The Pauli exclusion principle is the principle, formulated by Wolfgang Pauli in 1925, which states that:
No two electrons can occupy the same quantum-mechanical state within a given quantum system simultaneously.
In terms of the quantum numbers:
No two electrons in an atom can have the same values of all four quantum numbers.
It is impossible for two electrons of a multielectron atom to have the same values of the four quantum numbers:
- n – the principal quantum number,
- ℓ – the angular momentum quantum number
- mℓ – the magnetic quantum number,
- ms – the spin quantum number.
Mathematically this means the wavefunctions of the two particles must be antisymmetric which leads to the the probability amplitude of the wavefunction going to zero if the two fermionic particles are the same.
It is the Pauli exclusion principle that requires the electrons in an atom to occupy different energy levels instead of them all condensing in the ground state. The ordering of the electrons in the ground state of multielectron atoms, starts with the lowest energy state (ground state) and moves progressively from there up the energy scale until each of the atom’s electrons has been assigned a unique set of quantum numbers. This fact has key implications for the building up of the periodic table of elements.
It must be noted, chemical properties of atoms are determined by the number of protons, in fact, by number and arrangement of electrons. The configuration of these electrons follows from the principles of quantum mechanics as well as the Pauli exclusion principle. The number of electrons in each element’s electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. As such, without the Pauli exclusion principle, there would be no chemistry.
This principle must be considered for any particles whose spin quantum number s is not zero or an integer. Therefore, this principle applies not only to electrons but also to protons and neutrons, all of which have half-integer spin.