De-exiting of hydrogen atoms can occur in presence of an external electromagetic field. In this case we can speak about stimulated and spontaneous emission. Since we have the interaction of the atom with the external field the angular momentum of the hydrogen atom is not a conserved quantity.
This process is well described by a semi-classical treatment, but, if you are looking for a (classical) phenomenological intuition you can imagine the atom like a rotating disk. When an emission occur, it lose angular momentum because of the emission of a photon with momentum $p = h \nu$.
It is always a no-man's-land to give classical interpretation of quantum mechanical problems, and very often they are counterproductive since they anchor us to the wrong side of nature.
Still we have some good example of classical physics applied to atoms systems. You can look at the Larmor precession (very usefull in medical applications: NMR)