Normally when an electron gains energy there is a random time delay before it spontaneously emits the energy as light. Sometimes this emission is said to come from a 'forbidden transition' and the time delay is much longer, though still random. This is called Spontaneous emission.
If during this waiting period the electron is hit by a photon of light the electron will instantly emit its energy. This is called Stimulated emission. An unusual feature of this is that the photon emitted will be travelling in the same direction as the original photon.
For this process to be sustained the rate of stimulated emission needs to be greater than that of spontaneous emission. This state is called a Population Inversion, where there are more excited electrons than un-excited electrons. However, with just two energy state involved this will never be achieved. Three or four energy levels are generally used.
When a photon is absorbed by an electron and becomes excited there is a rapid transition into another long lived energy state. Thus, this long-lived state soon becomes more populated than the unexcited state, which ensures a sustained process of stimulated emission.
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