# User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/e/m Ratio Summary

## e/m Ratio Summary

### purpose

In this lab we were trying to experimentally determine the charge to mass ratio of an electron. We attempt to do this using an apparatus that allows us to create and view an electon beam, that can be deflected by a magnetic feild in to a circle. By measuring the radius of this circle, and at varying currents and voltages we can calculate three different values of the e/m ratio.

### setup and theory

We view our electron beam inside the e/m tube which looks like a large light bulb and is filled with helium. Our electron beam is created by the electron gun which has a heating element that heats the electrons until they "boil" off the cathode they are then accelerated across a potential difference to the anode. This acceleration increases their energy until it is enough to excite the electrons of the helium atoms into a higher state. It is actually the light given off by the electrons of the helium as they drop back down to lower energy states that we see as our electron beam. Once we have a beam we deflect it into a circle with a magnetic field produced by the Helmholtz coil. The radius of this glowing, electric blue, beam can now be measured by aligning the beam with its reflection in the anti-parallel scale at the back of the apparatus.

### results

The accepted value (given in the lab manuel) of the e/m ratio is

• e/m = 1.76E+11 coul/kg

When we took measurments of the radius of the electron beam while varying both voltage and current, my experimental value for e/m is

• e/m = (3.0±.8)E+11 coul/kg

This value compares rather poorly to the accepted value, with in a 68% confidence interval, this value will fall outside the accepted value for e/m. I can say from my data that there is a 5% chance that a value from data collected in this manner will fall on or close to the accepted value. It is hard in this case to evaluate the source of this error, since everything is being varied.

Holding voltage constant and varying the current produced this value for e/m

• e/m = (2.0±.46)E+11 coul/kg

This is my best caluculated value for e/m, within the 68% confidence interval it includes the accepted value, meaning that there is a 32% chance that a value from data this type of data collection will equate to the accepted value. I can think of two factors could lead to this being our best value. The first is that Daniel was measuring the radius of the electron beam during this trial, and his technique might have been better than mine. Secondly, in this case the voltage to the electrodes was constant, and at a rather high value (over 400V). The lab manuel indicated that the velocity of the electrons in this experiment is less than the theortical value because of lack of uniformity in the accelerating field, and because of collisions between the electrons and the helium atoms. The high voltage would have minimized the effect of the collisions, and having the voltage constant might reduce its overall contribution to the error.

Holding current constant and varying the voltage produced this value for e/m

• e/m = (1.0±.21)E+11 coul/kg

This is my worst calculated value for e/m, at least my first set of data had a 5% chance of coming up with the accepted value, even using 3 times my error will not bring this value into the range of the accepted value. I am taking this result to confirm the note in the lab manuel about the velocity of the electrons (computed from the potential difference) being the greatest source of error.

Here is my Excel data sheet

### what I learned

SJK 02:14, 18 December 2008 (EST)
02:14, 18 December 2008 (EST)
Well, this is like a month later, and it's cool to see how you were learning and how quickly you've arrived at the point you're at now where you're very comfortable with a wide variety of data analysis techniques, various software applications, and all the various equipment. I think you did a good job on this lab, especially in working to get the best data possible out of the (flawed) equipment. I am a little suspicious of some of your calculations, based on the values you got, but at this point, that doesn't really matter so much.

I am getting a better feel for error analysis, and for keeping a readable lab notebook. This class is posing lots of questions, so sometimes it seems like all I see is what I don't yet know, but I am getting more familure with the basics, and so slowly I am getting to put more thought into the physics.

I did not try to add graphs to this summary, because they didn't add a whole lot in my opinion, but I will spend a little time on Wednesday (if I can) learning quickly how to add multiple curves onto one graph. The ability to do this might have allowed me to make a better visual picture of my data.

I did try to use Maple to format my equations if a more readable fassion, but I then learned that the wikki doesn't like maple worksheets (which makes sense since you need Maple to open them). I also learned I can't just copy my Maple equations and expect them to show up here in the same form. Also the wikki doesn't do htmls and when I transfered my equations into a firefox document they didn't come out in the desired form either. This was good information, because I will try something else next time.

I also learned not to fear the equiptment (by this I don't mean I am going to leave myself open to electric shock through carelessness), I mean that on the first day when nothing was working both Dan and myself were reluctant to disconnect the various cables attaching the different componets to the apperatus out of fear that we might not be able to put it back together again. At a loss for anything else productive to do we overcame our reluctance, and realized in the process, that we were perfectly capable of hooking everything back together, and gained a greater understanding of how the different componets worked.