T H E E L E C T R O M A G N E T I C S P E C T R U M
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When an electron is accelerated, electromagnetic (EM) radiation is released. This radiation can be interpreted as either wave-like (an oscillating disturbance in the EM field) - or particle like (a massless particle called the photon) moving outward at the speed of light. According to Quantum Mechanics, these interpetations are equivilant: they are both valid mathematical descriptions of a quantum phenomena. In the quantum world, there is no definitive physical reality, math is our only working guide.
The electron, likewise a quantum particle or wave, can only emit or absorb radiation in discrete quantities. The change in energy of the electron is the energy of the photon that is absorbed or released.
The more energentic the photon, the shorter it's wavelength. A photon with an energy greater than 13.6 eV has enough energy to ionize (strip the electron away) a hydrogen atom. The collision of an electron and a positron produces two photons of energy greater than half a million eV.