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Electron spins affect an electron's behavior because it prevents two electrons with parallel spins from occupying the same orbital. The configuration is most stable when electrons are paired with electrons with opposite spins.
The spin number, or the spin magnetic quantum number (ms), is +1/2 or -1/2 since an electron can be spin up or down. The significance is that no two electrons in the same atom can have the same four quantum numbers. It tends to be pretty arbitrary as long as the combination of the four quantum numbers is possible; the principle quantum (n) and angular momentum quantum (l) numbers are typically the definite ones.
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