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The quantum number ms is the magnetic spin of the electron. In the Pauli Exclusion principle, it states that there can only be a maximum of two electrons per orbital, and that the two electron spins must be paired. That basically means that one electron will spin in an upwards direction and one in a downwards direction. The magnetic spin quantum represents that, with +1/2 representing the upwards spin and the -1/2 representing the downwards spin. This value can only be +1/2 and -1/2.
I think that all you need to know is that the quantum number ms is only valid if its value is + or - 1/2 and that it refers to the spin of the electron, with the 2 electrons in an orbital having opposite spins (one has +1/2 one has -1/2).
ms is usually pretty arbitrary unless the question specifies that the electron is +1/2 or -1/2. The most important thing to remember is that no two electrons in an atom can have the exact same four quantum numbers, so if one electron is +1/2, the other in the pair is -1/2.
ms can only have the value of +/- 1/2. When drawing the electron configurations with arrows pointing up and down, you can see that each orbital can only have 2 arrows, one pointing up and one pointing down. This represents ms. One electron can have the value of 1/2 while the other electron has the value of -1/2 (down)
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