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When the electrons in the element are excited, they jump to higher energy levels. As the electrons fall back down, and leave the excited state, energy is re-emitted, the wavelength of which refers to the discrete lines of the emission spectrum.
The emission spectrum can be used to determinate the composition of a material, since it is different for each element of the periodic table. For example, it is used to identify the composition of stars by analysing the received light.
Interestingly, the emission spectrum of an element is the exact opposite of its absorption spectrum; that is, the frequencies emitted by a material when heated are the only frequencies that will be absorbed when it is lighted with a white light.
See also: Rydberg formula
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