What causes atoms to have their specific colors?

Basically: What intrinsic property causes the differences between how the varying wavelengths of light are reflected at the atomic scale? Also, how do photons factor into this?

These are absorption lines in the solar spectrum

Fraunhofer lines coincide with characteristic emission lines identified in the spectra of heated elements.6 It was correctly deduced that dark lines in the solar spectrum are caused by absorption by chemical elements in the Solar atmosphere.

Emission lines of Iron are shown below.

If you have some physics background you will know that both these spectra depend on photon emission and absorption by the electronic states around atoms and molucules.

As there are many elements in the sun part of the observed continuity of the spectrum is due to the overlap of frequencies and the multiple possible states for each atom and molecule to absorb/emit photons.

There exists also continuous emission of photons when electrons ( charged particles) are accelerated or decelerated in external spill over electric and magnetic fields that exist around all atoms and molecules. This spectrum, called black body, will be continuous, and is what one sees in an incandescent lamp or very hot iron; photons are emitted continuously by all bodies , even though not in the visible spectrum.

So the role of photons is crucial to all electromagnetic radiation, including that from our sun. As an ensemble they form the classical light wave, the creation process is a quantum mechanical one involving photons.

Reflection is again an interaction of the individual photons of the beam with the material they impact. The frequencies that are not absorbed will define the color of the material that scattered the beam. So photons are crucial to defining the colors we see.

The photons are coherently scattered by the field of the electrons of the atoms and molecules of the scatterer. The classical view of an electromagnetic wave can be shown to coincide with the quantum mechanical one and is much easier in calculating the behavior of beams, which are huge ensembles of coherent photons.

Color is a purely psychophysical creation of the human eye, in response to EM radiation in the single octave from 400 to 800nm wavelength (air), but most older people have negligible response from 700 to 800 nm. "Light" is likewise a creation of the human eye. That's why we use separate units of measurement for it; lumens, candelas etc.

Atoms etc have NO color. They create EM radiation energy,at various wavelengths, only some of which evoke the human eye "light" response. Scientists need to watch their language, and use correct terminology, if they want to convey useful information, and not confuse students, with loose language.

"Light" by definition, IS visible. It IS NOT UV or IR.