Speeds of molecules

You will write functions for the three speeds of a gas and for the fast tail of the Maxwell distribution. The molar mass is given in g/mol, as in a data table, and the functions must change it to kg/mol themselves.

The idea. $u_{\text{mp}} = \sqrt{2RT/M}$, $\bar{u} = \sqrt{8RT/\pi M}$ and $u_{\text{rms}} = \sqrt{3RT/M}$, with $M$ in kg/mol and $R = 8.314\ \text{J K}^{-1}\ \text{mol}^{-1}$. The fraction of molecules faster than a speed $u_0$ is $\text{erfc}(x) + \dfrac{2}{\sqrt{\pi}}xe^{-x^2}$, where $x = u_0/u_{\text{mp}}$.

Your tasks.

1. Complete u_rms(M, T).
2. Complete u_avg(M, T) and u_mp(M, T).
3. Complete fraction_faster(speed, M, T) so that it returns a fraction between 0 and 1.