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In reading Feynman's lectures, he mentions the quantization formula E = hf, where Planck's Constant, h, is multiplied by the frequency of radiation. He then says that though the constant is a certain step size, since the frequency of light can be anything whatsoever, then the energy of a photon can have any value whatsoever.

This is all good and well, but my question is along the lines of: if radiation from atoms is only ever created and only ever absorbed at very specific energy levels (because of the finite shells for an electron to jump), then what happens to light that doesn't exactly "fit the bill"? If radiation can be created by other means outside of electron jumps, then what are the chances this radiation will be the exact amount required for an electron jump of any of the finite number of elements?

Or, perhaps more encompassing, if a photon's energy is affected by collisions, gravity, and other interactions, then how does even a single photon maintain the precise energy needed to be reabsorbed? Clearly my picture is a little skewed.

My guess would be that when people say that energy can only be absorbed in particular amounts, it's not that there's only certain kinds of photons that can be absorbed atomically, but instead that atoms can only absorb a set amount but they reflect the excess energy as a lower frequency photon(s).

Is this correct? What are the limitations of absorption for photon's that excessively "fit the bill"? Obviously the only criteria for atomic absorption isn't just having the required amount of energy, otherwise all light with sufficient energy would be partially absorbed and the remainder reflected. Certain materials have certain colors, which wouldn't be the case (as far as I can tell) if there were really no limitations for absorption other than a photon having adequate energy. But, equally, it doesn't make sense to me to say that there are exact absorption energies which must be matched exactly by the energy of a photon (so that the photon is completely absorbed, with no excess energy remaining) if the energy of a photon is dynamic and can scale an infinite range.

Summarized: if a photon can have any energy level, and if that energy is continually nudged by interaction, how can a photon ever have the exact energy any electron jump demands? And if the photon's energy doesn't exactly have to match to be absorbed, then what are the limitations that allow for colors to be isolated in their reflections?