Pauli Exclusion Principle

2.6.4b Pauli Exclusion Principle

The Austrian physicist Wolfgang Pauli (1926) gave a fundamental restriction on how many electrons can occupy an orbital. The principle has two equivalent statements:

No two electrons in an atom can have the same set of all four quantum numbers.

Only two electrons may exist in the same orbital, and these electrons must have opposite spins.

This means that two electrons in the same orbital share the same values of $n$, $l$, and $m_l$ (the three quantum numbers that define the orbital), but they must have opposite spin quantum numbers ($m_s = +\frac{1}{2}$ and $m_s = -\frac{1}{2}$).

Calculating Subshell Capacities

The Pauli principle directly gives the maximum number of electrons in any subshell. Since each orbital can hold at most two electrons (one with each spin), the capacity of a subshell is simply twice the number of orbitals in that subshell.