# Physics307L:People/Josey/e over m Ratio

Steve Koch 03:16, 21 December 2010 (EST):As noted in your primary notebook, I think you have a calculation error with one of the methods. Also, as I noted, it is not appropriate to take an average of the two methods, since they clearly do not represent the same parent mean.}}

## e/m Ratio

For this experiment, my lab partner, Kistin, and I attempted to measure the ratio of e/m for electrons. This experiment is highly significant both historically and scientifically. Historically speaking, this experiment was first performed, in a different manner, by the famous physicist J.J. Thomson, in the late 1800's in the early advent of quantum mechanics and modern physics. Scientifically speaking, this experiment allows us to find the ratio between two of the most fundamental constants in nature, the charge and the mass of a single electron. Then using the Milikin oil drop experiment, we can determine the charge of a single electron, and use this two results to derive the mass.

To do this, we released electrons from a piece of metal in a tube filled with a very dilute amount of helium. We then focused this beam of electrons, and manipulated them by changing an external magnetic field and the voltage at which they were accelerated at. Doing this we created rings of the electrons, (unfortunately we have no pictures of this because of the difficulty in taking them) and measured the radii of these rings. These rings we measured at both a constant acceleration voltage, and a constant current through a Helmholtz coil, and in turn magnetic field. Then using the following relationship and the plots of our data we were able to determine the ratio:

$B = \frac {\mu R^2 N I}{(R^2+x^2)^{3/2}}$

Unfortunately, our experimental values where not great. We measured a final ratio of e/m of (5.6 ± 0.4)*109 C/kg. This value is two order of magnitudes different from the accepted value of 1.76 * 10 11 C/kg. This indicates that there was some source of error or miscalculation in our data. It is possible that the way we measured the radii of the rings, where we aligned the ring with its reflection on a ruler, was the source of this error. However, by reviewing our data and procedure it is impossible to pinpoint the exact source of the error at this time, and in order to produce a more accurate example would require repeating the experiment.