I think that the normal Zeeman effect is experimentally observed only when we can neglect the spin i.e. if we consider a spin-singlet state with total spin $S=0$. Since in the hydrogen atom there is only one electron, we cannot observe the normal Zeeman effect in the Hydrogen atom. Am I right?
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asked Feb 12, 2022 at 7:45
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Yes, you are correct. The "normal" Zeeman effect refers to the splitting of spectral lines into an odd number of components, which could occur for integral orbital angular momentum (e.g., the $M_L = -1, 0, +1$ levels of a $p$ orbital). When there is a single unpaired electron spin, $S=1/2$, so an even number of spectral lines results and this is called the "anomalous" Zeeman effect. In the hydrogen atom, the unpaired electron spin means that a "normal" Zeeman effect is not observed.
