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To ionize atom at some state, as understand, it must receive the energy of that state, so for a hydrogen atom, being in the ground state it $13.6\ eV$. In the second state, the ionization energy is lower - $3.4\ eV$ and so on.

The important thing, is that the difference between the ground state and the second state is greater than half of the difference between the ground state and the infinite state, i.e., the ionization energy.

So, this means, that if a hydrogen atom will be excited from the ground state to the second with $a 10.2\ eV$ photon, and while being at the second state receive the same $10.2\ eV$ photon, it should be ionized.


At the same time, considering the laser system, where atoms being excited to some state, receives the same excitation photons, but instead of being ionized, they even lose their energy, moving to a lower state.

Why are atoms not ionized in that case?

My thoughts

I tried to search, yet have not found anything, but I assume that simply not each chemical element has a difference between the ground state and the second state (or any two other) greeter than half of the ionization energy.

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  • $\begingroup$ "At the same time, considering the laser system, where atoms being excited to some state, receives same excitation photons, but instead of being ionized, they even lose their energy, moving to lower state." can you give a link for this statement? AFAIK Lasers have a particular frequency width and the main frequency has nothing to do with the energy of atomic excitations of the target . (E=hν) $\endgroup$
    – anna v
    Commented Mar 25, 2023 at 18:28
  • $\begingroup$ @annav as I know, main process, that occurs in laser is stimulated emission, when atom, being at state $E_n$ receives photon with energy $𝐸_n− E_{n-1}$ 𝑎𝑛𝑑 ℎ𝑎𝑠 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡𝑜 𝑑𝑒𝑐𝑎𝑦 to $E_{n-1}$, emitting photon and absorbing original one, and then two phased photons exist. en.m.wikipedia.org/wiki/Stimulated_emission $\endgroup$ Commented Mar 25, 2023 at 19:13
  • $\begingroup$ Yes, but the effect comes on a single frequency , lasers are monochromatic, for a specific population inversion. Then statistics enter, and optics. If the frequency coming from the population inversion and amplification is ionizing, there will be no laser action. that is why when there is lasing there is no ionization. $\endgroup$
    – anna v
    Commented Mar 25, 2023 at 19:32
  • $\begingroup$ @annav, 1) I do not understand why You are referring to the fact that laser radiation is (almost) monochromatic; 2) From Your last part of comment, I think, the only I should determine — do all chemical elements have difference between first and second state greater or equal then half of ionization energy $\endgroup$ Commented Mar 25, 2023 at 19:46
  • $\begingroup$ That difference has nothing to do with population inversion and choice of elements to use for lazing. azooptics.com/Article.aspx?ArticleID=1346 $\endgroup$
    – anna v
    Commented Mar 25, 2023 at 20:14

2 Answers 2

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The lifetime of the hydrogen $2p$ state is $1.6$ nanoseconds, so for the atom to be ionised it would have to absorb a second photon within this very short time. This will happen, and some ions will be formed, but the probability that the excited hydrogen atom will absorb a second photon in the $1.6$ ns it exists is very small so the number of ions formed will be very small.

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  • $\begingroup$ I understand, that lifetime in excited states is low, hence probability of receive photon, being at that level is low, however, this is what happens in big amounts in laser, so either that assumption about lower different between states wrong, and, lasers has a lot of ionizations, or the assumption is correct, so ionizations are not happen $\endgroup$ Commented Mar 25, 2023 at 17:36
  • $\begingroup$ @Stdugnd4ikbd Lasers involve three states. From the ground state the lasing medium absorbs a photon to form a short lived excited state that quickly decays to a long lived metastable state. It is this third state that lases due to stimulated emission. So it is not an excited state absorbing a second photon as you ask in your question. $\endgroup$ Commented Mar 25, 2023 at 20:46
  • $\begingroup$ Okay, two questions then: 1) There are, as I know, four-level, and maybe even more lasers, where atoms a being excited already to metastable level, hence, there should be a lot of ionization. 2) As for systems, where atom, receiving excited photon go to unstable level, and fast jump to metastable with lower energy, it is question then, is that energy + excitation photon energy enough to ionize atom. $\endgroup$ Commented Mar 26, 2023 at 8:44
  • $\begingroup$ That's a good question. It's certainly possible that the energy needed to create the initial excited state is large enough to ionise the lasing state. I think you've have to look at a particular laser and see what the energies of the states were. Bear in mind that hydrogen is unusual in having such a large gap from the ground to the first excited state and in multielectron atoms the first excited state energy will be much lower. I guess you'd have to Google for a list of the common lasers and see what their excited states are. $\endgroup$ Commented Mar 26, 2023 at 11:14
  • $\begingroup$ I tried, for ruby, for example, but didn’t found exact values. Also, I understand, that for non-hydrogen atoms, because there are multiple orbitals and with multiple electrons on them, things are not as easy as for hydrogen, but I have some leak in knowledges in this area, need to learn it, that I didn’t learn in school. And also there are multiple chemical elements, not one. I think simpliest is helium-neon, but it is excited by electricity $\endgroup$ Commented Mar 26, 2023 at 11:37
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It is not such a simple question. Lasers are complicated.

If an atom absorbs some energy (perhaps a photon), an electron can be promoted from a low energy state to a high energy state. If the atom sits undisturbed for a while, it can spontaneously decay. The electron returns to the low energy state and a photon of wavelength $hc/\lambda$ is emitted.

Another possibility is that a photon of wavelength $\lambda$ can pass by the excited atom and stimulate the emission of another photon. The electron drops to the low energy state. The emitted photon has wavelength $\lambda$, is in phase with the first one, and travels in the same direction. This is stimulated emission.

Excited-state Absorption can happen too. In most lasers, the photons are not so energetic that a second absorption will ionize the atom. That means a third state with the right energy must be present. In many lasers, there is no such state. When it is present, there are techniques to reduce the effect. On the other hand, some lasers take advantage of it to double the frequency of the laser light.

There is another issue related to your question.

Lasers work by stimulated emission in an optical cavity. Suppose you have a population of excited atoms between two mirrors. Some of them spontaneously decay. Some of the photons happen to be in the right direction to be reflected back and forth, passing through the atoms again and again. These photons can stimulate emission of more photons. The number of photons grows, creating a producing coherent laser beam.

This glosses over many complications. For growth:

  • The cavity must be designed carefully. Light must repeat its path and interfere constructively after a round trip. Diffraction makes the beam spread. The mirrors must slightly focus the beam to counteract this. Otherwise more photons will leak out the sides than are created by stimulated emission. See laser modes and Gaussian beams.
  • One of the mirrors must be perhaps 99% reflective and 1% transmissive so the beam can get out of the cavity. Not too transmissive, or more photons will escape than are created.
  • Atoms decay. Atoms in the low energy state absorb photons instead of emitting a second one. For growth, a photon must encounter more excited atoms than low energy atoms.

This last point is a big one. At thermal equilibrium there will be some excited atoms, but more low energy atoms. You can add raise the temperature to get more excited atoms, but never as many as lower energy. Having more excited atoms is called a population inversion. It takes some tricks to arrange one.

Even if you start with a population inversion, you have to keep adding energy to maintain it. The first thing you might think of is making a gas discharge lamp, like an ordinary neon light. You add lots of energy and make lots of excited atoms. You can see lots of photons being given off of the correct wavelength. But this doesn't work. Even though it is not at equilibrium, it is in a steady state. The lower energy population is always larger for any system with 2 energy levels.

The simplest lasers have 3 energy levels with $E_1 < E_2 < E_3$. The lifetimes of the excited states are different. $E_3$ very quickly decays to $E_2$. $E_2$ lasts much longer. State $2$ winds up with all the electrons you might have expected to be in in either $2$ or $3$. This can outnumber State $1$. So the energy source pumps electrons to state $3$, but the laser transition is $E_2 \rightarrow E_1$.

This works, but lasers with 4 levels are more efficient.

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  • $\begingroup$ Thanks, I think it’s a good explanation of laser device, however, most part of the answer is not related. Important are first four paragraphs, and the general explanation atoms in lasers in excited states, instead of hydrogen atoms (is there hydrogen laser also?) has ionization energies, that is higher than excitation photon energies. It would be great, if someone provide specific information about energy levels and which of them used in lasers, for example for Ruby $\endgroup$ Commented Mar 26, 2023 at 11:02

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