Overview on the Formulation of the Pauli Exclusion Principle

Quantum mechanics is a complicated and confusing part of science, and many discoveries are yet to be made in quantum mechanics. Pauli’s exclusion principle is among one of the important principles in quantum mechanics.

Pauli’s exclusion principle states that two or more similar Electrons/Fermions, Fermions are the particles with half-integer spin, and cannot occupy the same quantum state in a quantum system at the same time. This principle was discovered by Wolfgang Paul in 1925 for electrons and then extended to fermions in 1940. Let us study the Pauli exclusion principle and its applications.

The Pauli Exclusion Principle

As stated above, the Pauli exclusion principle states that two or more identical particles with half integers speed are not able to occupy the same quantum state at the same time. The causes of the Pauli exclusion principle are related to electrons.

As for the electrons found in an atom, the Pauli exclusion principle is applicable, as given below.

It is not possible for two electrons in a poly-electron atom to have the same value of four Quantum numbers n, l, ml, and ms.

The four Quantum numbers are:

• n that is the principal quantum number.

• l that is the azimuthal quantum number.

• ml is the magnetic quantum number.

• ms is the spin quantum number.

The electrons which reside in the same orbital have the same values for the Azimuthal quantum number, principal quantum number, and magnetic quantum number. However, their pin quantum number must be different. That is, they should have opposite half-integer spins. These half-integer spins are in the projections of 1/2 and -1/2. 

If all the quantum numbers, that is, then l, ml, and ms of two electrons, are the same, that means both the electrons occupy the same quantum position and have similar half-integer spin. According to the Pauli exclusion principle, this is impossible.

The Causes of the Pauli Exclusion Principle

Indistinguishability of particles is formulated in quantum mechanics in terms of the total wave function symmetry. Based on their arguments, the wave functions can be symmetric or Antisymmetric.

The particles which are anti-symmetric are known as fermions and cannot occupy the same Quantum state. These are the causes of the Pauli exclusion principle.

In other terms, the causes of the Pauli exclusion principle are that when the electrons are Boston, it is possible for all of the electrons of an atom to be in 1S orbital for an atom. However, this isn’t true. It is found in nature that only two electrons can occupy each distinct orbital as the spin of both electrons should be different. This is the Pauli exclusion principle.

Pauli Exclusion Principle and Bosons

The particles which obey the Pauli exclusion principle are the fermions, and particles that do not obey the Pauli exclusion principle are the Bosons. This answers the question of whether the Bosons obey Pauli’s exclusion principle.

Bosons are the subatomic particles whose spin quantum number has integer values as opposed to the fermions, which have half-integer values as the spin quantum number. Now that we have seen the causes of the Pauli exclusion principle let’s take a look at the applications of the Pauli exclusion principle.

The Pauli Exclusion Principle and its Applications

The applications of the Pauli exclusion principle can be seen in the following things:

• Atoms

The Pauli exclusion principle helps explain the electron cell structure of atoms and how the electrons are shared by atoms. The Pauli exclusion principle also explains a variety of chemical elements and their chemical reactions.

In an atom that is electrically neutral, the number of electrons is equal to the number of protons. Since electrons are, for me, once they cannot occupy the same Quantum state as the other electrons, hence they cannot be bound together and are stacked within the atom. And if they are at the same electron orbital, then they have different spins.

• Solid-State Properties

The semiconductors and conductors contain a very large number of molecular orbitals. They effectively form a continuous band structure of energy levels. In elements that are strong conductors, the electrons are so degenerate that they cannot even contribute much to the thermal capacity of a metal. 

Many electrical, magnetic, and mechanical properties of solids are directly caused by the Pauli exclusion principle. The optical properties of solids can also be attributed to the Pauli exclusion principle.

Conclusion

Many laws in quantum mechanics are used to explain the structure of an atom. The Pauli’s exclusion principle is one such law. The Pauli exclusion principle was formulated by Wolfgang Pauli, and it states that any two or more fermions which are identical cannot occupy the same quantum state at the same time. 

The Pauli exclusion principle states that all the four quantum numbers that are the principal azimuthal, magnetic, and the spin quantum number of any two electrons cannot be the same. The particles that obey this principle are called fermions, and which don’t obey are Bosons.