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I’ve been reading a book, and in one part the author explains how electrons only absorb the wavelengths of light that can take them to an excited state, i.e. that can take the electrons to a higher orbital. The author doesn’t mention where the photons that don’t have enough energy go, so I assumed (and I may very well be wrong) that they were refracted, or “bounced off” of the electrons. In the a later stage of the book, the author writes that we see colors because the electrons absorb all the light to warm up the atom but also to reach an excited state. They then emit light as they fall back from their excited state and that’s what we see. My question is :What’s actually true here? Is the light we see the light that’s being absorbed and then reemitted with the same frequency, or do we see what’s not absorbed? Is all light always absorbed? Which of the explanations are correct? Is it a mix of the two?

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It's a mix of the two. The sequence:

[incoming photon and atom; interaction; outgoing photon and atom]

is called scattering. There can be elastic scattering, where both the photon and the atom retain their energies, and inelastic scattering, where the energies change. In elastic scattering the photon 'bounces' off the atom, so as to change direction but not energy. In inelastic scattering the photon usually loses energy and the atom gains some, but if the atom was not in its ground state to begin with then it can also happen that the atom loses energy and the photon gains some. There are further possibilities, such as an atom emitting more than one photon, but let's ignore those for now.

In a typical situation all these types of process can happen, but they will happen with different probabilities. The elastic process dominates when the photon energy is off-resonance; the inelastic process dominates when the photon is resonant or near-resonant. Here by 'resonant' I mean that the photon energy matches an energy level gap in the atom. Far off resonance the elastic scatting will be weak, which means the photon mostly goes straight on through or is only steered a little bit.

When materials such as glass change the direction of incident light without absorbing it, this can be seen as an example of elastic scattering.

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