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Two electrons in the ground state (e.g. He) will have opposite spins. This is the Pauli Exclusion principle. Two Fermions can't occupy the same state.

 

To add to that: if one wrote down the set of quantum numbers for all the electrons of an atom in the ground state, each electron would have a unique set of quantum numbers describing its energy and location with respect to the others. The two electrons in the Helium atom would only differ by spin (assuming ground state).

Edited by mississippichem

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