A Brief Note on Importance and Application of Pauli’s Exclusion Principle

Pauli’s exclusion principle was depicted by Austrian physicist Wolfgang Pauli in 1925. This principle was limited to the behaviour of electrons only. Later on, he prolonged the principle to include Fermions in 1940. He was awarded the Nobel Prize in 1945. Pauli’s Exclusion principle by depicting that each and every electron must be in its extraordinary way. No electrons should have an identical set of quantum numbers in an atom. We can say that Pauli’s exclusion principle demonstrates the heart of chemistry. It explains the arrangements of electrons in atoms and molecules. In defining electrons in an atom, there are very important quantum numbers. 

• n- the principal quantum number 

• l- azimuthal quantum number

• m- magnetic quantum number 

• s- spin quantum number

Importance of Quantum Numbers in Pauli’s Exclusion Principle 

According to Pauli’s exclusion principle, no two electrons in an atom or molecule consist of identical four electronic quantum numbers. A single orbital can hold two electrons only with opposite spin. A shell contains a number of subshells with the same in principle quantum number. And the nutshell comprises an orbital with the same azimuthal quantum number l. The s subshell has l=0, a p subshell l=1, a d subshell with l=2, and an f subshell with l=3. The magnetic quantum number varies from -m to +m depending on the increments of one. The s spin quantum number ranges from -s to +s depending on the increment of 1.  If one electron has an allocated spin up (+½) electron, then the other electron has (-½) spin-down allocation. The first three quantum numbers are the same for the electron in the same orbital. For the 1s subshell, n=1, l=0,m=0. Electron spin moment must either have +½ or -½. If there is only one electron in 1s, then there is only one value m, and the electronic configuration is written as 1s1. If the 1s contains both the electrons, we have two m values leading to the electronic configuration being 1s2.The set of quantum numbers provides a base for orbital, shell, and subshell. 

The Physical Significance of Pauli’s Exclusion Principle

This principle illustrates a wide variety of physical phenomena like the electron’s shell structure of atoms and how atoms share electrons. Which helps in describing the chemical elements and participation in the formation of chemical bonds. A neutral atom contains the same number of electrons as well as protons. Electrons are fermions. That’s why they can’t invade the same quantum state. If there is only one electron, it could spin up or spin down. But if both the electrons are present in the orbital, both would have each of them. As an example, there is a neutral Helium atom. Helium has both the electrons bound with occupying the lower energy level (1s) with opposite spin. The two electrons bear two different quantum states and hence do not violate Pauli’s Exclusion principle. Electrons don’t fall closer to the nucleus if the lower energy level is filled. As an example, we can consider white dwarfs and neutron stars. The particles that are making up these small stars are under tremendous gravitational force. If there were a little more mass, these stellar remnants would be attracted to the black hole.  

Application of Pauli’s Exclusion Principle

• Pauli’s exclusion principle is used to denote the electronic configuration of the elements 

• It is also used in demonstrating the formation of the chemical bond.

• In establishing the modern periodic table, this principle is also utilised. 

• In quantum mechanics, Pauli’s exclusion principle is its fundamental principle.

• This principle itself is used in astrophysics.

Conclusion

According to Pauli’s exclusion principle, in an atom, no two electrons can have an identical set of four quantum numbers. Bosons do not follow Pauli’s exclusion principle. Any of the numbers of the same bosons can invade the same quantum state. Fermions are particles with half-integer spin. Fermions are antisymmetric states according to the theory of quantum mechanics.