User:Darrell Bonn/Notebook/307L Lab book/lab 2 e over m summary

^{SJK 17:05, 18 December 2008 (EST)}

17:05, 18 December 2008 (EST)
Good job with the data and analysis for this lab. It's interesting that the lower filament voltage improved your number and your ability to read the image--I didn't expect that. Another clue.

e/m

Lab Partner: Boleszek

Summary

Complete notes on our data acquisition can be found in our Lab Manual

The purpose of this lab was to measure the electon charge to mass ratio: e/m. The procedure is fairly straight forward. Utilizing the e/m device, an electron beam is manufatcured and accelerated into an evacuated tube. A magnetic field is placed perpendicular to the beam path and the path curvature is then measured. By accurately measuring the magnetic field strength and the initial velocity of the electrons and the curvature of the beam the charge to mass ratio is simple to compute.

There are several variables in this lab. The obvious ones are the accelerating voltage, the magnet current and the measured path radius that are used in the calculations. Another is the heating element voltage, which does not go into those calculations, but which I believe had a significant impact on our data as discussed below. Finally, there is the "focus" which was not understood and seemed to have little effect. This was left in a single position throughout.

Two basic sets of data were taken, one keeping the accelerating voltage constant and another keeping the magnet current constant. These data were evaluated separately to look for systematic errors associated with either variable. Each set of data was taken on two separate days with the second days data being far more complete.

The data was ported to a matlab file for processing. It's format was very simple. Data is entered into appropriate arrays, magnetic field is calculated based on the e/m setup. The radius data is then averaged and e/m produced for each data point. From these a mean and standard deviation are calculated and the followind output is produced:

Day 1, Constant magnet current: E/m = 4.606E+011 with std dev of 6.645E+010

Day 1, Constant accelerating voltage: E/m = 4.169E+011 with std dev of 4.872E+010

Day 2, Constant magnet current: E/m = 3.706E+011 with std dev of 1.947E+010

Day 2, Constant accelerating voltage: E/m = 3.729E+011 with std dev of 2.369E+010

These are all fairly far away from the accepted value of -1.76E11 C/kg. in spite of the fact that the standard deviation of this data would indicate some decent accuracy. Note that the data from day one has a significantly larger than that taken on day two. Also that for each day the two methods produce similar numbers within each others error range. This would seem to indicate a systematic error.

Looking back over the data acquisition notes it seems the likely primary culprit is the filament voltage. The thermionic emmision which is the source of the electrons imparts some energy to the electron. The first day we kept the filament voltage up at 10V, the second day this was lowered to about 6.5V (It should be noted that this second number is from memory as we did not record this in our lab notebook). As the second day produced data much closer to the accepted value, I expect that the trend would continue. Indeed, there is no place in our calculations that account for the energy imparted to the electrons from the filament itself. If we were to repeat this lab, it would be of interest to take more data with progressively smaller filament voltage to see if this is indeed the case.