User:Joseph Frye/Notebook/Physics Junior Lab 307L/FormalReport: Difference between revisions
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The electron charge to mass ratio was first measured by J.J. Thompson and established the the electron was a particle [2]. This experiment is an attempt to measure the electron charge to mass ratio. We used an apparatus designed for this experiment which consists of an electron beam in a tube of gas. The tube is inside of Helmholtz coils. By varying the strength of the magnetic field and the energy of the electrons we are able to see how the radius of curvature of the electron beam changes and from that calculate the ratio of e/m. I calculated e/m to be 2.109(23)x10^11 C/kg and 2.238(15)x10^11 C/kg using two slightly different methods. | The electron charge to mass ratio was first measured by J.J. Thompson and established the the electron was a particle [2]. This experiment is an attempt to measure the electron charge to mass ratio. We used an apparatus designed for this experiment which consists of an electron beam in a tube of gas. The tube is inside of Helmholtz coils. By varying the strength of the magnetic field and the energy of the electrons we are able to see how the radius of curvature of the electron beam changes and from that calculate the ratio of e/m. I calculated e/m to be 2.109(23)x10^11 C/kg and 2.238(15)x10^11 C/kg using two slightly different methods. | ||
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==Introduction== | ==Introduction== | ||
{{SJK Comment|l=05:19, 17 December 2010 (EST)|c=Missing from introduction is a historical perspective and / or motivation for the experiment. This would also have allowed for inclusion of some citations to peer-reviewed original research.}} | |||
This experiment was an attempt to measure the electron charge to mass ratio. We used a piece of equipment designed for this purpose. The apparatus consists of a sealed bulb filled with neon gas. Inside the tube is an electron gun that produces a beam of electrons. The tube itself is inside Helmholtz coils that create a magnetic field. When a charged particle is moving in a magnetic filed it feels a force perpendicular to the magnetic field and the particle's motion. The result inside the bulb is that the beam is curved into a circular path. We varied both the accelerating voltage on the electron gun, and the strength of the magnetic field and measured the radius of curvature of the electrons. We then calculated the ratio of the electron charge to its mass. | This experiment was an attempt to measure the electron charge to mass ratio. We used a piece of equipment designed for this purpose. The apparatus consists of a sealed bulb filled with neon gas. Inside the tube is an electron gun that produces a beam of electrons. The tube itself is inside Helmholtz coils that create a magnetic field. When a charged particle is moving in a magnetic filed it feels a force perpendicular to the magnetic field and the particle's motion. The result inside the bulb is that the beam is curved into a circular path. We varied both the accelerating voltage on the electron gun, and the strength of the magnetic field and measured the radius of curvature of the electrons. We then calculated the ratio of the electron charge to its mass. | ||
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==Equipment and Setup== | ==Equipment and Setup== | ||
Revision as of 03:19, 17 December 2010
E over M ratio
SJK 05:16, 17 December 2010 (EST)
More descriptive title needed
Author: Joseph Frye
jfrye01@unm.edu
Performed by: Joseph Frye and Alex Benedict
Date: This lab was performed on October 11, and October 18 with a follow up on Monday December 6, 2010
Location: Junior laboratory in the UNM physics building
Abstract
SJK 05:18, 17 December 2010 (EST)
Good abstract...ending with a concluding statement about whether you saw huge systematic error would be good.
The electron charge to mass ratio was first measured by J.J. Thompson and established the the electron was a particle [2]. This experiment is an attempt to measure the electron charge to mass ratio. We used an apparatus designed for this experiment which consists of an electron beam in a tube of gas. The tube is inside of Helmholtz coils. By varying the strength of the magnetic field and the energy of the electrons we are able to see how the radius of curvature of the electron beam changes and from that calculate the ratio of e/m. I calculated e/m to be 2.109(23)x10^11 C/kg and 2.238(15)x10^11 C/kg using two slightly different methods.
Introduction
SJK 05:19, 17 December 2010 (EST)
Missing from introduction is a historical perspective and / or motivation for the experiment. This would also have allowed for inclusion of some citations to peer-reviewed original research.
This experiment was an attempt to measure the electron charge to mass ratio. We used a piece of equipment designed for this purpose. The apparatus consists of a sealed bulb filled with neon gas. Inside the tube is an electron gun that produces a beam of electrons. The tube itself is inside Helmholtz coils that create a magnetic field. When a charged particle is moving in a magnetic filed it feels a force perpendicular to the magnetic field and the particle's motion. The result inside the bulb is that the beam is curved into a circular path. We varied both the accelerating voltage on the electron gun, and the strength of the magnetic field and measured the radius of curvature of the electrons. We then calculated the ratio of the electron charge to its mass.
Equipment and Setup
We followed the setup and procedure for this lab in Dr. Gold's lab manual, experiment number 2
Equipment
- e/m Experimental Apparatus Uchida model TG-13
- 3 Power supplies
- Gelman Deluxe, 6-9V 2A
- Soar DC PS 3630, 6.0V 1.5A
- Hewlett Packard 6236B, 150-300V 40mA
- 3 Digital Multimeters
The equipment was set up already when we began this lab. We used Dr. Gold's lab manual to check the connections and confirm that everything was hooked up properly.
Procedure
Inside the sealed bulb is an electron gun and helium gas. The bulb is in the center of Helmholtz coils which produce a magnetic field. A beam of electrons shoots from the gun into the bulb and the magnetic field curves the beam into a circle. We are able to measure the radius of the circle with a ruler on the back of the apparatus. By measuring the radius of curvature as we vary the accelerating voltage of the electron gun and the current supplied to the coils we are able to calculate the ratio of the electron charge(e) over the electron mass(m). According to the equation given on the front of the apparatus:
[math]\displaystyle{ \frac{e}{m}=\frac{2*V}{B^2*r^2} }[/math]
where
- e is the electron charge
- m is the electron mass
- V is the accelerating voltage
- B is the magnetic field
- r is the radius of curvature
The idea is that if we know the radius of curvature then we know the acceleration of the electrons. Knowing the strength of the magnetic field and the kinetic energy of the electrons we can find the force as a function of the electron charge from:
[math]\displaystyle{ F=(e*v)X(B) }[/math] [1]
and with Newton's second law,
[math]\displaystyle{ {F}={m}*{a} }[/math] [1]
we find that
[math]\displaystyle{ \frac{e}{m}=\frac{a}{v*B} }[/math]
we arrive at the first formula by noticing that velocity(v) is related to the Accelerating voltage, and that acceleration(a) is radial and thus related to the radius of curvature.
We vary the current in the Helmholtz coils to change the magnetic field. We vary the accelerating voltage on the electron gun to change the kinetic energy of the electrons. We then measure the radius of curvature using a ruler that is attached to the back of the apparatus.
Data
The first trial we kept the current to the coils constant at 1.5A (constant B field) and varied the accelerating voltage from about 175V to about 225V in steps of 25V. We then measured and recorded the radius of curvature in a google docs spreadsheet. The second trial we kept the accelerating voltage constant at 200V and varied the current to the coils from 1.5A to 2.0A and again measured and recorded the radius of curvature. our data is hereFile:Benedict Frye E M ratio.ods
Results
I chose to analyse the two trials separately. The analysis is also in the spreadsheet.
Accepted Value C/kg 1.75882017x10^11
Trial 1: Constant B field varying accelerating voltage
e/m: 2.109(23)x10^11 C/kg
relative error 0.20
Fractional Error 0.01
Trial 2: Constant accelerating voltage varying B field
average e/m 2.238(15)x10^11 C/kg
relative error 0.27
Fractional Error 0.01
The standard error of the mean in both cases was relatively good meaning that our measurements were taken consistently. This suggests that the large relative error seen in both trials is due in large part to systematic sources. Alex Benedict came up with a way to model this experiment using the mean free path which greatly reduces the relative error. I recommend reading his report as well. here is a link to his page: Benedict's Page
Notes From the lab
Here are my notes from each day of the lab if you are so inclined.
Links
Acknowledgments
- I would like to thank Alex Benedict for all of his help on this experiment and more generally throughout the semester.
- Thanks to Dr. Koch Katie Richardson for discussion of the issues encountered in this lab and general guidance.
References
[1] Young, Hugh D. and Roger A. Freeman. University Physics, 11th Edition with Modern Physics, (C)Pearson Education. San Francisco, California 2004
[2] Wikipedia. Mass-to-charge ratio. [1]. 24 November 2010 at 11:27
[3]
[4]
General SJK Comments
13:25, 6 December 2010 (EST):Joe, sorry for not having graded this yet. Since today is the "extra data" day, please see Alex's notebook and talk with him about ideas for what to pursue today. One example would be whether the beam radius depends on filament temperature.
