Bohr Model - Revision history

Abagwell3: /* Main Idea */

2023-11-27T04:15:24Z

Main Idea

← Older revision		Revision as of 00:15, 27 November 2023
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	==Main Idea==		==Main Idea==

	[[File: Bohrmodel2.png\|frame\|right\|A visualization of the Bohr model and the hydrogen spectrum]] The Bohr model of the atom was proposed by Niels Bohr in 1913 as an expansion on and correction of the Rutherford model. His model depicted atoms as having negatively charged electrons which orbited as small, positively charged nuclei containing most of the atom's mass, as Rutherford had done. ~~The~~ Bohr Model's incorporation of quantum theory set it apart from other models~~; in~~ this model, electrons can only exist in discrete energy levels, which are quantized. This model is very simplistic and is useful in introducing students to quantum mechanics. It also provides a decent first-order approximation of more complicated theories. Although this model successfully predicts energy levels of the hydrogen atom, it has major shortcomings once expanded to other atoms and more complex real-world situations.		[[File: Bohrmodel2.png\|frame\|right\|A visualization of the Bohr model and the hydrogen spectrum]] The Bohr model of the atom was proposed by Niels Bohr in 1913 as an expansion on and correction of the Rutherford model. His model depicted atoms as having negatively charged electrons which orbited a small, positively charged nuclei containing most of the atom's mass, as Rutherford had done. However, the Bohr Model's incorporation of quantum theory set it apart from other models. In this model, electrons can only exist in discrete energy levels, which are quantized. The electrons orbit the nucleus at energy levels increasing (n= 1,2,3 ..) with their distance from the nucleus. Similar to stepping up a staircase, these energy levels are quantized. This model is very simplistic and is useful in introducing students to quantum mechanics. It also provides a decent first-order approximation of more complicated theories. Although this model successfully predicts energy levels of the hydrogen atom, it has major shortcomings once expanded to other atoms and more complex real-world situations. For example, one of the weaknesses of his analysis was not offering a reason for why only certain energy levels or orbitals were allowed.

	===Bohr's Assumptions===		===Bohr's Assumptions===
	* Electrons travel in a circular orbit around the nucleus, similar to how planets orbit around the sun. (This was Bohr's inspiration for the model, electrons orbiting the nucleus.) Holding these electrons in these orbits are electrostatic forces rather than gravity.		* Electrons travel in a circular orbit around the nucleus, similar to how planets orbit around the sun. (This was Bohr's inspiration for the model, electrons orbiting the nucleus.) Holding these electrons in these orbits are electrostatic forces rather than gravity.
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	* The energy of electrons is inversely related to their distance from the nucleus and which energy level they occupy at that distance. The further away from the electron, the more energy it has. (Electric Potential Energy) <math> U = ((k)q_{1}q_{2})/d</math> (With the k constant representing the electrostatic/Coulomb constant)		* The energy of electrons is inversely related to their distance from the nucleus and which energy level they occupy at that distance. The further away from the electron, the more energy it has. (Electric Potential Energy) <math> U = ((k)q_{1}q_{2})/d</math> (With the k constant representing the electrostatic/Coulomb constant)
	* When electrons gain or lose energy they jump from one orbit to another. The energy is quantized - the orbitals have discreet radii or exact distances from the nucleus where electrons are allowed to exist, which Bohr called "stationary orbits."		* When electrons gain or lose energy they jump from one orbit to another. The energy is quantized - the orbitals have discreet radii or exact distances from the nucleus where electrons are allowed to exist, which Bohr called "stationary orbits."
	* When an excited electron returns back to its ground state, then it releases the energy that is absorbed, in the form of a photon. All photons are produced by an electron transitioning to a lower energy level, or smaller radius. Conversely, an input of energy is required to transition an electron to a higher energy level. This quantized energy - in both cases - is equal to the difference between the respective energies of the orbits.		* When an excited electron returns back to its ground state, then it releases the energy that is absorbed, in the form of a photon. All photons are produced by an electron transitioning to a lower energy level, or smaller radius or becoming closer to the nucleus. Conversely, an input of energy is required to transition an electron to a higher energy level. This quantized energy - in both cases - is equal to the difference between the respective energies of the orbits.
	[[File:Stairsbohr.jpg]]		[[File:Stairsbohr.jpg]]

Abagwell3: /* Introduction */

2023-11-27T04:07:37Z

Introduction

← Older revision		Revision as of 00:07, 27 November 2023
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	This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.		This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.

	The Bohr Model was proposed in 1913 by the physicist Niels Bohr and is a description of the structure of atoms in which there is a dense positive core surrounded by orbiting electrons. In this model, the electrons orbit the nucleus in circular orbits, accounting for the series of discrete wavelengths in the ~~H_2~~ emission spectrum. Bohr's model of the hydrogen atom was the first to incorporate quantum theory, and the key idea of his model was that electrons occupy discrete orbitals.		The Bohr Model was proposed in 1913 by the physicist Niels Bohr and is a description of the structure of atoms in which there is a dense positive core surrounded by orbiting electrons. In this model, the electrons orbit the nucleus in circular orbits, accounting for the series of discrete wavelengths in the H2 emission spectrum. Bohr's model of the hydrogen atom was the first to incorporate quantum theory, and the key idea of his model was that electrons occupy discrete orbitals.

	==Main Idea==		==Main Idea==

Abagwell3: /* Introduction */

2023-11-27T04:06:50Z

Introduction

← Older revision		Revision as of 00:06, 27 November 2023
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	This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.		This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.

			The Bohr Model was proposed in 1913 by the physicist Niels Bohr and is a description of the structure of atoms in which there is a dense positive core surrounded by orbiting electrons. In this model, the electrons orbit the nucleus in circular orbits, accounting for the series of discrete wavelengths in the H_2 emission spectrum. Bohr's model of the hydrogen atom was the first to incorporate quantum theory, and the key idea of his model was that electrons occupy discrete orbitals.

	==Main Idea==		==Main Idea==

Ealicea at 21:20, 20 August 2022

2022-08-20T21:20:11Z

← Older revision		Revision as of 17:20, 20 August 2022
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	==~~Claimed by McKenna Taylor 2022 Spring~~==		==Introduction==

	This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.		This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.

Mtaylor363: /* Shortcomings of the Bohr Model */

2022-04-24T22:57:40Z

Shortcomings of the Bohr Model

← Older revision		Revision as of 18:57, 24 April 2022
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	== Shortcomings of the Bohr Model ==		== Shortcomings of the Bohr Model ==
	While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation] ~~<math> {{math\|1=''iħ''{{sfrac\|''d''\|''dt''}}{{ket\|''ψ''(''t'')}} = ''Ĥ''{{ket\|''ψ''(''t'')}}}} </math>~~		While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation] for the hydrogen atom. Normalized wavefunctions and their series typically include the value of the first Bohr's radius as a reference point.
	for the hydrogen atom. Normalized wavefunctions and their series typically include the value of the first Bohr's radius as a reference point. The current working model of the atom is the quantum mechanical model of the atom, which displays the electron orbit shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.		For example, the R(r) component of the Hydrogen Separated Equation Solution for n=1, 1s is
			<math> \frac{2e<sup>-r/a<sub>0</sub>}{a<sub>0</sub><sup>3/2</sup> </math>
			The current working model of the atom is the quantum mechanical model of the atom, which displays the electron orbit shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.
	[[File:Quantumorbitals.jpeg]]		[[File:Quantumorbitals.jpeg]]

Mtaylor363: /* Shortcomings of the Bohr Model */

2022-04-24T22:44:09Z

Shortcomings of the Bohr Model

← Older revision		Revision as of 18:44, 24 April 2022
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	== Shortcomings of the Bohr Model ==		== Shortcomings of the Bohr Model ==
	While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation]for the hydrogen atom. Normalized wavefunctions and their series typically include the value of the first Bohr's radius as a reference point. The current working model of the atom is the quantum mechanical model of the atom, which displays the electron orbit shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.		While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation] <math> {{math\|1=''iħ''{{sfrac\|''d''\|''dt''}}{{ket\|''ψ''(''t'')}} = ''Ĥ''{{ket\|''ψ''(''t'')}}}} </math>
			for the hydrogen atom. Normalized wavefunctions and their series typically include the value of the first Bohr's radius as a reference point. The current working model of the atom is the quantum mechanical model of the atom, which displays the electron orbit shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.
	[[File:Quantumorbitals.jpeg]]		[[File:Quantumorbitals.jpeg]]

Mtaylor363: /* Shortcomings of the Bohr Model */

2022-04-24T22:40:32Z

Shortcomings of the Bohr Model

← Older revision		Revision as of 18:40, 24 April 2022
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	== Shortcomings of the Bohr Model ==		== Shortcomings of the Bohr Model ==
	While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation]for the hydrogen atom. The current working model of the atom is the quantum mechanical model of the atom, which displays the electron ~~orbits~~ shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.		While the Bohr model is an important predecessor to the current quantum mechanical models of the atom, it doesn't correctly describe some aspects of electron orbitals. It does not provide any reasoning as to why certain spectral lines are brighter than others. Its main shortcoming is that it violates the uncertainty principle, as it considers electrons to have a definite radius and momentum, not considering more advanced quantum theories and properties that have been discovered since the Bohr first theorized the model. This model is very basic, and in order to know more specific details about spectra and charge distribution, more calculations must be done. Many of the failures of the Bohr model can be corrected by the [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2 Schrodinger equation]for the hydrogen atom. Normalized wavefunctions and their series typically include the value of the first Bohr's radius as a reference point. The current working model of the atom is the quantum mechanical model of the atom, which displays the electron orbit shapes very different from the orbits of the solar system and accounts for the fact that the electrons do not exist in one specific location in the orbit, but rather exists at many certain locations in the orbital as probabilities and frequencies. See the picture below for a visual representation of this quantum mechanical atomic model.
	[[File:Quantumorbitals.jpeg]]		[[File:Quantumorbitals.jpeg]]

Mtaylor363: /* A Computational Model */

2022-04-24T20:15:34Z

A Computational Model

← Older revision		Revision as of 16:15, 24 April 2022
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	[[File:2022-04-24.png]]		[[File:2022-04-24.png]]
	[[File:2022-04-24(1).png]]		[[File:2022-04-24(1).png]]

			The images above are stills taken from the PhET simulation. As the electron absorbs energy, it will move to a higher orbit (energy level), and when it drops back to the steady-state, it releases photon(s).

	==Examples==		==Examples==

Mtaylor363: /* References */

2022-04-24T20:12:30Z

References

← Older revision		Revision as of 16:12, 24 April 2022
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	==References==		==References==

	[https://phet.colorado.edu/sims/cheerpj/hydrogen-atom/latest/hydrogen-atom.html?simulation=hydrogen-atom]		[https://phet.colorado.edu/sims/cheerpj/hydrogen-atom/latest/hydrogen-atom.html?simulation=hydrogen-atom] and image included
	Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 (https://phet.colorado.edu).		Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 (https://phet.colorado.edu).

Mtaylor363: /* A Computational Model */

2022-04-24T20:10:22Z

A Computational Model

← Older revision		Revision as of 16:10, 24 April 2022
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	[[File:2022-04-24.png]]		[[File:2022-04-24.png]]
	[[File:2022-04-24 (1).png]]		[[File:2022-04-24(1).png]]

	==Examples==		==Examples==