Quantum Theory - Revision history

Aparida31 at 19:39, 27 April 2026

2026-04-27T19:39:42Z

← Older revision		Revision as of 15:39, 27 April 2026
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	Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.		Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.

	==~~Study Guide:~~ The Bohr Model & Quantum Mechanics==		==The Bohr Model & Quantum Mechanics==
	Classical mechanics failed to explain why electrons don't spiral into the nucleus due to electromagnetic attraction, and it couldn't explain the discrete emission spectra of gases. The Bohr Model, and subsequently quantum mechanics, solved this by introducing '''quantization'''.		Classical mechanics failed to explain why electrons don't spiral into the nucleus due to electromagnetic attraction, and it couldn't explain the discrete emission spectra of gases. The Bohr Model, and subsequently quantum mechanics, solved this by introducing '''quantization'''.

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	''https://glowscript.org/#/user/anubhavparida24/folder/MyPrograms/program/Bohr/edit''		''https://glowscript.org/#/user/anubhavparida24/folder/MyPrograms/program/Bohr/edit''

			== Limitations of the Bohr Model ==
			While the Bohr model was a revolutionary step in quantization, it is incomplete and has several critical limitations that are frequently tested:

			* '''Single-Electron Limit:''' The Bohr model only accurately predicts the energy levels of "Hydrogen-like" atoms (atoms with only one electron, such as <math>H</math>, <math>He^+</math>, or <math>Li^{2+}</math>). It fails for any system with two or more electrons due to electron-electron repulsion.
			* '''Violation of Uncertainty:''' Bohr's model describes electrons as having both a defined radius and a defined momentum/velocity. According to the '''Heisenberg Uncertainty Principle''' (<math>\Delta x \Delta p \ge \hbar/2</math>), we cannot know both with such precision.
			* '''Wave Nature:''' Bohr treated electrons as particles in orbits. Modern quantum mechanics treats them as stationary waves (wavefunctions).

	=== Core Mathematical Applications ===		=== Core Mathematical Applications ===
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	Bohr's planetary model is a simplification. A complete spatial description of electrons requires the three-dimensional Schrödinger Equation, where the probability of finding an electron is determined by its wave function <math>\Psi</math>.		Bohr's planetary model is a simplification. A complete spatial description of electrons requires the three-dimensional Schrödinger Equation, where the probability of finding an electron is determined by its wave function <math>\Psi</math>.

	[[~~Image~~:Hydrogen_Density_Plots.png\|thumb\|~~right~~\|~~400px~~\|Probability densities for various electron orbitals in the Hydrogen atom. (Source: Wikimedia Commons)]]		[[File:Hydrogen_Density_Plots.png\|thumb\|center\|500px\|Probability densities for various electron orbitals in the Hydrogen atom. (Source: Wikimedia Commons)]]

	The probability <math>P(r)</math> of an electron existing at a given radius <math>r</math> is:		The probability <math>P(r)</math> of an electron existing at a given radius <math>r</math> is:
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	The first several solutions to the wavefunction of the hydrogen atom are given below.		The first several solutions to the wavefunction of the hydrogen atom are given below.

	[[File:~~hydAtom~~.~~png~~]]		[[File:Hydrogen_transitions.svg\|thumb\|center\|450px\|Electron transitions in the Hydrogen atom corresponding to the Lyman, Balmer, and Paschen series. (Source: Wikimedia Commons)]]

	The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:		The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:

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	==Examples==		==Examples==
	===Excitation of Hydrogen's Electron===		===Excitation of Hydrogen's Electron===
	[[File:~~Adsporption and~~ emission of ~~photon and~~ energy ~~levels~~.~~jpg~~]]		[[File:Emission_spectrum-H.svg\|thumb\|center\|500px\|The visible emission spectrum of hydrogen (Balmer series). The distinct lines correspond to specific quantized energy drops. (Source: Wikimedia Commons)]]

	Adsorption and Emission of Energy by Electrons.		Adsorption and Emission of Energy by Electrons.

	If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.		If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.

	~~[[File:photonEmission.gif]]~~

	~~Computational model of photon emission from a hydrogen atom.~~

	~~[[File:Energy levels.jpg]]~~

	~~Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.~~

	Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.		Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.

	[[File:~~BLSC~~.~~png~~]]		[[File:Hydrogen_absorption_spectrum.svg\|thumb\|center\|600px\|The absorption spectrum of Hydrogen. The dark lines correspond to specific wavelengths absorbed by electrons transitioning to higher energy states. (Source: Wikimedia Commons)]]

	Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.		Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.
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	Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.		Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.

	[[File:~~HydAtomProbs~~.~~png~~]]		[[File:Hydrogen_Radial_Probability_Density.svg\|thumb\|center\|500px\|Radial probability density functions for the first three energy levels. Note how the number of 'nodes' (zero probability points) increases with n. (Source: Wikimedia Commons)]]

	Probability densities for the first couple levels of the hydrogen atom.		Probability densities for the first couple levels of the hydrogen atom.
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	==Connectedness==		==Connectedness==
	Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.		Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.
	<gallery>
	File:Energy ~~analysis~~.~~png~~		<gallery widths="200px" heights="200px" perrow="4">
	File:Product ~~determination~~.~~png~~		File:Hydrogen_Emission_Spectrum.svg\|Energy Analysis: The distinct emission lines of Hydrogen, proving electrons only exist in discrete energy states.
	File:Further ~~study~~.~~gif~~		File:Flame_test_copper.jpg\|Product Determination: Using flame tests to identify chemical composition based on the unique photon emission of metal ions.
	File:~~Reactor~~.~~gif~~		File:Atomic_absorption_spectrometer_schematic.png\|Further Study: Modern spectroscopy setups used to determine concentrations of elements in unknown samples.
			File:Tokamak_schematic.svg\|Large Scale Application: Research into nuclear fusion and high-energy plasma physics depends on Bohr-level energy transitions.
	</gallery>		</gallery>


	=== Intro to Spin (Electrons) ===		=== Intro to Spin (Electrons) ===

Aparida31: Added condensed study materials (prior to history deepdive) & mathematical formulations

2026-04-27T18:47:34Z

Added condensed study materials (prior to history deepdive) & mathematical formulations

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 ==The Main Idea==
 Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.
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+=== Intro to Spin (Electrons) ===

Aparida31 at 18:34, 27 April 2026

2026-04-27T18:34:27Z

← Older revision		Revision as of 14:34, 27 April 2026
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	===Claimed by ~~Nathan Donagi Fall 24~~===		===Claimed by Anubhav Parida Spring 26===

NathanDonagi at 04:35, 8 December 2024

2024-12-08T04:35:53Z

← Older revision		Revision as of 00:35, 8 December 2024
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	===Claimed by Nathan Donagi Fall 24===		===Claimed by Nathan Donagi Fall 24===

	~~<html><iframe src="~~ https://www.glowscript.org/#/user/Nathan_Donagi/folder/MyPrograms/program/HydrogenAtom~~" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe></html>~~
			[[File:Hydrogen-3-0-1.png]]

			https://www.glowscript.org/#/user/Nathan_Donagi/folder/MyPrograms/program/HydrogenAtom


	Visualization of the Bohr Model of the atom.		Visualization of the Bohr Model of the atom.

NathanDonagi: Trying to get iframe embed to work

2024-12-07T09:12:56Z

Trying to get iframe embed to work

← Older revision		Revision as of 05:12, 7 December 2024
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	===Claimed by Nathan Donagi Fall 24===		===Claimed by Nathan Donagi Fall 24===

	<iframe src=" https://www.glowscript.org/#/user/Nathan_Donagi/folder/MyPrograms/program/HydrogenAtom" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>		<html><iframe src=" https://www.glowscript.org/#/user/Nathan_Donagi/folder/MyPrograms/program/HydrogenAtom" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe></html>

	Visualization of the Bohr Model of the atom.		Visualization of the Bohr Model of the atom.

NathanDonagi at 09:11, 7 December 2024

2024-12-07T09:11:12Z

Show changes

NathanDonagi: Added a glow script visualization of a hydrogen atom (hopefully it works)

2024-12-07T09:08:36Z

Added a glow script visualization of a hydrogen atom (hopefully it works)

Show changes

NathanDonagi at 02:38, 5 December 2024

2024-12-05T02:38:21Z

← Older revision		Revision as of 22:38, 4 December 2024
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	===Claimed by ~~Kaimai Shi Summer 22~~===		===Claimed by Nathan Donagi Fall 24===

	[[File:BohrModel2.jpg]]		[[File:BohrModel2.jpg]]

Kaimai at 00:29, 25 July 2022

2022-07-25T00:29:07Z

← Older revision		Revision as of 20:29, 24 July 2022
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	[[File:Electron_Spin_(I_made_this!).jpg]]		[[File:Electron_Spin_(I_made_this!).jpg]]

	One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.		One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.

			Spin quantum numbers describe the angular momentum of electrons. The electron rotates around the axis and has both angular momentum and orbital angular momentum. And because one orbit can only hold two electrons, one electron is positive 1/2 and the other is -1/2

Kaimai at 20:50, 24 July 2022

2022-07-24T20:50:04Z

← Older revision		Revision as of 16:50, 24 July 2022
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	==Intro to Spin(Electrons)==		==Intro to Spin(Electrons)==
	what is spin of electrons in Quantum Mechanics		what is spin of electrons in Quantum Mechanics
	[[Electron_Spin_(I_made_this!).jpg]]		[[File:Electron_Spin_(I_made_this!).jpg]]

	One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.		One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.