User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/2008/10/29
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E/M ratioSJK Incomplete Feedback Notice
SJK 02:07, 18 December 2008 (EST)
There are thee power supplies for the e/m apparatus.
Power supply 1: powers Helmholtz coils (6-9V) set at 9V
electron gun has two power supplies:
Power supply 2: powers electrodes (150-300V) set at 200V for initial value of accelerating voltage
Power supply 3; powers heater (Do Not Exceed 6.3V) set at 6.1 V
Confirmed voltage on power supplies by checking their corresponding voltmeters.
We set the above mentioned power supplies, turned on the apperatus, allowed a few minutes for the coil in the electron gun to heat up, and adjusted the voltage on the apperatus to bend our electron beam into a circle, and ran into problems. With everything set as specified we could not get our circular elecrton beam to a size of suficient radius to take measurments. I took the following notes at that time.
We are experiencing difficulties with our set up. Our power supply to the heater is supposed to remain at 6.3V, but at the same time it should be supplying a current 1.5A in order to get a circle with a large enough radius, but we cannot get a current of over .7A with the voltage at 6.3. In an attempt to get a better adjustment on our current we switched the cables going into the multimeter from voltage to current. Doing this allows us to adjust the current up to 1.5A, but at the same time we seem to lose our voltage entirely, according to the power supply voltage decreases to zero. When looking at the e/m apperatus, switching the cables to the multimeter causes the heat in the coil in the electron gun to die down, then our circle dissapears. Once we switch back to voltage (re-adjusting the cables to voltage in the multimeter) our current goes back to a max of about .7.
In an effort to learn and possibley fix our problem, we rewired all the power supplys, and tried running the volt meters in paralle where we were trying to measure voltage. We learned in detail how the apperatus and its power supplies are set up, got the voltmeters to measure what we wanted to know (current off the power supply to the Helmholtz coil, current or voltage off the power supply to the heater. For the actual experiment both should probably be set to current, both of these power supplies have gages that allow us to read their voltage with enough precision for our purposes.) After Daniel, myself and Aram, our TA, spent most of the lab trying to get the apperatus working, Dr Koch was called in. He went over everything we had already tried, and produced a circle of decient radius by turning up the voltage on the power supply to the electrodes to over 400V. So our procedure from here forward is to take the recomended setting loosely, keeping the voltage to the electrodes to aprox 300V, as in under around 500V. We hypothisized that the filliment in the bulb could be reaching the end of its life expectancy, because from reading the lab notebooks of some of the students that completed this lab earlier in the semester it seems like a current from the heater source of .7A was enough for them to get an acceptable radius. Every thing seemed to be working correctly, but the filliment did not seem to have the energy to produce a very strong beam. Dr Koch also said we might be able to go above the specified voltage of 6.3 on the heater power supply if we had to.
We need to take three seperate sets of data and determine the e/m ratio from all three:
1) Vary current and voltage and measure the change in radius (10 trials)
2) Hold voltage constant, vary current, measure change in radius
3) Hold current constant, vary voltage, measure change in radius
Looking at both the left and the right side of the circle and averging them. Trying to make reading from the center of the electron beam. Taking the radius from each side of the circle, adding them together and dividing by 2 to get the reported radius. The error we are using for the radius is just a guess, this is a hard measurment to take in that it is hard to find a technique that you can replicate for each measurment, so in reality our error is probably greater than .1cm.
Constant Current of 1.6A
Vary Current and Voltage
the error in current and voltage are listed in the trials above
This Excell sheet contains all my data analysis
By mesuring voltage, current and radius of e- beam, we can determine the B-field produced by the Helmholtz coils and obtain an experimental measurment of the charge to mass (e/m) ration of an electron. To really clarify the physics needed to derive an equation for the e/m ratio, I poked around a bunch of sites on the internet, the clearest source (in my opinion) is linked here..., there is a typo in the final equation of the e/m ratio at this link, but it is easy to follow the math, do the derivation yourself and correct your equation.
Here is my math...Image:M ratio.mw
note; this is a maple work sheet so if your computer doesn't have maple, good luck. I was just trying to type out the math in a more readable format and copy it in here, but the copyping part didn't really work. Basically you get a formula for e/m by equating the force on an electron in a perpendicular B-field, F=evB (where v is velocity) to the radial componet of the acceration (since the path of the beam is circular) F = (mv^2)/r, and using the fact that eV is the KE of the electron KE = 1/2(mv^2). Use the KE to solve for v^2 in terms of voltage, and plug it in to your force equation and you get...
e/m = (2V)/(B^2*r^2)
where B = 7.8*10^-4 * I (this value is derived from the measurments of the Helmholtz coils and is given by the lab manuel)
We took three sets of data, one where we varied current and measured the radius of the e- beam (at constant voltage), in the next we varied voltage, and in the final one we varied both current and voltage. From these three separate sets of data we have three different ways of calculating e/m. Where both current and voltage vary I can compute e/m from each trial and then compute an average value of e/m with error. When one quantity is a constant I can rearrange my equation for e/m so that I have an equation y = (e/m)x, the quantity I am varying is in my y value and in this lab also in x, and the value of the slope is my value for e/m.
A few notes on error, the error in voltage and in current is fairly small, as far as our reading are concerned. We were able to adjust these values quite precisely using the voltmeters. The lab manuel notes that the velocity of the electrons is a great source of error though becaue there is a lack of uniformity in the accerating field, and because collisions between the Helium atoms would also decrease the velocity. This might be why my calculated values of e/m are better at a constant (high) voltage. There is also great error in the radius of the path followed by the electron beam. Both myself and Dan took the measurments of the radius (we switched off jobs)he read the radius on the 1st data set and I did it on the last two. Dan said as the radius got larger he had a harder and harder time seeing the reflection of the beam in the anti-parallax scale. We stoped taking measurments when he claimed he could no longer see a reflection. I did not fare any better, the refelction was fleeting at best, I tried to line the beam up with its reflection, but I did not feel there was any real consistancy in my technique, I tried to see a reflection, but it felt like wishfull thinking. We both tried to make our readings from the center of the electron beam, though now re-reading the lab it is suggested that we take the reading at the outside edge of the beam. I did not notice a large discrepency in the shape of the beam, it was not an obviously lopsided circle, maybe a little flattened, but is was not centered on the scale. Both Dan and myself read a radius for each side of the circle and took the average.
Since we lost the whole first day (didn't really loose it sense we really learned our set up) as far as data collection went we did not pursue much more than just the data collection. We probably would have done nothing more than data collection, except that our TA, Aram, begged me to (for once) do some data analysis, before we collected all of our data to see how our technique was working. I calculated a seemingly satisfactory value for e/m (at least it had the right number of digits), but I was at a bit of a loss as to how to improve my technique, since the big area that needed inprovment seemed to be in reading the radius of the beam, all I did was that I tried to use the focus knob more consistantly to narrow the width of the beam. This could have had a positive effect since the last set of data that I took was the data were both voltage and current vary, and I got a better value than for the first set of data that I took, where I varied voltage. The other ineresting question Aram posed was this; first he decreased the size of our circle using the current adjust knob, and then asked us why we thought the top half of the beam was now a purple color, compared to the electric blue color of the lower half. I proposed that the purple color indicated a higher frequency and therefore a higher energy, but as to why the electrons would gain and then loose energy as they followed their circular path was a question that had both Dan and myself stumped. We made some suggestions, Aram shot holes in them, and then he left us to continue to persue the answer on our own. This is a question that for me is still unanswered, I have not had the time to look into it. Thinking about the way you obtain an equation for e/m, equating two forms of the force on the beam, I am wondering about the circular path. If the circle traveled by the electron beam is not uniforme in circumfrence, could the particles be speeding up where the distance along the path is greater so that angular mometum is conserved. My physics is not very intuitive in this area, but earlier I described a circle that appeared fairly uniforme, but maybe a little flattened on top. This is probably not the answer, but the continual streem of questions being posed by both Professor Koch and Aram definitely have me thinking.SJK 02:06, 18 December 2008 (EST)Arianna Pregenzer-Wenzler 23:02, 10 November 2008 (EST):