# How can electron in hydrogen ever get in the 2s state?

1. Jan 17, 2016

### misko

I am trying to understand selection rules in atomic transitions.
So, one of the selection rules says that only transitions where orbital quantum number is changed by 1 are possible. If that is the case how can hydrogen in ground state get to 2s state? Can we detect spectroscopic line that corresponds to 2s->1s transitions in H atom?

PS. I used "possible/impossible" where instead I should have used "probable/improbable" as selection rules don't forbid states just make them improbable (though in my book this is not stated, I found this online). So in that case, answer to my question is "yes but it's improbable". But in my course we exercise problems and assume that selection rules really do forbid certain transitions. Anyway, that is not main point of my questions but it would be nice to know in what case selection rules are "broken" and improbable transition happens?

2. Jan 17, 2016

### M Quack

Not sure if the 2s --> 1s line is observable, but one "allowed" way to get to 2s is of course indirectly, e.g. 1s --> 3p --> 2s.

Selection rules for dipole transitions are just that - they apply for dipole transitions only. Higher order transitions, e.g. quadrupole transitions also exist, albeit with much smaller transition probabilities and correspondingly smaller observable intensities. Quadrupole transitions have their own set of selection rules.

Furthermore the selection rules always assume certain perfect symmetries, e.g. spherical symmetry and inversion symmetry for a lonely, isolated atom. In a real gas such symmetries are always approximate, and in case of collisions, for example, completely different things can happen.

3. Jan 17, 2016

### misko

Ok 1s --> 3p --> 2s makes sense...
What about when we have hydrogen in 2s state which is the lowest energy state of the atom if we don't count the ground state.
Will the hydrogen then be able to spontaneously deexcitate into ground state? Selection rules forbid that (or to be more precise it makes it improbable).

4. Jan 17, 2016

### Staff: Mentor

It will eventually deexcite, but the process is slow. The lifetime of the 2s level is 0.12 s, which is quite long for an atom.

5. Jan 17, 2016

### misko

Oh I see... Is that what is called a "metastable" state?

Also, what happens with the conservation law for angular momentum in the 2s->1s transition? I mean, photon has the angular momentum of 1 but electron in both 1s and 2s states has orbital angular momentum of 0 (quantum number l=0). So when photon is emitted it takes away one ħ so how is angular momentum then conserved?

Last edited: Jan 17, 2016
6. Jan 18, 2016

### Staff: Mentor

Yes.

The main decay is through the emission of two photons.