Editing Spin quantum number (section)

== History ==
{{Also | Spin (physics)#History }}
During the period between 1916 and 1925, much progress was being made concerning the arrangement of electrons in the [[periodic table]]. In order to explain the [[Zeeman effect]] in the Bohr atom, Sommerfeld proposed that electrons would be based on three 'quantum numbers', n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing.<ref>Manjit Kumar, Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality, 2008.</ref> [[Irving Langmuir]] had explained in his 1919 paper regarding electrons in their shells, "Rydberg has pointed out that these numbers are obtained from the series <math>N = 2(1 + 2^2 + 2^2 + 3^2 + 3^2 + 4^2)</math>. The factor two suggests a fundamental two-fold symmetry for all stable atoms."<ref>{{Cite journal |last=Langmuir |first=Irving |date=1919 |title=The arrangement of electrons in atoms and molecules |url=https://linkinghub.elsevier.com/retrieve/pii/S0016003219910970 |journal=Journal of the Franklin Institute |language=en |volume=187 |issue=3 |pages=359–362 |doi=10.1016/S0016-0032(19)91097-0|url-access=subscription }}</ref> This <math>2n^2</math> configuration was adopted by [[Edmund Stoner]], in October 1924 in his paper 'The Distribution of Electrons Among Atomic Levels' published in the [[Philosophical Magazine]]. 

The qualitative success of the Sommerfeld quantum number scheme failed to explain the Zeeman effect in weak magnetic field strengths, the [[anomalous Zeeman effect]]. In December 1924, 
[[Wolfgang Pauli]] showed that the core electron angular momentum was not related to the effect as had previously been assumed.<ref>{{Cite journal |last=Giulini |first=Domenico |date=September 2008 |title=Electron spin or "classically non-describable two-valuedness" |url=https://linkinghub.elsevier.com/retrieve/pii/S1355219808000269 |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |language=en |volume=39 |issue=3 |pages=557–578 |doi=10.1016/j.shpsb.2008.03.005|arxiv=0710.3128 |bibcode=2008SHPMP..39..557G |hdl=11858/00-001M-0000-0013-13C8-1 |s2cid=15867039 }}</ref>{{rp|563}} Rather he proposed that only the outer "light" electrons determined the angular momentum and he
hypothesized that this required a fourth quantum number with a two-valuedness.<ref>Wolfgang Pauli. [https://www.nobelprize.org/uploads/2018/06/pauli-lecture.pdf Exclusion principle and quantum mechanics] Nobel Lecture delivered on December 13th 1946 for the 1945 Nobel Prize in Physics.</ref> This fourth quantum number became the spin [[magnetic quantum number]].