Pauli Exclusion Principle

Wolfgang Pauli stated, in 1926, that no two electrons in the same atom can ever have an identical set of all four quantum numbers. An equivalent, more practical way to state this is that any single orbital can hold at most two electrons, and if it holds two, those two electrons must have opposite spin. This is because, within one orbital, the first three quantum numbers (n, l and mₗ) are automatically the same for both electrons — an orbital is, by definition, one particular (n, l, mₗ) combination — so the only quantum number left free to differ is the spin quantum number mₛ, which can take only two values, $+\frac{1}{2}$ and $-\frac{1}{2}$. Two electrons occupying the same orbital with opposite spins are together called an electron pair. Helium (Z=2), with electronic configuration $1s^2$, is the standard illustration: both its electrons share $n=1, l=0, m_l=0$, but one has $m_s=+\frac{1}{2}$ and the other $m_s=-\frac{1}{2}$ — their four-quantum-number sets, $(1,0,0,+\tfrac{1}{2})$ and $(1,0,0,-\tfrac{1}{2})$, are therefore never identical, exactly as Pauli's principle requires. Because each orb …