Scattering: Collisions in 2D and 3D - Revision history

Sydney: /* Connectedness */

2019-07-08T21:05:33Z

Connectedness

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	==Connectedness==		==Connectedness==
	Scattering is most closely connected to the [http://physicsbook.gatech.edu/Rutherford_Experiment_and_Atomic_Collisions Rutherford Experiment], which has large implications in chemistry. This experiment led to the discovery of the nucleus acted as a vital stepping stone to other discoveries in the structure of atoms and characteristics of periodic elements. This increased awareness of the parts that make up atoms also led to advances in medicine and nuclear physics.		Scattering is most closely connected to the [http://physicsbook.gatech.edu/Rutherford_Experiment_and_Atomic_Collisions Rutherford Experiment], which has large implications in chemistry. This experiment led to the discovery of the nucleus and acted as a vital stepping stone to other discoveries in the structure of atoms and characteristics of periodic elements. This increased awareness of the parts that make up atoms also led to advances in medicine and nuclear physics.

	==History==		==History==

Sydney: /* Simple */

2019-07-08T21:04:38Z

Simple

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	'''Answer'''		'''Answer'''

	~~Electrons~~ are deflected because their positive charge is repulsed by the positive charge of the nucleus. The repulsive force is stronger with smaller distance between the alpha particle and nucleus by principles of electromagnetism. Therefore, the closer the alpha particle is shot to the center of the nucleus, the stronger the force on the alpha particles, and the larger the angle of deflection.		Alpha particles are deflected because their positive charge is repulsed by the positive charge of the nucleus. The repulsive force is stronger with smaller distance between the alpha particle and nucleus by principles of electromagnetism. Therefore, the closer the alpha particle is shot to the center of the nucleus, the stronger the force on the alpha particles, and the larger the angle of deflection.

	===Middling===		===Middling===

Sydney: /* A Computational Model */

2019-07-08T21:03:47Z

A Computational Model

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	===A Computational Model===		===A Computational Model===
	'''Rutherford's scattering'''		'''Rutherford's scattering'''

	[[File:Rutherford.gif]]		[[File:Rutherford.gif]]

Sydney: /* A Computational Model */

2019-07-08T21:03:30Z

A Computational Model

← Older revision		Revision as of 17:03, 8 July 2019
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	===A Computational Model===		===A Computational Model===
			'''Rutherford's scattering'''
	[[File:Rutherford.gif]]		[[File:Rutherford.gif]]


	A simulation that shows the difference between [https://phet.colorado.edu/sims/html/rutherford-scattering/latest/rutherford-scattering_en.html Rutherford's model and the plum pudding model].		A simulation that shows the difference between [https://phet.colorado.edu/sims/html/rutherford-scattering/latest/rutherford-scattering_en.html Rutherford's model and the plum pudding model].

Sydney: /* The Main Idea */

2019-07-08T21:02:47Z

The Main Idea

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	After collision with the gold nucleus, the alpha particle gets deflected some angle θ. The gold nucleus recoils at some angle Φ. It is important to pick optimal time frames ("before" early enough and "after" late enough) so that the two particles are far enough away from each other to minimize their electric potential energies. The speeds in this approach are small in comparison to the speed of light.		After collision with the gold nucleus, the alpha particle gets deflected some angle θ. The gold nucleus recoils at some angle Φ. It is important to pick optimal time frames ("before" early enough and "after" late enough) so that the two particles are far enough away from each other to minimize their electric potential energies. The speeds in this approach are small in comparison to the speed of light.

	The case of Rutherford scattering of alpha particles with gold nuclei is an example of elastic scattering because the initial and final velocities and energies ~~stay~~ are the same.		The case of Rutherford scattering of alpha particles with gold nuclei is an example of elastic scattering because the initial and final velocities and energies are the same.

	'''Impact Parameters'''		'''Impact Parameters'''

Sydney: /* Connectedness */

2019-07-08T03:21:19Z

Connectedness

← Older revision		Revision as of 23:21, 7 July 2019
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	==Connectedness==		==Connectedness==
	Scattering is most closely connected to the [http://physicsbook.gatech.edu/Rutherford_Experiment_and_Atomic_Collisions Rutherford Experiment], which has large implications in chemistry. This experiment led to the discovery of the nucleus ~~and~~ acted as a vital stepping stone to other discoveries in the structure of atoms and characteristics of periodic elements.		Scattering is most closely connected to the [http://physicsbook.gatech.edu/Rutherford_Experiment_and_Atomic_Collisions Rutherford Experiment], which has large implications in chemistry. This experiment led to the discovery of the nucleus acted as a vital stepping stone to other discoveries in the structure of atoms and characteristics of periodic elements. This increased awareness of the parts that make up atoms also led to advances in medicine and nuclear physics.

	This increased awareness of the parts that make up atoms also led to advances in medicine...

	==History==		==History==

Sydney: /* References */

2019-07-08T03:09:11Z

References

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	Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.		Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

			“Rutherford Scattering.” MIT OpenCourseWare, MIT Department of Physics , ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2016-spring-2017/experiments/rutherford-scattering/MIT8_13-14F16-S17exp15.pdf.

	[[Category:Collisions]]		[[Category:Collisions]]

Sydney: /* Difficult */

2019-07-08T03:07:24Z

Difficult

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	'''Question'''		'''Question'''

			Imagine you are looking at a scattering simulation. Using the same formula <math> F_{θ} ≈ e^{(−θ/θ^2_m)} </math> as the previous question, at what deflection angle would you have to look at such that only 1 in a million particles are scattered at that angle?

	'''Answer'''		'''Answer'''

			1 in a million would correspond to a <math> F_{θ} </math> of <math> \frac{1}{1000000} = .000001 </math>

			Using the formula <math> F_{θ} ≈ e^{(−θ/θ^2_m)} </math>, we can rearrange to solve for θ by taking the log of both sides:

			<math> log(F_{θ}) = −θ/θ^2_m </math>

			Then, we can multiple by <math>-θ^2_m</math> to find:

			<math> θ = −(θ^2_m)log(F_{θ}) </math>

			Plugging in the given information, <math> θ = −(1^2)log(.000001) = 6</math>. Only 1 in a million particles are scattered at an angle of 6 degrees or greater.

	==Connectedness==		==Connectedness==

Sydney: /* Middling */

2019-07-08T00:46:18Z

Middling

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	'''Question'''		'''Question'''

			Rutherford found that the fraction of particles scattered at an angle <math>θ</math> or greater can be modeled by the equation <math> F_{θ} ≈ e^{(−θ/θ^2_m)} </math>. At what angle would Rutherford have found a fraction of <math>10^{45}</math> particles to be at that angle or greater than? (<math>θ_m ≈ 1</math> for a gold leaf foil)

	'''Answer'''		'''Answer'''

			Using the formula <math> F_{θ} ≈ e^{(−θ/θ^2_m)} </math>, we can rearrange to solve for θ by taking the log of both sides:

			<math> log(F_{θ}) = −θ/θ^2_m </math>

			Then, we can multiple by <math>-θ^2_m</math> to find:

			<math> θ = −(θ^2_m)log(F_{θ}) </math>

			Plugging in the given information, <math> θ = −(1^2)log(10^{45}) = 45</math>. Therefore, a fraction of <math>10^{45}</math> particles are scattered at about an angle of 45 degrees or greater.

	===Difficult===		===Difficult===

Sydney: /* Connectedness */

2019-07-08T00:44:18Z

Connectedness

← Older revision		Revision as of 20:44, 7 July 2019
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	==Connectedness==		==Connectedness==
			Scattering is most closely connected to the [http://physicsbook.gatech.edu/Rutherford_Experiment_and_Atomic_Collisions Rutherford Experiment], which has large implications in chemistry. This experiment led to the discovery of the nucleus and acted as a vital stepping stone to other discoveries in the structure of atoms and characteristics of periodic elements.

			This increased awareness of the parts that make up atoms also led to advances in medicine...

	==History==		==History==