Related: Decay from excited state to ground state

My confusion arose initially from the definition of binding energy being the lowest energy state (n=1) in the hydrogen atom. This, I assume, is simply because hydrogen only has one atom, and electrons don't exist in higher energy states stably. Then my next question was, why not? If these higher energy states exist, why can't electrons maintain those orbits? The above question seems to answer that question, but then I don't understand why bigger atoms CAN hold these higher energy eigenstates. Is is just because the lower electrons "prevent" the higher ones from decaying? I can see where the exclusion principle comes from, but I can't see how it would prevent decay, only how it would prevent more than two electrons from inhabiting the same orbit.

  • $\begingroup$ Not sure I understand your question. PEP restricts electrons from occupy the same orbit, and so electrons CAN'T decay to lower-energy orbits because if they did, they would have to occupy the same orbit as another electron. "but I can't see how it would prevent decay, only how it would prevent more than two electrons from inhabiting the same orbit.": In the case of a ground-state atom, these two are mutually inclusive statements. $\endgroup$
    – xish
    Dec 11, 2013 at 5:22
  • $\begingroup$ How can I understand it classically though? There is a state of higher energy-why won't it decay? Is it just the other electrons "pushing" it away? But really it is the exclusion principle? It just seems strange to me, because the reason you can't decay is because Pauli, but a priori, if I were to add an electron to some system, I would assume it would take on the ground state energy.... $\endgroup$
    – user24082
    Dec 11, 2013 at 5:40
  • $\begingroup$ In a ground-state atom, electrons fill orbitals in order of increasing energy. If any electron is in a higher energy orbit and an unfilled lower energy orbit exists, it will quickly decay to that orbit. I think there's something you aren't quite understanding. Can you give an example of an electron configuration that you think does not follow this lowest-energy principle? $\endgroup$
    – xish
    Dec 11, 2013 at 5:46
  • $\begingroup$ Nononono I understand that it occurs. What I don't understand is why other electrons can't decay to filled orbitals. I KNOW there is the exclusion principle, but that just comes from the fact that fermions have to have antisymmetric equations. Physically, what is the Pauli Exclusion Principle? What prevents excited electrons from decaying how they want? $\endgroup$
    – user24082
    Dec 11, 2013 at 5:49
  • $\begingroup$ I'm not sure I have a good answer for that. I think quantum degeneracy pressure might be related, though. $\endgroup$
    – xish
    Dec 11, 2013 at 5:53

1 Answer 1


Here is a representation of the hydrogen atom energy levels.

hydrogen energy levels

It displays the availabe solutions of the Schrodiner equation for an atom composed of a proton in the nucleus and an electron existing in their mutual potential.

Systems stay in the minimum energy state, and for the single electron of hydrogen the minimum energy state is the n=1 state and the value of that energy is -13.6 eV.

It can happen that a photon of 10.2 eV scatters the electron to the n=2 state. This will be an unstable solution because there exists an empty lower energy state and the electron will radiate back to n=1. The same is true for the higher n states to which the electron can get scattered, and then can cascade down to the ground state. The radiation from these excitations is a spectrum measurable in the lab and it is how we know we have the correct quantum mechanical model of the hydrogen atom.

A second electron has no meaning in this solution of the hydrogen atom, which has zero charge as an atom. A second electron will not be attracted because there is no potential atom+ second electron .

Each atom has as many electrons as there are protons in the nucleus and there will be solutions that will give the energy levels those electrons can occupy.

For Z=2 and higher the Pauli exclusion principle does not allow two electrons in the same energy state. It is worth looking up Helium to get an idea of the complexity of the energy levels of multi electron atoms and the role of the Pep.

  • $\begingroup$ But again, those energy levels get occupied in order- and while I understand that mathematically the exclusion principle locks electrons out of already filled states, I see no reason non-quantum-mechanically why these states would be off limits. $\endgroup$
    – user24082
    Dec 12, 2013 at 2:33
  • $\begingroup$ But that is why quantum mechanics was found/invented! Classical mechanics saw no reason for the stability , the grounds state for classical mechanics is right on top of the proton, no atoms possible. Bohr postulated steady orbits in his model, and it fitted the easy atoms of Hydrogen whose radiation spectrum had been already studied and the spectrum fitted, just because classical mechanics does not allow a ground state above the proton. Then quantum mechancis with Schrodinger's equation became a theory that incorporated all observations, and made successful predictions for new ones. $\endgroup$
    – anna v
    Dec 12, 2013 at 5:09
  • $\begingroup$ ${H^-}$ does happen, though. $\endgroup$
    – Stian
    Jun 6, 2019 at 18:27
  • $\begingroup$ @StianYttervik sure, but it has different solutions in energy levels, not the atomic hydrogen ones. Note the difference in the ground level $\endgroup$
    – anna v
    Jun 6, 2019 at 18:50

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