# Can an atom absorb a photon that matches the ionization energy of the atom, without ionizing? What would the resulting orbital state be?

Can an atom absorb a photon that matches the ionization energy of the atom, without ionizing? What would the resulting orbital state be? Let's take as an example atom argon (or hydrogen, if that is easier to reason about? But hydrogen would exist as a molecule, not an atom, so maybe harder to reason about?).

(Alternatively, if it is not possible for an atom to absorb a photon that exactly matches the ionization energy of the atom, without ionizing; is it possible to absorb such a photon when the atom is not in its ground energy state? If so, what would the resulting orbital configuration look like?)

I don't need an exact orbital configuration, just something handwavingly correct enough that if I create a plasma simulator that uses such an orbital configuration, I won't be bombarded with people saying "it's clearly wrong". For example, if it turns out that the orbital configuration would always change from s to p (eg because of angular momentum of a photon is 1), then if I just changed from 1s to eg 2s, that would be clearly wrong. But also, I have no idea how much $$n$$ should change at energies around the ionization level. I imagine that $$n$$ changing from 1 to 2 would be much smaller than the ionization energy? What about $$n$$ going from 1 to ... 10? 1 to 3?

Edit: looks like, no way for an atom to absorb the ionization energy without ionizing. The ionization energy is basically the energy to move an electron to infinity. It's essentially the energy to move to $$n = \infty$$ (I think...)

Edit2: Still, would like to hav econfirmation that it's not possible for an atom to absorb the ionization energy without ionization. One might say that it's "obvious" that it could not. But, I don't know for sure that there isn't some weird "metastable" kind of thing where the electrons can contain more energy than ionization energy, without ionizing, vanising to inifnity etc. It's not like the electrons obey the classical laws of macroscopic physics in general.

• If your question is no longer relevant it should be taken down. Commented Jun 9 at 13:31
• Well, I have an answer t oth question now. Even if the answer is 'no', does that mean it should be removed altogether? Commented Jun 9 at 13:35
• Also, I'm not like 100% sure, I'm like 85% sure. I'm a complete noob at this. Would appreciate a confirmation of the answer, from someone who knows what they are talking about, ideally. Commented Jun 9 at 13:35
• If you ionize hydrogen you just have an electron and proton, nothing resembling orbitals anymore. Presumably each would be in some (combination of?) free particle states that have momentum and energy consistent with the ionization process and the original state of the system. Commented Jun 9 at 13:41
• I think there's some resonance states - ionisation would not be necessarily immediate. Commented Jun 9 at 21:14

Can a man who has a bank account balance of -50 dollars still have a negative balance when he deposits 50 dollars into said bank account? Sure- he could very quickly take on more debt and go back to being in the negatives, but he will at least temporarily not have any debt. If an atom absorbs a photon that has enough energy to ionize an electron, that electron is going to be ionized, unless some other process absorbs some of that energy simultaneously or very quickly to cause recombination.

Clarifying remark: Keep in mind that ionization usually happens upon absorption of energy greater then then ionization energy, giving the electron excess kinetic energy. It also need not be a photon that causes ionization- in a plasma a collision between a neutral atom and an ion can be sufficient.

• Yes, I'm considering ionization in a plasma in fact. Recombination of an ion and an electron, when we cool the plasma down, will create a photon, physics.stackexchange.com/questions/817402/… . And I'm trying to figure out how that photon turns back into kinetic energy. I think I figured out the answer in physics.stackexchange.com/a/817786/337710 The answer being that the photon gets absorbed by an ion, I postulate, which has a higher ionization energy. But just tidying up some loose ends here. Commented Jun 9 at 18:13
• When you say the ion has higher ionization energy do you mean for a secondary ionization? That is usually true, and during a recombination the photon can either leave the plasma (causing glow) or participate in some secondary process- if it's a mixed species plasma you can have penning ionization. Commented Jun 10 at 0:52
• Yes, I meant for secondary ionization, right. Commented Jun 10 at 11:22

It is not possible to excite an atom to the ionization energy i.e. to a state $$n=\infty$$.

The transition probability between a lower state $$m$$ and an upper state $$n$$ can, for large $$m,n$$, generally be approximated by the formula

$$A_{m,n} = 1.3\cdot 10^9 \cdot m^{-1.8}\cdot n^{-3.2}$$

so for either of the states going to infinity, the transition probability is zero.

Essentially, it has to do with the fact that in this case there is no overlap between the wave functions of the two states anymore. The wave function for $$n=\infty$$ is just zero at any finite value for the radius. The same applies for the ionization probability resulting in an photoelectron with kinetic energy $$E=0$$, or for recombination of a free electron into state $$n=\infty$$. Either of these have zero probability.

• Ok. and just to confirm, there is no way to store the ionization energy in an electron which wouldn't involve moving to state n = \infty ? Commented Jun 10 at 6:42
• @HughPerkins I am not quite sure how to understand your question. If you have a photon with an energy corresponding to the ionization energy, then it could only go to $n=\infty$ (as this transition would be the only resonance matching the photo frequency). But the probability for this is zero as explained Commented Jun 10 at 7:25