Glowing, Glowing, Glowing, . . . . Gone?
As the brief description noted, phosphorescence requires the excitation of an electron in the material's crystal structure to an energy level where it will stay for a while - a metastable state. The process can also involve energy transfer between the crystal and extrinsic states coming from the presence of "impurity" atoms in the crystal structure. (Sometimes, the impurity atoms are put into the crystal structure just for this kind of purpose.) Phosphorescence, as a quantum process, involves at least three electronic states of the atom.
Once in a metastable state, the electron cannot return directly back to its ground, or lowest, energy state. The indirect transition that has to occur is less likely to take place and the electron remains in the metastable state for a longer time. It will transition back to its ground state, releasing its excess energy as visible light when it does so. The probability law that describes this time behavior is governed by a kind of average state lifetime - or half life τ. (The half life is the time needed, on average, for half of the electrons to return to their ground state. It is a statistical result from a large sample of such atoms.)
As the population of electrons in the metastable state decreases with time, the likelihood of actually seeing a transition back to the ground state also decreases. This means that the phosphorescent glow is brightest just after the excitation source is turned-off, and that it decreases with time. If there is only one half life (only one metastable process involved), the brightness of a phosphor at constant temperature will vary as
I = I0 e-t/τ
Real phosphor materials can be more complicated, involving several metastable processes and their respective half lives. Among other uses, these materials produce the glow in the dark objects we are familiar with. Glow in the dark objects get their excitation energy from the ultraviolet light that is part of normal sunlight or most artificial lighting. While we can't see the ultraviolet light, it supplies more energy to the atom than is given off by the visible phosphor glow.
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