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Does the distance between an atom emitting a photon and an atom interacting with that emitted photon set a upper bound on what that photon's wavelength could be?

For example, two atoms are a distance x apart. Would it be nonsensical to say that an interacting photon could have a wavelength of 1.1 x? Or is photon wavelength simply a concept that defies an intuitive explanation?

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Photon wavelength does not defy an intuitive explanation. It can be directly measured. The wavelength of a photon emitted by an atom is determined by the energy difference between a high energy state and a low energy state between which the atom "moves". (Not translational motion, motion in state space)

Within a molecule or crystal, proximity of neighboring atoms can under some circumstances modify the energies of the states of an atom, but the distance between atoms does not directly relate to the wavelengths of emitted photons.

It would not be nonsensical to use, e.g., the spacing between atoms in a silicon crystal at a certain temperature, as a unit of distance. In a silicon crystal the nearest-neighbor distance is 0.235 nanometers. So, we could say that the red emission line of a HeNe laser (633 nm) has a wavelength of 633/(0.235) "SiNeighbor" units. It's easier though simply to use the wavelength of a particular emission line of hydrogen as a reference.

Some further information that might be helpful to you:

The wavelength range of visible-light photons is roughly 650 nanometers to 400 nanometers, whereas the typical distance between atoms in a solid is on the order of angstroms. Photons with angstrom-range wavelengths are X-rays.

There are nanoscale structures called "photonic crystals", with periodically varying refractive index (on a scale much larger than spacing between atoms), that allow light only of certain wavelengths to propagate, due to volume diffraction effects.

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