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When we draw out an electron diagram, we indicate the first electrons in orbitals with the up arrow first. Does this imply that all electrons prefer to spin one way (the up arrow spin, counterclockwise) when occupying an orbital by itself?
When we denote two electrons as up spin and down spin, we are just referring to the fact that these two electrons have different spins, but we actually cannot know for sure which electron is spinning in what direction. Think of the spin as a "name" we give to the electrons.
They have no preference themselves to spin up or spin down, we just simply tend to write arrows pointing upwards to save time and for consistency. Although when two electrons occupy a single orbital, one must spin up while the other spins down.
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