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$^{2S+1}L_J$ was the term symbol.

I watched a video online saying $2J+1$ was the fold of degeneracy to the term symbol.

Specifically, for nitrogen, the term symbol for the lowest energy was $^4S_{3/2}$ which means it has 4 fold degeneracy. But I couldn't figure out how this could be(?) as all the electron are at spin up states, and there's only 3 orbit in $2p$ shell.

Further, what's the meaning of multiplicity $2S+1$ mean here?

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The multiplicity$(2S+1)$ in the term symbol shows the number of possible orientation of TOTAL spin, of electrons in an orbital. Here $2S+1=4 $, gives $S=3/2$, have 3 unpaired electrons in 2p shell. Thus the possible total spin orientations are (-3/2,-1/2,1/2,3/2). Number of possible total spin values are, hence 4.

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