How come an excited electron can emit two photons before returning to a ground state?

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How come an excited electron can emit two photons before returning to a ground state?

Chemistry
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It relaxes to allowed quantum states two times, separately.|dw:1442362736543:dw|
Yeah energy levels are quantized; there's only certain energies that can be taken on and emitted, if I remember that correctly.
why does the same electron relax and send off two photons with differing wavelengths when it only absorbed the energy given by one photon, and what does relaxing to allow quantum states to happen twice say about the original energy of the photon that excited the electron or what does it say about the threshold frequency of the material that contains the electron?

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energy is conserved right? so the energy of the two emitted photons will be equal to the energy of the original absorbed photon. "what does it say about the threshold frequency of the material that contains the electron?" what is this about? you didnt talk about the photoelectric effect here at all.
What I was looking for was for someone to tell me that the path an electron takes back to its ground state will be random. And I now realize that I was overlapping the atomic spectra with the photoelectric effect when they are actually two different things.

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