# Can an excited atom have multiple electrons in excited states?

For an excited atom, is it possible for the atom to be excited twice, having multiple electrons in higher energy levels than for the atom in its ground state? If it is indeed possible, what is the mechanism for this, can one photon excite more than one electron or are two required?

My intuition is that the atom would return to its ground state too quickly for this too happen. Also, I would suspect that if the atom could be excited twice, the already-excited electron would be excited (or ionised) a second time, not a new one.

Thanks in advance.

• A mathematical answer could be given based on probability(which is why I'm not posting it. A given photon has a small probability of exciting a specific electron. I do not have exact figures, but let's say it is one in a thousand. Then, the probability of a given photon to excite the same electron again is one in a million (the application is a little vague, but I think you'll get the point). – Shubham Feb 21 '15 at 9:50

## 4 Answers

Multielectron atom has much more complex energy spectrum than hydrogen atom. As the electrons interact with each other, the hydrogenic energy levels get shifted, and much of the hydrogen-specific degeneracy, as well as degeneracy resulting from electrons mass&charge equality, is lifted. Moreover, since the electrons do interact with each other, we can't, strictly speaking, speak about single-particle states of electrons. This means that when we shine light on a multielectron atom, it can't excite one electron. It instead changes the configuration of the whole atom, and the final state is approximately what we would call an atom with single electron excited.

Now, as the energy levels are partially split by electron-electron interaction, there's a way$^\dagger$ to directly (i.e. via single photon) get to the state, which we approximately (i.e. in terms of the shell model) describe as twice-excited state. We just have to shine the appropriate frequency of light at the atom. This way we could even excite more than two electrons. Doing another way, we could shine light composed of two frequencies corresponding to transition from ground to singly excited state and from singly excited to doubly excited state. Then it'll also be possible for the atom to appear in doubly excited state, but this would be a sequential transition.

For some atoms though, doubly excited states are unstable in the sense that the corresponding energy is above ionization energy, so such states are likely to decay into ionized atom instead of directly going to ground state. This is true for e.g. doubly excited helium atom.

My intuition is that the atom would return to its ground state too quickly for this too happen

Note that transition from one state to another is not instant. The probability of occupying some state gradually changes with time, and if you shine the light driving transition to singly-excited state and mix the light driving transition from singly excited to doubly excited state into the same beam, you'll be able to "intercept" the atom's singly excited state and drive it to doubly excited one.

Also, I would suspect that if the atom could be excited twice, the already-excited electron would be excited (or ionised) a second time, not a new one.

Don't forget about quantization of energy and the fact that electron-electron interaction lifts much of the possible degeneracy. It's highly unlikely that energies of doubly excited atom and atom with single electron excited to higher level will coincide. Thus if you tune your light source well enough, you're unlikely to excite the already excited electron to higher level instead of getting doubly excited atom.

$^\dagger$ I may actually be wrong if it appears that such optical transition is forbidden for all atoms. If you find some evidence of this, please let me know.

The simplest example I can think of to illustrate this is the spectrum of the hydrogen atom.

The excitation of the electron from the ground state, n = 1 produces a series of absorptions known as the Lyman series. The first line is excitation of the electron from n = 1 to n = 2, the second line is n = 1 to n = 3 and so on. But there are also absorptions due excitation of an electron from the n = 2 excited state to higher states, and these are called the Balmer series. Likewise we have the Paschen series starting at n = 3 and so on.

You are correct that the lifetime of an excited state is usually short, but if we put a gram ($\approx 10^{23}$ atoms) of hydrogen into our spectrometer and excite it by light, radiation, heat or whatever, there will be a small but non-zero equilibrium concentration of excited states and we can measure their absorption spectra.

Hydrogen is a single electron system, but the same applies to many electron atoms - it's just that their spectra get fearsomely complicated, which is why I chose hydrogen as my example!

The answer to your question is yes and there are experiments which use multiple excitations. A very famous one is the Lamb-Rutherford-Experiment where they could prove the existence of the lamb shift.

First they excited a beam of hydrogen atoms which were in the $1S_{1/2}$ groundstate into the $2S_{1/2}$ state by bombarding them with electrons. This has a very long lifetime since optical transition to the groundstate is forbidden by selection rules.

The $2S_{1/2}$ atoms then pass through electromagnetic radiation in a tunable resonator. In the experiment they could induce a transition from $2S_{1/2}$ to $2P_{1/2}$ and prove this because $2P_{1/2}$ atoms decay quickly to the groundstate. So one just needed to measure how many atoms were still in the $2S_{1/2}$ state after leaving the resonator.

You see, it is not only possible to excite an excited atom, it has also lead to important discoveries.

I think it's pretty typical in nature. Some elements have a a very large number of electrons, too. I would be interested if somebody could answer what the lifetime of an excited electron is.

In classical QM the excited electron would stay excited forever. QED is needed to explain the electron dropping back to the ground state and releasing a photon before doing so.