How are frequency and energy in electromagnetic waves related?
Well, there are two models for a electromagnetic radiation. One is ofcourse the wave model and the other being the particle model which assumes radiation to be composed a stream of particles with discrete energies called light quanta.
The two models lead to some different concepts of energy associated with radiation.
In the wave model, the radiation is considered to be an EM wave and in such a case, the energy is stored in the EM fields propagating in a region.
Energy in the wave model is contained in the wave oscillations.
In such a case, one may write the expression for energy density of diffuse radiation as,
The particle model is slightly different conceptually. When you consider radiation to be composed of discrete particles, each particle then contains a discrete amount of energy and so many particles together sum up to the total energy of the radiant beam.
In such a case, energy of each quantum is given as