Physics307L:People/Klimov/Eoverm
e/m Ratio Lab Summary
In this lab, the charge to mass ratio of the electron was measured. The experiment was based on the fact that moving electrons feel a force in the presence of a magnetic field, which causes them to spin. So, in this experiment, electrons were accelerated into a magnetic field, and the radius of the resulting circular beam was measured. Using the values of the radius, the accelerating voltage of the electrons and the current flowing through the coils, the e/m ratio was calculated.
Important Links:
Summary of Data
Actual e/m Ratio
[math]\displaystyle{ \frac{e}{m}_{act}=1.7563 \cdot 10^{11} \frac{C}{kg} }[/math]
We computed the e/m ratio in 3 different ways, from 2 different experiments:
- First, we held the coil current constant and varied the accelerating voltage. Then, we computed the charge to mass ratio using the slope of the least squares line, which returned:
[math]\displaystyle{ \frac{e}{m}=3.4409 \cdot 10^{11}\frac{C}{kg} }[/math]
giving us a percent error of:
[math]\displaystyle{ %_{error}=95.9% }[/math]
- Second, we held the accelerating voltage constant, varying the current in the coils. Then we computed the charge to mass ratio using the slope of the least squares line:
[math]\displaystyle{ \frac{e}{m}=3.3154 \cdot 10^{11}\frac{C}{kg} }[/math]
giving us a percent error of:
[math]\displaystyle{ %_{error}=88.7% }[/math]
- Lastly, the e/m ratio was computed directly for each point, and then averaged:
[math]\displaystyle{ \frac{e}{m}=3.3142 \cdot 10^{11}\frac{C}{kg} }[/math]
with a standard deviation of:
[math]\displaystyle{ \sigma = 0.31407 \cdot 10^{11} \frac{C}{kg} }[/math]
giving us a percent error of:
[math]\displaystyle{ %_{error} = 88.7% }[/math]
This mean was obtained by averaging the e/m ratios of all measured data points. WIth each measurement, there was also an uncertainty that resulted from our limited ability to measure the radius of the beam correctly. While these uncertainties are represented in the figures that I have posted in the lab notebook, I have chosen not to report them here -- there were so many possible sources of error that it would not be reasonable to account for only one of them numerically in this summary.
I must also note that the results with the Earths magnetic field include changed the e/m ratio quite a bit (opposing our initial beliefs). I made these estimates in the lab notebook, however, I will not present them here because we never measured the exact direction of the field, so we cannot be sure that I used the right values for the field in my calculations.
Conclusions
- I am not happy with the result, given how much effort was put into making good measurements. However, after analyzing the possible sources of error, I think its clear that it would be very hard to get a great measurement of the charge to mass ratio. The entire setup was pretty bad, and in my lab notebook I wrote down an extensive list of things that could improve the experiment in the future.
- The discrepancy from the accepted value is likely due to systematic error. The apparatus has a great number of limitations, and I don't think it is possible to get a great value for the e/m ratio using it. I am not claiming that the experiment was completely rid of random errors, but I think that they are incomparable in magnitude given the large number of systematic errors.
- If I had more time with the experiment, I would take apart the electron gun and rebuild it to shoot electrons straight up (instead of out of the side). From there, I would have to set up a set of plates that could produce an electric field perpendicular to the magnetic field produced by the coils. This would allow me to make the e/m ratio measurement by balancing the force from the E field with the force from the B field, like Thompson did. Such an experiment would remove many possible sources of error.
- Lab manual questions answered in lab notebook.
References
1. Helium. Used to find ionization energy. Given in kJ/mol, and then converted.
2. NOAA. Used to find the earth's magnetic field in Albuquerque.
