# Physics307L:People/Ierides/The Ratio e/m for Electrons

## The Ratio e/m for Electrons

The main overview and summary of the procedure and lab is provided by this link:

Prof. Gold's Lab Manual
The following link leads to our Ratio m/e for Electrons Lab entry that includes the data, procedure, and observations that were made:
The Ratio e/m for Electrons Lab Notebook Entry

Please note that Alexandra Andrego was my lab partner for this lab.

### Data Summary & Observations

The purpose of this lab was to accelerate electrons through a magnetic field using Helmholtz Coils and a helium bulb with an electron gun. Using various values of voltage at constant current, we achieved a plot of r^2 vs V that gave us a slope which could be used to calculate the e/m ratio. Likewise, we were able to use different values of current whilst keeping the voltage constant and using the slope from a plot of 1/r vs I, we were able to calculate the e/m ratio as well. (Our calculations for both of these are included in the "Calculations and Analysis" section of our lab [1].) We arrived at these values:

From the r^2 vs V plot:
$\displaystyle \frac{e}{m}_{average}\simeq3.666\times10^{11}\frac{C}{kg}\,\!$
with a range of
$\displaystyle 3.204\times10^{11}\frac{C}{kg}\leq \frac{e}{m}\leq 4.283\times10^{11}\frac{C}{kg}\,\!$
From the 1/r vs I
$\displaystyle \frac{e}{m}_{average}\simeq3.301\times10^{11}\frac{C}{kg}\,\!$
with a range of
$\displaystyle 2.408\times10^{11}\frac{C}{kg}\leq \frac{e}{m}\leq 3.699\times10^{11}\frac{C}{kg}\,\!$
SJK 15:36, 14 November 2009 (EST)
15:36, 14 November 2009 (EST)
You're including too many digits on your numbers, since your uncertainty is so big. It'd be better to report a number such as 2.4 and 3.7. This is especially noticeable, given that you only include two decimal places on the accepted value!

Our values are close in magnitude to the current accepted value of the e/m ratio:

$\displaystyle \frac{e}{m}=1.76\times10^{11}\frac{C}{kg}\,\!$ (Steve Koch 15:33, 14 November 2009 (EST):cite source of accepted value!)

The only problem we had in this experiment was measuring the radius of the loop of the electron beam. Human error, including eyesight, played a large role in this. Although our values were approximately twice that of the accepted value, the fact that the magnitude of our values was equal to that of the accepted value leads us to believe that we've made good measurements.

SJK 15:33, 14 November 2009 (EST)
15:33, 14 November 2009 (EST)
It's good that you're comparing to the accepted value, but you're forgetting to compare how far away you are relative to the uncertainty, or even whether it's in your range. So, you're missing discussion of proving that you have a systematic error. As I said to Alex: Do you really think it's only you ability to measure the radius is the major problem? I don't think so. Unfortunately, we didn't get to discuss this during the lab time, sorry about that! There are many things about the apparatus, which basically make it impossible to eliminate systematic error.

### Conclusion

In conclusion, although our values lead to a rather large error, we found that the magnitude of our measured values was equivalent to that of the accepted value. The only error that we perceived in this lab was that of using our naked eye to measure the radius of the electron beam loop. Perhaps a camera placed in front of the bulb to take exact measurement of the radius would be a commodity. Other than that this lab has proved to be useful in bettering our skills with linear fits and data taking.