is normalized, i.e. [P(v)dv=1. Derive expressions for the most probable speed (the speed at which P(v) is a maximum) and the average speed (v) = vP(v)dv. Evaluate both expressions numerically for Ar atoms at T=298 K. 0