MadSci Network: Science History
Query:

Re: Where do the quantum numbers(n,l,m_l,m_s) and sublevels (s,p,d,f) come from

Date: Sun Jan 3 19:20:22 1999
Posted By: John Christie, Faculty, School of Chemistry, La Trobe University, Bundoora, Victoria, Australia
Area of science: Science History
ID: 909456191.Sh
Message:

The origins are English, and slightly messy.

To do the harder and more obscure ones first, 'n' is simply a common algebraic convention for an integer variable or constant; 'l' is a typical thrid choice, and has some angular momentum connotations in other applications. 'm' stands for magnetic, 's' for spin, so the two azimuthal or magnetic quantum numbers were distinguished by subscripts 'l' for orbital component (related to the 'l' quantum number) and 's' for spin component.

The other letters, s,p,d,f have their origins in the analysis of the spectrum of the hydrogen atom and the alkali metals, where several series of lines were seen, and these were classified as 'sharp', 'principal', 'diffuse', and 'faint'.

It is important to stress that there is not a simple and consistent relationship between spectral lines and energy levels, since 2 levels are associated with each line. So, for example, the sharp series of lines arises from np --> s transitions, the principal from ns --> p transitions, the diffuse from nd --> p , and the faint from nf --> d.


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