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

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[[/notes|Notes]]
[[/notes|Notes]]


=='''DAY 1 (October 11, 2010):'''==
=='''Data'''==


We ran two trials today. 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 here[[Image:Benedict Frye E M ratio.ods| Data]]
We ran two trials today. 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 here[[Image:Benedict Frye E M ratio.ods| Data]]
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[[Image:FryeFinalReportRvV.jpg|1200px]]


=='''DAY 2(October 18, 2010):'''==


we spent day 2 taking photos for the lab report and again trying to figure out why there is so much error in this experiment.  We also tried to figure out why the beam is not violet but is instead green.  Our observations are recorded on tab 2 of the included spreadsheet. Here are some of the anomalies that we observed.  
we spent day 2 taking photos for the lab report and again trying to figure out why there is so much error in this experiment.  We also tried to figure out why the beam is not violet but is instead green.  Our observations are recorded on tab 2 of the included spreadsheet. Here are some of the anomalies that we observed.  
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[[Image:FryeEoverMLowVoltageWierdness5.jpg |200px]]


=='''Follow up (December 6, 2010):'''==
 
One of our thoughts about why the beam was a different color than the lab manual says is that perhaps the bulb contained a different gas than helium.  To test this we used helium lab and a spectroscope.  Using the equipment and technique similar to another lab we did([[User:Joseph Frye/Notebook/Physics Junior Lab 307L/BalmerSeries|Balmer Series Lab]]). We found that the spectral lines from the electron beam are consistent with helium.  There were no lines present that are not present in the helium spectrum.  This means that the gas in the bulb is indeed helium.  We also found that the violet light is present at normal experimental conditions but is not visible to the eye because of the brightness of the green light.  Another interesting note is that I could see no other lines besides the violet and green.  I had expected to see other faint lines from the helium spectrum.  This does not mean they are not there just that I could not see them in the scope.  We were unable to come to a satisfactory explanation for this phenomena.
One of our thoughts about why the beam was a different color than the lab manual says is that perhaps the bulb contained a different gas than helium.  To test this we used helium lab and a spectroscope.  Using the equipment and technique similar to another lab we did([[User:Joseph Frye/Notebook/Physics Junior Lab 307L/BalmerSeries|Balmer Series Lab]]). We found that the spectral lines from the electron beam are consistent with helium.  There were no lines present that are not present in the helium spectrum.  This means that the gas in the bulb is indeed helium.  We also found that the violet light is present at normal experimental conditions but is not visible to the eye because of the brightness of the green light.  Another interesting note is that I could see no other lines besides the violet and green.  I had expected to see other faint lines from the helium spectrum.  This does not mean they are not there just that I could not see them in the scope.  We were unable to come to a satisfactory explanation for this phenomena.



Revision as of 14:14, 12 December 2010

E over M ratio

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

The electron charge to mass ratio was first measured by J.J. Thompson and established the the electron was a particle. 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

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]

(Young and Freeman, pg 1023)

and with Newton's second law,

[math]\displaystyle{ {F}={m}*{a} }[/math]

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.

Notes From the lab

Notes

Data

We ran two trials today. 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

after looking at the data we had a relative error of about 23% which according to Dr. Koch is normal for this experiment with this e/m apparatus. We spent the rest of day 1 discussing why there would be so much error in the experiment. Thats to say why is 23% relative error normal for this experiment? In an attempt to gain insight into this question we varied the voltage and current some more and noticed some strange things.

  • In the lab manual the beam is supposed to be violet, ours was green. however at low accelerating voltages we are able to get portions of the beam to be violet.
  • The filament voltage should not affect the radius of curvature but it does change the radius quite a bit







we spent day 2 taking photos for the lab report and again trying to figure out why there is so much error in this experiment. We also tried to figure out why the beam is not violet but is instead green. Our observations are recorded on tab 2 of the included spreadsheet. Here are some of the anomalies that we observed.


The electron beam will form a helix when the velocity of the electrons is not perpendicular to the magnetic field shown here:



When the accelerating voltage is low and the current in the coils is high we are able to get the violet color described in the lab manual in part of the beam.



One of our thoughts about why the beam was a different color than the lab manual says is that perhaps the bulb contained a different gas than helium. To test this we used helium lab and a spectroscope. Using the equipment and technique similar to another lab we did(Balmer Series Lab). We found that the spectral lines from the electron beam are consistent with helium. There were no lines present that are not present in the helium spectrum. This means that the gas in the bulb is indeed helium. We also found that the violet light is present at normal experimental conditions but is not visible to the eye because of the brightness of the green light. Another interesting note is that I could see no other lines besides the violet and green. I had expected to see other faint lines from the helium spectrum. This does not mean they are not there just that I could not see them in the scope. We were unable to come to a satisfactory explanation for this phenomena.

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


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

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

  • Young, Hugh D. and Roger A. Freeman. University Physics, 11th Edition with Modern Physics, (C)Pearson Education. San Francisco, California 2004

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.