The Pauli Exclusion Principle

Atomic orbitals are the regions where an atom’s electrons are most likely to be found. But how many electrons can each orbital hold?

The Pauli exclusion principle answers this question, as it means that no two electrons in an atom can have the same set of four quantum numbers.

Every orbital corresponds to fixed principal; angular momentum, or azimuthal; and magnetic quantum number values. For example, an electron in the 1s orbital always has a principal quantum number of one and azimuthal and magnetic quantum numbers of zero.

Accordingly, electrons must have different spin quantum number values, or spins, to reside in the same atomic orbital. Recall that the spin quantum number has only two possible values: +1/2 and −1/2. Therefore, only two electrons can occupy the same orbital.

Hence, each s subshell, which has one orbital, can accommodate only two electrons, and each p subshell, which has three orbitals, can hold six electrons. Each of the d and f subshells has a maximum capacity of ten and fourteen electrons, respectively.

The distribution of electrons among an atom’s atomic orbitals is represented by its electron configuration in text or diagram form.

Consider a ground-state hydrogen atom, where one electron occupies the lowest-energy orbital: 1s. The written electron configuration denotes each occupied subshell with the number of the corresponding shell, the letter of the subshell, and a superscript number specifying the number of electrons in the subshell.

The orbital diagram style of the electron configuration denotes each orbital within an occupied subshell as a box or line and each electron as an arrow. An upward arrow indicates a +1/2 spin, or spin-up, and a downward arrow signifies a −1/2 spin, or spin-down. The orbital diagram of hydrogen, therefore, has one upward arrow.

The electron configuration of helium is 1s². The two electrons have three identical quantum numbers, as they belong to the same shell and subshell. Their spin quantum numbers are different, in accordance with the Pauli exclusion principle.

Electrons with opposite spins are called “paired” if they occupy the same orbital.

For lithium, which has an atomic number of three, the two electrons in the 1s orbital are paired and the electron in the 2s orbital is unpaired. Conventionally, unpaired electrons are represented as spin-up.