The ground state of Hydrogen has a spin
electron coupled to a spin
proton, giving total angular momentum state of
We have computed in first order perturbation theory that
The energy difference between the two hyperfine levels determines the wave length of the radiation emitted in hyperfine transitions.
For Hydrogen, this gives
Recall that at room temperature, is about eV, so the states have about equal population at room temperature. Even at a few degrees Kelvin, the upper state is populated so that transitions are possible. The wavelength is well known.
Jim Branson 2013-04-22