This article provides an overview of the Pauli Exclusion Principle and its enduring relevance.
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In January 1925, Austrian physicist Wolfgang Pauli, after empirically analyzing the electron emission spectrum, proposed that each electron in an atom has a different combination of quantum numbers than any other electron present in the same atom. This is known as the Pauli exclusion principle. This theory is true for electrons and half-integer spinning fermions and their combinations such as quirks, protons, and neutrons but not valid for integer spinning bosons such as photons produced by a laser or atoms in a Bose-Einstein condensate.
The meaning of half-integer spin is that the intrinsic angular momentum of each fermion is a half-integer (1/2, 3/2/5/2…) multiple of reduced Planck constant (ℏ = ℎ/2π). Moreover, other than fermions, many atoms such as helium-4 or nuclei such as sodium-23 nucleus also obey the exclusion principle owing to the asymmetric half-integer spinning.
The exclusion principle is also the base of the accepted quantum mechanics theory that everything in the universe has a discrete or combination of discrete energies state, which is contrary to the continuity assumption in classical mechanics. There are four quantum numbers viz. principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms) that describes the specific state of an electron in an atom such as energy level, distance from the nucleus, number of sub-shell, the shape of orbitals, and spin orientation.
Ramifications of Pauli Exclusion Principle
Based on the nuclear shell model, an atom of an element in a stable state has a fixed number of protons and an equal number of electrons, also known as the atomic number, and each electron has a specific quantum number set, this is the fundamental basis of arrangement of each element in the modern periodic table.
Furthermore, this principle helps explain certain astrophysical phenomena such as the stability and collapsing of stars. As we know, stars have enormous mass, which produces a massive gravitational pull to gas particles towards their core, but it is counterbalanced by the pressure generated during the fusion process; thus, only a few stars of certain minimum mass survive the formation process.
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Subsequently, when the internal temperature of a star approximately surpasses a hundred million Kelvin, its core fails to sustain the fusion process and they become red giants followed by a catastrophic collapse under massive gravitational pull.
For small and medium-sized stars this collapse is halted to a certain degree by the opposing electron degeneracy pressure and neutron degeneracy pressure. As explained by the Paul exclusion principle, each fermion has a specific quantum state and they repulse each other during compression, resulting in the generation of opposing force.
If the mass of the star is below 1.4 times the solar mass, the electron degeneracy pressure dominates, and a white dwarf is formed, whereas if the mass of the star is between 1.4 – 3 times the solar mass, the neutron degeneracy pressure leads, and a neutron star is formed. However, both degeneracy pressures fail when the mass of the star is too high, resulting in the formation of a black hole.
Although the Pauli exclusion principle gives the idea of the unique state of each electron or fermion in an atom, it can not explain the uncertainty principle in quantum mechanics, which states that it is not possible to assign exact instantaneous value to the position and momentum of an electron in an atom.
References and Further Reading
Pauli Exclusion Principle (anu.edu.au)
Pauli Exclusion Principle: What Is It & Why Is It Important? (sciencing.com)
Pauli Exclusion Principle (gsu.edu)
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