Our universe has been continuously expanding since its formation at the Big Bang, thus gradually reducing the density of its major constituents - hydrogen and helium, and the average temperature to 2.7K (associated with the so-called microwave background radiation left over from the Big Bang). What is the rms speed of hydrogen molecules at this temperature?
183 m/s
Since the H2 molecules in outer space can be considered an ideal gas on a very large scale, our kinetic theory should give good results (the theory works best for low gas densities in large volumes). We can use out vrms -T relation -
vrms=√3RTM,
where M = 2 gms,
=√3×8.314×2.72×10−3=183.5 m/s.