User:Joseph Frye/Notebook/Physics Junior Lab 307L/FormalReport

Experimentally measured electron charge to mass ratio using an electron beam in a magnetic field

^{SJK 05:16, 17 December 2010 (EST)}

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)}

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)}

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

^{SJK 05:41, 17 December 2010 (EST)}

05:41, 17 December 2010 (EST)
Lists of equipment are not common in formal write-ups, but instead they are described in paragraph form. See other students' reports for examples.

We followed the setup and procedure for this lab in Dr. Gold's lab manual, experiment number 2

Equipment The main piece of equipment used for this experiment was a e/m Experimental Apparatus made by Uchida. This apparatus consists of an electron gun inside of a sealed bulb filled with gas. The bulb itself is mounted inside of a pair of Helmholtz coils. We also used 3 power supplies for this experiment. One was used to supply current to the Helmholtz coils to induce a magnetic field. Another was used to apply a voltage to the electron gun filament. The third was used to apply an accelerating voltage to the electrons in the electron gun. We also used 3 digital multimeter one to measure the heating voltage, a second to measure the accelerating voltage, and a third to measure the current supplied to the Helmholtz coils. Here is a list of specific equipment model numbers Figure 1 shows the equipment when it was all connected. Figure 2 shows a closer view of the e/m apparatus.

Figure 1. The equipment with power supplies and multimeter hooked up.

Figure 2. A closer view of the front of the e/m apparatus

^{SJK 05:42, 17 December 2010 (EST)}

05:42, 17 December 2010 (EST)
All figures throughout need to be numbered; need titles; need descriptive text; and need to be referred to in the text.

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. Figure 3 shows the electron beam curving inside of the magnetic field for typical voltage and current recommended in the lab manual. We are able to measure the radius of the circle with a ruler on the back of the apparatus (see figure 4). 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.

^{SJK 05:21, 17 December 2010 (EST)}

05:21, 17 December 2010 (EST)
All figures need to be numbered and have descriptive captions. They need to be referred to in the text by number.

Figure 3. This is a photo of the electron beam in the magnetic field. This is typical for the voltage and current ranges suggested in the lab manual.

Figure 4. Similar to figure 3 this figure shows the ruler that is at the back of the apparatus used to measure the radius of curvature of the beam.

Results and Discussion

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

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^{SJK 05:45, 17 December 2010 (EST)}

05:45, 17 December 2010 (EST)
The data and the results sections could probably be combined into a "results and discussion" section. The two trials below would be better presented as a table, which would be numbered and have a descriptive legend. In general, your two sections, "data" and "results", do not have enough text, and are mostly unlabled graphs and lists of 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

^{SJK 05:48, 17 December 2010 (EST)}

05:48, 17 December 2010 (EST)
Conclusions section is missing, although there are some conclusions above.

Here are my notes from each day of the lab if you are so inclined.

Notes

Links

[Dr. Gold's Lab Manual]

Alex Benedict's Notebook

Alex Benedict's Formal report

My lab summary

My Lab Notebook

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

^{SJK 05:49, 17 December 2010 (EST)}

05:49, 17 December 2010 (EST)
No peer-reviewed research reports cited.

[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.