Pauli exclusion principle - Revision history

Shanumasagar6 at 17:46, 25 April 2022

2022-04-25T17:46:52Z

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	===Simple===		===Simple===

	Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is suffice to say that due to electrons not being able to possess the same quantum state, each atomic orbital (e.g., 1s, 1p, etc.) may only possess a maximum of two electrons, one being spin-up and the other spin-down. The fill in accordance to the diagram below.		Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is suffice to say that due to electrons not being able to possess the same quantum state, each atomic orbital block (e.g., 1s, 1p, 1/3 of 2p etc.) may only possess a maximum of two electrons, one being spin-up and the other spin-down. The fill in accordance to the diagram below.

	[[File:Orbital_Filling_Diagram.PNG]]		[[File:Orbital_Filling_Diagram.PNG]]

			It is important to note that the s orbital possesses two possible electron slots, and p possesses 6. D possesses 10 and f 14. As such, for a simple example, if one wanted to compute the electron configuration for neutral Phosphorus, one would only need to follow the diagonals on the orbital filling diagram until the number of electrons in Phosphorus is reached (15). From this, one may see that the orbital level follows as below:

			[[File:]]

	==History==		==History==

Shanumasagar6 at 17:43, 25 April 2022

2022-04-25T17:43:53Z

← Older revision		Revision as of 13:43, 25 April 2022
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	Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is suffice to say that due to electrons not being able to possess the same quantum state, each atomic orbital (e.g., 1s, 1p, etc.) may only possess a maximum of two electrons, one being spin-up and the other spin-down. The fill in accordance to the diagram below.		Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is suffice to say that due to electrons not being able to possess the same quantum state, each atomic orbital (e.g., 1s, 1p, etc.) may only possess a maximum of two electrons, one being spin-up and the other spin-down. The fill in accordance to the diagram below.

	[[File:Orbital_Filling_Diagram.PNG]]		[[File:Orbital_Filling_Diagram.PNG]]

Shanumasagar6 at 17:43, 25 April 2022

2022-04-25T17:43:26Z

← Older revision		Revision as of 13:43, 25 April 2022
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	===Simple===		===Simple===

	Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is		Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is suffice to say that due to electrons not being able to possess the same quantum state, each atomic orbital (e.g., 1s, 1p, etc.) may only possess a maximum of two electrons, one being spin-up and the other spin-down. The fill in accordance to the diagram below.
			[[File:Orbital_Filling_Diagram.PNG]]

	==History==		==History==

Shanumasagar6 at 17:38, 25 April 2022

2022-04-25T17:38:12Z

← Older revision		Revision as of 13:38, 25 April 2022
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	==Examples==		==Examples==

	==Simple==		===Simple===

			Considering the Pauli Exclusion Principle's correspondence to the orbital filling order for electrons, it is

	==History==		==History==

Shanumasagar6 at 17:36, 25 April 2022

2022-04-25T17:36:27Z

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	http://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html		http://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html

	==S==		==Examples==

			==Simple==

	==History==		==History==

Shanumasagar6 at 17:35, 25 April 2022

2022-04-25T17:35:44Z

← Older revision		Revision as of 13:35, 25 April 2022
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	http://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html		http://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html

			==S==

	==History==		==History==

Shanumasagar6 at 17:30, 25 April 2022

2022-04-25T17:30:40Z

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	In addition, should the Pauli Exclusion Principle hold true and enforce higher energy states, one would expect an increase in luminosity for the stars as radius decreases. The figure above depicts just that for the case of a 2 Solar Mass star.		In addition, should the Pauli Exclusion Principle hold true and enforce higher energy states, one would expect an increase in luminosity for the stars as radius decreases. The figure above depicts just that for the case of a 2 Solar Mass star.

			Regarding the Pauli Exclusion Principle overall, the PhET simulation "Build An Atom" provides a resource towards understanding the order of orbital-filling and thus a fundamental aspect of the Pauli Exclusion Principle.

			http://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html

	==History==		==History==
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	Computational Models created by Shamita Hanumasagar		Computational Models created by Shamita Hanumasagar

			PhET Colorado, Creative Commons Attribution 4.0.

Shanumasagar6 at 00:03, 25 April 2022

2022-04-25T00:03:50Z

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	The typical method for expressing the Pauli Exclusion Principle is through the use of quantum states, primarily by probability amplitude. Expressing		The typical method for expressing the Pauli Exclusion Principle is through the use of quantum states, primarily by probability amplitude. Expressing
	<math> \psi=\psi_{1}(a)\psi_{2}(b) </math>, where <math> \psi </math> designates the overall state. ~~To begin with~~ the ~~proof of the Pauli Exclusion Principle, it first must be understood~~ that there are four quantum numbers, and we will consider electrons.		<math> \psi=\psi_{1}(a)\psi_{2}(b) </math>, where <math> \psi </math> designates the overall state. The principle works on the fact that there are four quantum numbers, and we will consider electrons.

	<math> n </math> designates the "principle quantum number" and denotes the innermost electron orbital level. As such, it designates the lowest energy level and may occupy values from 1, 2, 3,... but never 0, as this would correspond to no energy and thus no particle.		<math> n </math> designates the "principle quantum number" and denotes the innermost electron orbital level. As such, it designates the lowest energy level and may occupy values from 1, 2, 3,... but never 0, as this would correspond to no energy and thus no particle.

Shanumasagar6: /* Importance */

2022-04-25T00:02:39Z

Importance

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	Pauli's discovery and implementation of a fourth quantum number laid the groundwork and inspiration for quantum mechanics in the next years following its announcement. Much of Heisenberg's and Schrodinger's discoveries on wave mechanics were built off of the Pauli exclusion principle.		Pauli's discovery and implementation of a fourth quantum number laid the groundwork and inspiration for quantum mechanics in the next years following its announcement. Much of Heisenberg's and Schrodinger's discoveries on wave mechanics were built off of the Pauli exclusion principle.

	==Importance==		==Importance/Connectedness==
	The significance of the Pauli exclusion Principle is that it introduced a fourth quantum number. While spin is not a physical characteristic, it is crucial when determining shapes and wavelike behaviors of atomic particles. The principle dictates that bosons have probability waves which "flip" as they move and interfere with each other. The interference of these probability waves leads to collective behavior that can result in lasers, super fluids and superconductors. Conversely, fermions do not flip their probability waves and do not interact with each other. Fermions include electrons, protons and neutrons.		The significance of the Pauli exclusion Principle is that it introduced a fourth quantum number. While spin is not a physical characteristic, it is crucial when determining shapes and wavelike behaviors of atomic particles. The principle dictates that bosons have probability waves which "flip" as they move and interfere with each other. The interference of these probability waves leads to collective behavior that can result in lasers, super fluids and superconductors. Conversely, fermions do not flip their probability waves and do not interact with each other. Fermions include electrons, protons and neutrons.

			The Pauli Exclusion Principle, as denoted earlier, is additionally integral towards understanding stellar death and the process of evolution, for without the Pauli Exclusion Principle stars would have no form of support and would succumb to the crush of gravity. The Pauli Exclusion Principle works in tandem with other known laws of the universe, such as Heisenberg's Uncertainty Principle, to provide a counter force under weight. In short, it is vital to fundamental processes of the universe and provides information about astrophysics and solid state work.

	==See Also==		==See Also==

Shanumasagar6: /* A Computational Model: Stellar Degeneracy */

2022-04-24T23:51:30Z

A Computational Model: Stellar Degeneracy

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	[[File:Stellar N. Radius vs. Pressure.PNG\|Plot of Normalised Radius vs. Pressure for a 2 Solar Mass star]]		[[File:Stellar N. Radius vs. Pressure.PNG\|Plot of Normalised Radius vs. Pressure for a 2 Solar Mass star]]

	As depicted in the figure above, as radius decreases (i.e., the star contracts), the measurable outward pressure skyrockets, indicating the presence of the Pauli Exclusion Principle in the form of degeneracy pressure. This feature is present in neutron stars as well, contributing to "neutron degeneracy pressure".		As depicted in the figure above, as radius decreases (i.e., the star contracts), the measurable outward pressure skyrockets, indicating the presence of the Pauli Exclusion Principle in the form of degeneracy pressure. Additionally, if considering solely a single, non-contracting star, distance to the core denotes in the form of radius and demonstrates that the Pauli Exclusion Principle affirms Newton's Third Law of Equal and Opposite Reaction. As gravitational forces increase towards the centre of the body, the degenerate pressure caused by resisting electrons asserts itself more and causes an exponential growth in pressure. This feature is present in neutron stars as well, contributing to "neutron degeneracy pressure".

	[[File:Normalised_Radius_vs._Luminosity_Per_Cent.PNG]]		[[File:Normalised_Radius_vs._Luminosity_Per_Cent.PNG]]