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The spectrum of hydrogen was very well studied by the mid-19th century. However, if one were doing experimental spectroscopy for more complex atoms, one would see plenty of spectral lines in the spectra of sodium or potassium. A diagram for lithium by Grotrian "Graphische Darstellung der Spektren von Atomen und Ionen mit ein, zwei und dreivalenzelektronen" (1927) is attached below. What protocol was used to assign the terms associated with spectral lines?

The key question is how did physicists experimentally assign electron transitions say for example, 670 nm emission line is from 2s to 2p levels? How did they calculate energy of 2s and 2p for multi-electron atoms? Is the scale based on the hydrogen atom?

Historical diagram by Grotrian (1927) for atomic spectrum for 1, 2, and 3 valence electrons

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    $\begingroup$ Basically it’s a giant logic puzzle, but isn’t that hard given enough information. See also nuclear energy levels - same thing. You know there are some number of discreet energy levels and their differences are possible emission energies. Noodle about until consistent. $\endgroup$ – Jon Custer Mar 3 at 5:01

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