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When an electron absorbs energy and is in a higher energy orbit (I guess the atom would be in an unstable state), when the electron releases this energy, would all of this energy be released at the same time, or could it release energy one "level" at a time?

So for example if a Hydrogen atom absorbed a lot of energy and its electron went to some level n = 5, could it slowly make its way back down to level 1?

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Yes, it certainly can. In fact, it can do either, traverse gradually across excitation states down to its ground state, or jump from its current state to its ground state, or to any lower state for that matter. So essentially, as long as the target state is equal or lower in energy than the current one the electron can jump to it.

Those jumps have different probabilities though. Determining which process is more likely to occur, and what the probabilities are is a matter of quantum mechanic calculations. Have a look here for example: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/fermi.html

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In presence of an environment (a solvent), it is also possible that the excitation energy is dissipated as heat (vibrations) to the solvent… this is called non-radiative relaxation. –  F'x Jan 22 '13 at 20:42
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