What does the Pauli Exclusion Principle say?

The one known as the Pauli Exclusion Principle is a quantum mechanical principle that holds that two or more identical fermion-like particles, i.e. particles with half-integer spin, cannot be in or occupy the same quantum state simultaneously within the same system.

In other words, two fermions cannot have all their quantum numbers the same. And, more technically, two identical fermions within the same quantum system have an antisymmetric wave function.

Bosons, unlike fermions, have integer spin and are not subject to the Pauli Exclusion Principle. For example, photons are a type of boson, so any number of photons can occupy the same quantum state simultaneously, and their behavior corresponds to a symmetric wave function.

Have the rotation of half an integer (1/2, 3/2, etc) means that the intrinsic angular momentum is equal to the so-called reduced Planck constant or Dirac constant:

Consequently, fermions (quarks and leptons), according to quantum mechanics, present themselves in asymmetric states whose distribution is explained through Fermi-Dirac statistics. In turn, the bosons (photons, Cooper pairs, W and Z bosons, etc.) have an integer spin and are distributed according to Bose-Einstein statistics.

In addition to elementary particles, atoms and composite particles can also obey the Pauli Exclusion Principle based on their global spin.

For example, Helium-3 has a spin of 1/2 and would be a fermion that obeys the Exclusion Principle, while Helium-4 has a spin of zero and would be a boson, which appears at temperatures close to absolute zero when helium-4 starts to behave like a superfluid.

Pauli Exclusion Principle for Electrons

The Pauli Exclusion Principle owes its name to its author, wolfgang paulique enunciated this principle in 1925. Initially, Pauli applied it to electrons, and later it was applied to the rest of the fermions: to quarks, which form protons and neutrons, and to leptons, the group to which electrons and neutrinos belong.

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Each electron within an atom is completely defined by four quantum numbers:

n: Main quantum number. It represents the energy level of the electron and is related to the average distance between the nucleus and the electron. he: azimuthal quantum number, angular momentum quantum number or secondary quantum number. Indicates energy sublevels and is related to the shape of the electronic orbital. mmele: magnetic quantum number. Indicates the spatial orientation of the electronic orbital or energy sublevel. VĂ“Ss: spin quantum number. It indicates the intrinsic angular momentum and is related to the spin of the electron on itself. The electron can spin in the same direction as it spins in the orbital or in the opposite direction, and it can take on only two possible values, 1/2 and -1/2.

If two electrons have the same n, they will occupy the same orbital, the same energy sublevel and in the same spatial orientation, but for that they must have a different spin. One of the four quantum numbers has to be different for them to occupy exactly the same orbital, one will have spin 1/2 and the other -1/2.

Let’s take the electron configuration of Argon as an example:

1stwo 2 secondstwo 2p6 3 secondstwo 3p6

This means that argon’s 18 electrons are distributed in three energy levels, and within each level, in various sublevels or types of orbitals:

Level 1: can contain two electrons with the same numbers n, l and m, but with opposite spins to obey the Pauli exclusion principle. Level 2: At energy level 2 there are two sublevels, the 2s sublevel and the 2p sublevel, and within the p sublevel there are three possible orbitals perpendicular to each other according to their magnetic angular momentum (pxpS E Pz). Thus, the 2s level can contain another 2 electrons and the 2p level can contain a total of six electrons. Level 3: Similar to Level 2, but with a higher principal quantum number.
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Graphically it can be represented as follows (each up or down arrow represents an electron with positive or negative spin):

One of the consequences of the Pauli Exclusion Principle is the elaborate electron shell of atoms and would explain how atoms combine, the stability of matter on a large scale, and many other phenomena to which ordinary matter responds.

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