Physics307L F09:People/Allen/Eoverm Lab

Summary

SJK 17:21, 15 November 2009 (EST)
17:21, 15 November 2009 (EST)
overall in this lab, you did a very good job understanding the physics, the apparatus, and taking very good data. I think you lost steam on the analysis, or at least at a minimum you lost steam in clearly recording what you were doing. Thus, I'm not sure you completed it correctly, and importantly, as noted below, there is some missing statistical comparison with accepted value.

The ratio of e/m was researched and calculated by J.J. Thomson in his historical experiment of 1897 that was based on his hypothesis of the existence of electrons. The results of Thomson's experiment gave credence to the concept of atomic particles and opened the way for the development of the atomic theory theory of matter.

This lab is set up differently from Thomson's original experiment, but it still allows one to determine the ratio of the electron's charge to its mass by observing the curvature of an electron beam under the influence of a magnetic field. A vacuum tube filled with helium and containing an electron accelerator is placed at the center of a Helmholtz coil. The current of the coil that generates the magnetic field and the voltage of the electron gun that accelerates the electrons are varied to create different radii of the electron beam. The measurements of corresponding current, voltage and radius allow one to calculate the ratio of e/m for the electron.

The equations used were derived from the Lorentz force law which gives the relationship among charge, electric and magnetic fields and velocity. Velocity was then related to voltage through kinetic energy. This gave,

e/m = 2V/(BR)^2, where B = (7.8 x 10^-4 weber/amp-meter^2) x I Dr Golds Lab Manual

One set of ten data was taken with varied voltage and current, another with constant current and varied voltage, and a third with constant voltage and varied current. I found the average value of e/m to be (2.641 +/- 0.121) x 10^11 coulombs/kg. SJK 17:19, 15 November 2009 (EST)
17:19, 15 November 2009 (EST)
I have a lot of comments on this. First, see notes in your primary notebook, I was very unclear on how you obtained the slopes for the constant current and constant voltage measurements. Given those, I now see that you correctly calculated their mean and SEM and are reporting it here. A question, though: Is it appropriate to average those values? Are they equally valid measurements? Furthermore, in principle you could have had an uncertainty on each of those individual e/m measurements, and if you did feel it appropriate to combine them, a weighted mean would have been better.

Another issue is that you rightly conclude that you have significant systematic error. However, you don't explicitly say how you conclude this. What you should do is compare the discrepancy from the accepted value for e/m with the size of your uncertainty on e/m. Since it is many times farther away from the accepted value compared with the uncertainty, this means you very likely have substantial systematic error.

Comparing this to the accepted value of 1.76 x 10^11 Dr Golds Lab Manual gave a percent error of 50%. Further data and error analysis is included in my lab report. Lab #4:e over m ratio for electron Lab Notes|Notes

• Systematic Error: The velocity of the electrons is lowered by collisiions with the helium atoms in the vacuum tube that are present to make the electron beam visible. This causes the radius of the electron beam to be less than it would be in a true vacuum. There is also a diminishing effect on the radius due to the relationship between the accelerating field and the anode. These should lead to a measurement of e/m higher than the accepted value for a given voltage, which we found to be so in our data. The percent error is very large, and if I had time, I would rework the calculations to be sure they were right.
• Random Error: There is error due to aligning the electron beam with its reflection on the ruler which was made more difficult by reflections of other lights, even though dim, in the room.

I kept the electron beam radius well below that of the vacuum tube in order to minimize distortion of the radius readings from the curvature of the glass. As a result, I was not able to keep the voltage as high as reccommended in the lab manual at the current levels that we were able to apply to the coil.

During the collection of data, I did not understand the reason to measure the outer radius of the electron beam as measuring the electrons less slowed by collisions. At first it seemed simply an arbitrary choice that would make the calculations come out closer to the accepted value. Without understanding the actual reason, I was reluctant to make this shift in my measurements for this data.SJK 16:34, 15 November 2009 (EST)
16:34, 15 November 2009 (EST)
The reasoning has to do with conservation of energy, I think. The electrons that lose energy or that were not accelerated fully by the electric field will be on the inside. Electrons cannot gain energy from the helium, and cannot have more energy than applied by the electric field, so it seems to be a safe assumption to measure the outer radius.

If I were to work further on this lab, I would like to calculate the effects of the known sources of systematic error to allow for them in the analysis of data. I would also like to compare this with the original experiment by Thomson.