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Consider the case where I have 2 electrons in the outermost p orbital. Therefore. I have two electrons with $l = 1$ and capital $L= 2, 1, 0$.

I know that $S=0,1$ depending on the spins. My question is how to calculate $L$ based on the the possible $S$ values. The Wikipedia page on Hund's rules says that we can have $S=1$ leads to only one possible $L$ (in fact it is $L=1$) but $S=0$ has both $L=0,2$ allowed. Why is this so?

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