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Why does the spacing of the lines on a line spectra get closer together?

Line spectra in the visible and ultra-violet are caused by electron jumps between electronic energy levels. The higher electronic levels are energetically more closely spaced than the lower ones, so the energy gaps between jumps get progressively closer and closer together. The size of the energy jump and the frequency of the radiation emitted or absorbed are related by E = hn, where h is a constant. So the frequency and thus the position of the lines depends on this energy difference. So the lines converge towards the high frequency end of a series of lines.
 
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updated: 17 December 2003

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