Talk:Rydberg–Ritz combination principle

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What is a 'transition line' of an atom? please be more helpful here. wikipedia points nowhere.

I have added a section explaining and linking to other articles. This helps explain the atomic spectra for non-scientists. I am also going to casually suggest a merge with the Ritz Method.

• These articles describe roughly the same theory
• They provide two different levels of mathematical and conceptual rigor that could greatly complement each other if combined into one article
• The extremely incomprehensible Ritz method article could use the conceptual introduction provided by the Rydberg-Ritz combination Principle article
• This one could use the mathematical approach as a good follow-up for more advanced physics or chemistry students who want additional information. Nimur 13:59, 26 May 2006 (UTC)

Not sufficiently explanatory

For me, this article simply doesn't make it clear enough what Ritz contributed beyond the Rydberg starting point, at the level of an equation. I sort of get it that he extended the set of lines with sums and differences of two Rydberg lines (only two, or do the new Ritz lines also participate in summing/differencing, making available every linear combination, if perhaps with exponential decrease in emission intensity/probability?)

And why did this wait until later? Are the Ritz lines inherently weaker, and therefore largely unnoticed, for a long time? — MaxEnt 17:09, 16 October 2018 (UTC)

This is answered in the History section. Rydberg considered only the hydrogen atom. Ritz generalized the principle to apply to all atoms. Dirac66 (talk) 18:34, 16 October 2018 (UTC)

The question on Ritz's contribution has been partly answered and I will answer to the linear combinations. The second formulation that the wavenumber of each spectral line can be written as the difference of two terms should be regarded as the more fundamental one. The consequence is that the sums of the wavenumbers of some specific pairs of spectral lines (e.g. Lyman-alpha plus any spectral line from the Balmer series) give other existing spectral lines of the same atom, and the same for the differences of some other specific pairs of spectral lines (e.g. two lines from the same series). The form of the terms differs for different atoms, but the principle that the wavenumbers of all spectral lines of one atom can be written as the difference of two terms holds generally (it was later modified by selection rules, which don't apply to gross structure). 2A00:1028:9192:4E22:21E1:A552:805A:72C5 (talk) 22:35, 12 January 2021 (UTC)