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The total momentum J can appear as one of the following values L + S, L + S – 1, …, |L-S|, so if J = 2, S and L must be pointing in the same direction and be parallel, this is L + S. If L and S have opposite directions, they cancel each other out, leaving only J = 0, this is L – S. If L and S are perpendicular to each other, only one of these momenta can contribute to the total angular momentum J, resulting in J=1.
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