Pauli Exclusion Principle: Explanation, Formulation, Examples, and Applications

Pauli exclusion principle is a fundamental principle along with Aufbau’s Principle and Hund’s Rule in chemistry. 

• Wolfgang Pauli, an Austrian scientist, illustrated Pauli's exclusion principle in 1925.
• This principle was restricted to the behavior of electrons. 
• It states that no two electrons in the same atom can possess identical values for all four of their quantum numbers.
• In 1940, he modified the concept to include fermions.
• In 1945, he was awarded the Nobel Prize.
• It essentially benefits individuals to recognize the electron arrangements in atoms and molecules.
• It provides an explanation for the classification of elements in the periodic table as well.

Key Terms: Pauli Exclusion Principle, Atom, Electrons, Electron Spin, Quantum number, Structure of atom, Azimuthal quantum number, Fermions, Bosons, Helium, Hydrogen

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What is Pauli Exclusion Principle?

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The Pauli exclusion principle states that in a single atom, no two electrons will have a matching set or equal quantum numbers (n, l, m_l, and m_s). To explain it more simply, each electron must have or be in its own unique state.

There are two relevant procedures that the Pauli Exclusion Principle follows:

• Only two electrons can conquer a similar orbital.
• The two electrons that occur in a similar orbital should have opposite spins or must be antiparallel.

However, the Pauli Exclusion Principle does not only relate to electrons. It relates to other particles of half-integer spin-like fermions. It is not related to particles with an integer spin such as bosons which have symmetric wave purposes.

• Furthermore, bosons can share or consume the same quantum states, distinct from fermions.
• The nomenclature goes, fermions are named after the Fermi–Dirac statistical dissemination that they follow.
• Whereas Bosons get their name from the Bose-Einstein distribution purpose.

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Formulation of the Pauli Exclusion Principle

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The principle was developed in 1925 by Wolfgang Pauli, an Austrian scientist.

• He essentially explained how electrons behaved using this principle.
• He extended the principle later in 1940, using his spin-statistics theorem to include all fermions.
• Furthermore, the principle describes fermions, which are made up of fundamental particles like quarks, electrons, neutrinos, and baryons.
• Wolfgang Pauli was awarded the Nobel Prize in 1945 in recognition of his contributions to the field of quantum mechanics as well as his discovery of the Pauli exclusion principle.
• Albert Einstein put him forth for the honor.

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Pauli Exclusion Principle in Chemistry

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In chemistry, the law is essentially used to elucidate or define the electron shell structure of atoms and forecast which atoms are probable to donate electrons.

• Mostly it is asked how the principle works or where it can be applied.
• If we look at the atoms every time it advances a new electron or electrons it ordinarily changes to the lowest energy state or it moves to the outermost shell.
• If the state has one electron, then it can also spin up or spin down.
• Later if we ruminate the Pauli exclusion principle, if there are two electrons in a state, then all of the electrons will spin up or spin down-state but not similarly.

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Pauli Exclusion Principle Examples

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We can take a neutral helium atom as a mutual Pauli Exclusion Principle example. The atom has two bound electrons and they conquer the furthest shell with conflicting spins. Now, they discover that the two electrons are in the 1s subshell where n = 1, l = 0, and m_l = 0.

• Their spin flashes will also be diverse. One is m_s = -1/2 and the rest will be +1/2.
• If we draw a diagram, then the subshell of the helium atom will be characterized with 1 upper electron and 1 lower electron.
• In principle, 1s subshell will contain two electrons, which have conflicting spins.
• Likewise, if we take Hydrogen it will have 1s subshell with 1 upper electron (1s₁).
• Lithium will have the helium core (1s₂) and then one more upper electron (2s₁).

Above mentioned example further, presumes that succeeding larger elements will have shells of successively higher energy.

• The number of electrons in the furthest shell is directly connected to the dissimilar chemical belongings that elements possess.
• Elements with a similar number of electrons in the outermost shell will have some possessions.

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Important Applications of Pauli Exclusion Principle

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Several physical phenomena, including the electron shell structure of atoms and the way atoms share electrons, can be explained using the Pauli exclusion principle.

• It helps in understanding the nature of the different chemical elements and their roles in the formation of chemical bonds.
• This principle can also be used to define the periodic table.
• Pauli exclusion directly affects a number of solids' mechanical, chemical, optical, magnetic, and electrical properties.
• This principle helps in explaining the stability of large systems that contain a significant number of nucleons and electrons.
• The principle is essential to quantum mechanics, which is mostly studied in Physics, and not just in Chemistry.
• Astrophysics also makes use of it.

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Things to Remember

• Pauli Exclusion Principle is considered to be one of the significant principles along with Aufbau’s Principle and Hund’s Rule in chemistry.
• Pauli's Exclusion principle generally helps in order to make out the electron arrangements in atoms and molecules.
• Moreover, it also provides an explanation for the classification of elements in the periodic table. 
• Pauli Exclusion Principle not only applies to electrons, but it also applies to other particles of half-integer spin such as fermions as well.
• Additionally, it is not relevant for the particles with integer spin-like bosons that possess symmetric wave functions.
• Neutron degeneracy leads to the death of stars to the neutron star stage.
• No two electrons in an atom can possess an identical quantum number as this will lead us to model the grouping in the periodic table.

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