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Maxwell noted that if he combined his equations of electrodynamics, he ended up with an equation that had the characteristics of a wave equation, so he argued that light is an oscillating wave in which the oscillations of the electric field generate the oscillations of the magnetic field, and vice versa, and he predicted the velocity of light. The important point of this is that such radiation was generated by any accelerating electric charge including dipoles, etc. This led to a crisis with statistical thermodynamics, because in that, objects that were cooling should give off all frequencies. (That is a little oversimplified, to make the point that your cooling objects should give off ultraviolet radiation, but they did not; they gave off the grey body radiation.)
What Planck argued was that the oscillations could not simply give off the energy at any frequency but with correspondingly low amplitude, but instead the radiation had to be emitted as if the action associated with the transition was quantised. In effect, the radiation had to be emitted in discrete pulses, and not a sequence of continuous waves, even if the amplitudes fell away.
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