# Pauli's Exclusion Principle

**T**he Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. We are aware that in one orbital a maximum of two electrons can be found and the two electrons must have opposing spins. That means one would spin up ( +1/2) and the other would spin down (-1/2).

We have the first three quantum numbers n=1, l=0, ml=0. Only two electrons can correspond to these, which would be either ms=−1/2 or ms=+1/2. As we already know from our studies of quantum numbers and electron orbitals, we can conclude that these four quantum numbers refer to 1s subshell. If only one of the ms values is given then we would have 1s1 (denoting Hydrogen) if both are given we would have 1s2 (denoting Helium). Visually this would be represented as:No two electrons in an atom can have the same set of four quantum numbers ( n, l, m, s ).

As you can see, the 1s subshell can hold only two electrons and when filled the electrons have opposite spins.

**Incorrect; electrons must spin in opposite directions.**

**Correct; the electrons have opposite spins**

The nature of the Pauli exclusion principle can be illustrated by supposing that electrons 1 and 2 are in states a and b respectively. The wavefunction for the two electron system would be

but this wavefunction is unacceptable because the electrons are identical and indistinguishable. To account for this we must use a linear combination of the two possibilities since the determination of which electron is in which state is not possible to determine.

The wavefunction for the state in which both states "a" and "b" are occupied by the electrons can be written

The Pauli exclusion principle is part of one of our most basic observations of nature: particles of half-integer spin must have antisymmetric wavefunctions, and particles of integer spin must have symmetric wavefunctions. The minus sign in the above relationship forces the wavefunction to vanish identically if both states are "a" or "b", implying that it is impossible for both electrons to occupy the same state.

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