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Spectral lines appear when the frequency of light entering the atom is equal to the energy different between two different energy levels of the atom. I am not sure if I would say that there is one wave for every spectral line, but I would say that there is one wavelength for every spectral line. I believe that the standing wave model represents the different energy levels of an atom.
The circular standing wave model is just a math model that was developed to reconcile electrons having wave-like properties and having quantized energy states. In this model, each stable circular standing wave (with whole number wavelengths) around the nucleus represents an energy level (n=1, 2, 3...).
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