Potential Energy of a Pair of Neutral Atoms - Revision history

Parkercoye: /* Potential Energy of a Pair of Neutral Atoms */

2019-07-29T15:37:33Z

Potential Energy of a Pair of Neutral Atoms

← Older revision		Revision as of 11:37, 29 July 2019
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	We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>		We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>

	[[File:blue_parabola.png\|400px\|thumb\|When graphed, this equation gives us this graph\|center]] <br>		[[File:blue_parabola.png\|400px\|thumb\|When graphed, this equation gives us this graph <br> Note: Figure created by author\|center]] <br>

	However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.		However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.
	: '''Morse approximation'''		: '''Morse approximation'''
	:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>		:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>
	[[File:red_line_chart.png\|400px\|thumb\|The equation above equation yields this graph\|center]]		[[File:red_line_chart.png\|400px\|thumb\|The equation above equation yields this graph <br> Note: Figure created by author\|center]]

	We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:green_dots.png\|400px\|center]]		We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:green_dots.png\|400px\|center\|thumb\|Note: Figure created by author]]

	===A Computational Model===		===A Computational Model===

Parkercoye: /* A Computational Model */

2019-07-29T15:35:33Z

A Computational Model

← Older revision		Revision as of 11:35, 29 July 2019
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	[[File:Screen_Capture_6.gif]]		[[File:Screen_Capture_6.gif]]

	This simulation generated with VPython shows the spring like behavior of one neutral atom reacting to another. ~~In reality~~, ~~both~~ atoms would ~~be reacting to each other and would stop moving when~~ an equilibrium ~~distance was reached~~.		This simulation generated with VPython shows the spring like behavior of one neutral atom reacting to another. This model is very similar to the ball and spring model coded earlier in the course and as in that case, these two atoms would eventually reach an equilibrium with one another (this is only a short clip of the oscillatory behavior).

	=Simple Example=		=Simple Example=

Parkercoye: /* A Computational Model */

2019-07-29T15:03:52Z

A Computational Model

← Older revision		Revision as of 11:03, 29 July 2019
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	[[File:Screen_Capture_6.gif]]		[[File:Screen_Capture_6.gif]]

	This ~~simulations~~ shows the spring like behavior of one neutral atom reacting to another. ~~However~~, ~~in reality~~ both atoms would be reacting to each other and would stop moving when an equilibrium distance was reached.		This simulation generated with VPython shows the spring like behavior of one neutral atom reacting to another. In reality, both atoms would be reacting to each other and would stop moving when an equilibrium distance was reached.

	=Simple Example=		=Simple Example=

Parkercoye: /* A Mathematical Model */

2019-07-29T15:02:58Z

A Mathematical Model

← Older revision		Revision as of 11:02, 29 July 2019
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	We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>		We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>

	~~When graphed, this equation gives us~~ [[File:blue_parabola.png\|400px]]		[[File:blue_parabola.png\|400px\|thumb\|When graphed, this equation gives us this graph\|center]] <br>

	However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.		However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.
	: '''Morse approximation'''		: '''Morse approximation'''
	:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>		:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>
	~~The new graph looks like this~~ [[File:red_line_chart.png\|400px]]		[[File:red_line_chart.png\|400px\|thumb\|The equation above equation yields this graph\|center]]

	We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:green_dots.png\|400px]]		We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:green_dots.png\|400px\|center]]

	===A Computational Model===		===A Computational Model===

Parkercoye: /* A Mathematical Model */

2019-07-29T15:00:39Z

A Mathematical Model

← Older revision		Revision as of 11:00, 29 July 2019
Line 9:		Line 9:
	We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>		We know that interactions between atoms are similar to the behavior of a spring. And we can approximate the formula for interatomic potential energy as<math>U = (1/2)ks^2 - E_M</math>

	When graphed, this equation gives us [[File:~~Potential-energy-variation~~.~~gif~~]]		When graphed, this equation gives us [[File:blue_parabola.png\|400px]]

	However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.		However the potential energy approaches zero as the two atoms get further apart. The Morse approximation accounts for this.
	: '''Morse approximation'''		: '''Morse approximation'''
	:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>		:<math>U_M = E_M*[1-e^{-α(r-r_{eq})}]^2 - E_M</math>
	The new graph looks like this [[File:~~PEM~~.~~gif~~]]		The new graph looks like this [[File:red_line_chart.png\|400px]]

	We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:~~arrowgraph~~.~~jpg~~]]		We can determine a number of properties from this graph. The bottom of the graph represents the point where the potential energy is at a '''minimum''' and the change in potential energy with respect to time is '''0'''. This is the distance where no force acts on either of the atoms from the other, and known as the the '''equilibrium distance''', <math>r_{eq}</math>. If the two atoms are at a distance apart less than <math>r_{eq}</math> the two will travel in the positive <math>r</math> direction, or get ''further apart'' to reach the minimum potential energy. The opposite is also true. If the two atoms are at a distance apart greater than <math>r_{eq}</math> the two will travel in the <math>-r</math> direction, or get ''closer together''.[[File:green_dots.png\|400px]]

	===A Computational Model===		===A Computational Model===

Parkercoye: /* History */

2019-07-28T17:20:32Z

History

← Older revision		Revision as of 13:20, 28 July 2019
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	'''Philip Morse'''		'''Philip Morse'''

			The Morse approximation is accredited to Philip Morse, who wrote a paper in the 1930s about interatomic interactions. He was an engineer and physicists who wanted to get physically applicable results to his findings. Because of this he went on to assist the United States in World War II. He discovered a way to use acoustics to aid the US in detonating German mines. Like many well known physicists, Morse accomplished a great deal because he wanted to use physics to improve the world as it currently was.
	~~[[File:Morsep.jpg\|200px]]~~

	The Morse approximation is accredited to Philip Morse, who wrote a paper in the 1930s about interatomic interactions. He was an engineer and physicists who wanted to get physically applicable results to his findings. Because of this he went on to assist the United States in World War II. He discovered a way to use acoustics to aid the US in detonating German mines. Like many well known physicists, Morse accomplished a great deal because he wanted to use physics to improve the world as it currently was.

	== See also ==		== See also ==

Parkercoye at 21:29, 28 June 2019

2019-06-28T21:29:18Z

← Older revision		Revision as of 17:29, 28 June 2019
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	~~by Charlotte Bunch~~

	==Potential Energy of a Pair of Neutral Atoms==		==Potential Energy of a Pair of Neutral Atoms==

Cbunch8: /* References */

2015-12-03T20:13:17Z

References

← Older revision		Revision as of 16:13, 3 December 2015
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	https://en.wikipedia.org/wiki/Morse_potential		https://en.wikipedia.org/wiki/Morse_potential

			https://trinket.io/glowscript/31d0f9ad9e

	[[Category:Energy]]		[[Category:Energy]]

Cbunch8: /* External links */

2015-12-03T20:01:59Z

External links

← Older revision		Revision as of 16:01, 3 December 2015
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	===External links===		===External links===

	~~Internet resources on this topic~~		Online Textbook [http://www.webassign.net/ebooks/mi4/toc.html?page=7.3 click here]

	==References==		==References==

Cbunch8: /* References */

2015-12-03T19:57:51Z

References

← Older revision		Revision as of 15:57, 3 December 2015
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	http://asa.aip.org/encomia/gold/philipmorse.html		http://asa.aip.org/encomia/gold/philipmorse.html
	[[Category:~~Which Category did you place this in?~~]]
			https://en.wikipedia.org/wiki/Morse_potential

			[[Category:Energy]]