Do excited atoms always fall back to the ground state during de-excitation, or are there any intermediate states too where they stop?

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Do excited atoms always fall back to the ground state during de-excitation, or are there any intermediate states too where they stop?

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One of the best ways to understand this is to take a look at a Jablonski diagram. When you excite some atoms, if the photon has sufficient energy it can make an electron jump to a higher energy level. Now depending on many factors, the electron may relax in one of two ways. Either the electron relaxes nonradiatively (not emitting a photon) or radiatively. Radiative relaxation would necessitate that the electron falls back to a lower energy level releasing a photon of energy equivalent to the difference between those two levels. Now within each level you have sublevels, for example you may have excited an electron from s0 sublevel 2 to s1 sublevel 3. The electron may then relax from s1 sub3 to s1 sub0, as it’s still in the same energy level, this won’t emit a photon, but it will release energy like heat. This is called vibrational relaxation, a dissipation of kinetic energy to the surrounding. You go to a lower vibrational state within the energy level. Of course the electron is still considered excited, it’s still not in its native energy level. From s2 sub0, perhaps the electron relaxes to s1 sub3, this happens when there is an overlap in the vibrational and electronic energy states, meaning the high vibrational state of a lower electronic state overlaps with a low vibrational state of a higher electronic state. This is also nonradiative, called internal conversion. Then you also have intersystem crossing where the electron changes spin multiplicity. This gets quite tricky and I’m clearly not good at explaining simply. I think it’s best I refer you to a nice summary like the one here:
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Jablonski_diagram#Vibrational_Relaxation_and_Internal_Conversion

These things provide the basis for whether you get fluorescence, phosphorescence, luminescence, etc and all their different time scales.