A physics question came to mind while thinking about the Compton effect. I understand why we relate frequency to energy since color is related to energy. Additionally, color and frequency are constant in refraction experiments whereas speed and wavelength change. However why do we relate photon momentum to wavelength. I understand that the wavelength changes for Compton scattering as does the momentum of the photon. However since the speed of light is constant the "color" of the light (frequency) also changes.
A few possibilities that came to mind:
a. Conservation of energy is a symmetry is time and conservation of momentum is a symmetry in space so it kind of makes sense that since frequency is related to time it would be associated with energy and since wavelength is related to space it would be associated with momentum.
b. The Bohr atom indicates that angular momentum (not linear) is quantized. Usually this is shown as an electron exhibiting wavelike properties of a standing wave and thus not radiating and spiraling into the nucleus so it looks (based on diagrams) that the wavelength is important however without just the right frequency there wouldn't be a standing wave.
c. Since frequency is related to energy perhaps it would be better not to associate it with momentum so by default wavelength is related to momentum.
I know I missing something I just don't know what it is.