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The Pauli Exclusion Principle means that no two electrons can share the same four quantum numbers. Since three of the quantum numbers specify an orbital and the last quantum number, specifying spin, can only have two numbers, each orbital can only have two electrons.
It states that no more than two electrons can exist in the same orbital and that if they do they have opposite spins. This is because of the property of electrons(the exact property is too complicated) in the quantum world makes them impossible to have the exact quantum state(same n, l, ml, ms). Therefore, when two electrons exist in the same orbital, their ms must be different(different spin, as we say one spins clockwise the other spins counterclockwise). That being said, adding another electron to the same orbital would make it impossible for them to have different quantum state since an electron either spins clockwise or counterclockwise and the third electron would inevitably have the same quantum state with one of the two electrons that already exist in the orbital.
The Pauli Exclusion Principle essentially means that there cannot be more than 1 quantum number per election because, even if they share the same subshell, they will have different spin. If more than 2 electrons were to exist in an orbital they would have the same quantum numbers.
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