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How are we supposed to know what the spin state of an electron is? For all of the homework problems I've done so far they have only been asking about the first three quantum numbers, but I don't understand how we would know what the spin state is unless it is given.
The spin of an electron is only relevant when filling out electronic configurations. The quantum number ms in no way determines how many orbitals exist—that is all based on the principle quantum number (n), angular momentum quantum number (l), and magnetic quantum number (ml). ms comes into play when filling out electronic configurations, as we have to fill out configurations with respect to the Pauli exclusion principle, which states "in an atom or molecule, no two electrons can have the same four electronic quantum numbers." This means the two electrons in any given orbital must have opposite spins.
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