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There are quite a few questions similar to the one i am about to ask. However, non of the answers satisfied me so far.

Here i go :

In the Stern Gerlach Experiment, which was performed with a silver atom, you found two spots. One which corresponds to the atoms that aligned with a spin up and one for those with spin down.

To get the Spin number $S$, the way i always did it for some $n,l$ is : Start by filling each $m_l$ starting from the lowest with a spin up until they've all been filled, and then you repeat with spin down until you have no electrons left or there is no more room on that orbital. Add up all the spins, and you get $S$.

Now, after reading all related posts, it seems like this algorithm is just a quick and dirty way of getting the right $S$ ?

Otherwise, you would (as one user already asked) only one line in the Experiment. (You have $5s^1$ for silver, $S = 1/2$, and following that algorithm the "last" electron has the following quantum numbers $|n=5,l=0,m_l = 0, m_s = 1/2 >$). Am i wrong ?

Related Questions :

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  • $\begingroup$ My intuition says that passing the electron through that field is like measuring it. Therefore, before measurement the outer boundary electron is in a superpostition of both up and down. However, i don't understand why it would be half half (which is what i often heard). Does that also mean that for atoms with $S=2$ you get five different lines ? $\endgroup$
    – Pastudent
    Feb 1, 2022 at 12:37
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    $\begingroup$ Remember, you are measuring the spin on an axis defined by your laboratory experiment. The atom and electron don't care about your axis until you use it to measure. So, yes, the outer electron is in a superposition relative to your axis. $\endgroup$
    – Jon Custer
    Feb 1, 2022 at 13:37
  • $\begingroup$ Yes. This matches my intuition, but it does also imply that that 'algorithm' for determining the Ground State, is just that. $\endgroup$
    – Pastudent
    Feb 1, 2022 at 13:44

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