What Determines the Spin of an Unpaired Electron in an Atom?

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In an atom with an unpaired electron, what determines the spin of the unpaired electron? When writing electron configurations, I know that writing the unpaired electron as having spins of +1/2 and -1/2 are equally correct, so does this mean that spin is random? If not, what factors influence it?
 
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In the absence of a magnetic field (or other spin to couple to), it'll be random, yeah.
 
They are random, especially if there is no external magnetic field.

I am not sure and unfortunately I have temporarily no acces to my GenChem books, but as far as I remember we usually list +1/2 as first, but that's just convention and it has nothing to do with the real world.

Edit: alxm was much faster, I started with answering other threads...

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Thanks for the responses. I usually draw unpaired electrons with a spin of +1/2 out of habit, glad to know that's the convention.