Problem 3. [20%]: Maxwell-Boltzmann distribution:
(a) Using the Maxwell-Boltzmann distribution of speeds prove that the inequality $\frac{1}{v}\langle v \rangle > 1$ holds.
(b) Consider two gases, hydrogen and helium, each in thermal equilibrium at 200°C and described by the corresponding Maxwell-
Boltzmann distribution, $p_{H_2}(v)$ and $p_{He}(v)$. Find the speed, $v > 0$, at which the two curves intersect.