Why do materials absorb some frequencies of electromagnetic radiation and not others?
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because electrons absorb only certain fixed values of energy
Well energy absorption by a material depends upon their atomic properties. Energy is absorbed in discrete quanta of energy as predicted by quantum mechanics only if the corresponding energy state is available either it is absorbed by electrons or nucleus depends whether it can go to permissible energy state, if not system can't absorb energy at all.
it will be easy if you assume an electron as system of spring mass attached. Thus,it vibrates with its won frequency. when a light of frequency approaching matches with the frequency of the electron vibration-resonance. Therefore, the electron vibrates more vigorous and acquires thermal energy. This resonance effect could be said as discrete set of energy-quanta.