Pauli Exclusion Principle Definition

The Pauli exclusion principle states no two electrons (or other fermions) can have the identical quantum mechanical state in the same atom or molecule. In other words, no pair of electrons in an atom can have the same electronic quantum numbers n, l, m_l, and m_s. Another way to state the Pauli exclusion principle is to say the total wave function for two identical fermions is antisymmetric if the particles are exchanged.

The principle was proposed by Austrian physicist Wolfgang Pauli in 1925 to describe the behavior of electrons. In 1940, he extended the principle to all fermions in the spin-statistics theorem. Bosons, which are particles with an integer spin, do not follow the exclusion principle. So, identical bosons may occupy the same quantum state (e.g., photons in lasers). The Pauli exclusion principle only applies to particles with a half-integer spin.

The Pauli Exclusion Principle and Chemistry

In chemistry, the Pauli exclusion principle is used to determine the electron shell structure of atoms. It helps to predict which atoms will share electrons and participate in chemical bonds.

Electrons which are in the same orbital have identical first three quantum number. For example, the 2 electrons in the shell of a helium atom are in the 1s subshell with n = 1, l = 0, and m_l = 0. Their spin moments cannot be identical, so one is m_s = -1/2 and the other is m_s = +1/2. Visually, we draw this as a subshell with 1 "up" electron and 1 "down" electron.

As a consequence, the 1s subshell can only have two electrons, which have opposite spins. Hydrogen is depicted as having a 1s subshell with 1 "up" electron (1s¹). A helium atom has 1 "up" and 1 "down" electron (1s²). Moving on to lithium, you have the helium core (1s²) and then one more "up" electron that is 2s¹. In this way, the electron configuration of the orbitals is written.