Jamarcus Schroeder

2022-08-29

"Each such orbital can be occupied by a maximum of two electrons, each with its own spin quantum numbers."
I though that all electrons had same spin quantum number $s=1/2$, being the difference the $z$-component of the angular momentum, ${m}_{s}\in \left\{-1/2,1/2\right\}$.
I'm confusing the nomenclature ?

Rijpv7

Expert

Of course it would be nice if physicists were consistent in their wording, but I don't think this will ever happen. Therefore, my advice is that you don't try to concentrate too much on the definitions like "the spin quantum number is ${m}_{s}$", but instead try to understand the concept. Furthermore, this should be simple for you, because I believe that you already got it right:
- Electrons are spin $1/2$ particles. This means that the magnitude of the spin is equal to $1/2$.
- If a particle possesses the spin s, there are $2s+1$ different quantisation configurations: ${m}_{s}=\left\{-s,-s+1,\dots ,+s\right\}$. These configurations can visualise by assuming that the spin of the particle is only allowed to "point" in certain directions in space (w.r.t. the arbitrarily chosen quantisation axis). So, if $s=1/2$, we get $2\cdot 1/2+1=2$ configurations, ${m}_{s}=±1/2$. If instead the spin is $s=3/2$, we get $2\cdot 3/2+1=4$ different configurations, ${m}_{s}=\left\{-3/2,-1/2,+1/2,+3/2\right\}$.

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