User:Stephen K. Martinez/Notebook/Junior Lab/2008/10/15

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 * style="background-color: #EEE"|[[Image:BuckyTube s.gif|128px]] Electron Diffraction
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Introduction
This lab is based on the hypothesis of deBroglie who postulated in his doctoral thesis that like electromagnetic particles which have both wave and particle nature, that mass particles like electrons might also have this property. This appears to be the case following the experiment that we will conduct today: Electron Diffraction. Like photons put through a diffraction grating that have interference patterns, electrons will diffract in arcs based on the geometry of the apparatus through which they are directed - which in our case is the two spacing distances in graphite. This experiment led to the definition of particles by probability density wave functions. It is required for electrons to have a high speed to see wave nature effects.

Safety
Two major concerns here are the high voltage of 5kV that we will have emitted by our power source: we hope to be careful with the set up, turning the apparatus off if we are to make adjustments and keeping the amplitude slider down until we are ready to raise it, and all other general knowledge electric work. The other is to not allow the current in the graphite to exceed .25mA which we will accomplish by monitoring the current with an ammeter in series with our apparatus at all times. We will not worry too much about the glass bulb as we will not put it under any duress.

Equipment
The equipment was already set up when we arrived, not an elaborate setup but matched the set-up indicated in Golds lab manual
 * Vb is probvided by a Hewlett Packard 6216B Power Supply, although we will ignore this machinery.
 * Vf is a Teltron kV 813 power unit
 * TEL 2501 Universal Stand was our uh.. stand for the bulb.
 * TEL 2555.02 Magnet the magnet
 * Wavetech Meterman85xt multimeter
 * Carerra Precision Calipers

Procedure
We followed the lab manual and turned on all our equipment, allowing one minute for the heater to warm up before increasing the voltage, and carefully monitoring the current. We then turned off the lights and began taking measurements on the very difficult to see rings. We took the width of our rings as constant error: ±1.5mm

Data
At approximately 2.5 the beam was so faint that taking data at that point with our eyes would have been useless.

Day 2
This day we began by taking data different from our day 1 method: where we measured the width of the beam and used that uniformly as the error. Today we took two data points for the inner and outer limits on the circles and taking the mean and the difference between each point and the mean as the error. We took turns this time collecting data, to get unbiased values. Umfortunatley we got distracted and our data reset itself, so we didn't have much time to collect data. We stopped recording data when the rings got far too difficult to see, which was at about 2.7kV today.

Something important to note is that our data for this session was kind of screwy because we could not resolve the endpoints of each diameter as easily as we could resolve the center with our eyes. Also, there is a very bright spot at the center of the rings which corrupts our view of the small ring. We also noticed an anomalous fingerprint like diffraction pattern about an inch above the circles. We agreed that it must be part of the diffraction pattern because its size increased as the voltage decreased like the circles. This pattern flicked in and out much like the refraction of light across water, which is a feature that we were not obviously able to capture in our photo. This anomaly was most likely due to our magnet ring because we were figiting with this part of the equipment before we noticed it, and it seems to fit the bill that it might deflect the electrons up into this pattern.

Error
Possible sources of error are as noted in the lab manual have to do with the geometry of the bulb, in two ways that the actual length observed is affected by the curvature and the thickness of the bulb, Aram mentioned to us that the latter would be very ineffectual and we could easily ignore it. As for the curvature we determined that the ΔL would be equal to the radius of the bulb minus the length from the bulb to the plane that we expressed as RcosΘ because of the geometry. Then we solved without need of theta as the actual length being the given length ΔL=L*cos(sin-1(D/2L). This however, suggested that we would have a different value for L based on the diameter of the circle we were observing, which is bogus because the properties of the glass were unchanged, therefore we decided to use the factory value of the length, and account for its varience in the analysis when using error propagation. I think it is reasonable to ignore such a quantity as the other sources of error, our eye approximating both the diameter, the error of the diameter, and the voltage value would introduce more substantial error.

The more pressing concearn is that the material we are experimenting with is crystalline, and therefore the pattern we would be observing would only represent the characteristic spaceings as bragg peaks of intensity of a the graphite depending of the angle of incidence of our beam and that not all spacings might be represented, or that these might be minimally represented and introduce some observing error in what we assume are discrete lines representing certain spacings in the atomic structure. It seems that for this experiment since we are trying to more fundamentaly prove to ourselves that electrons can be waves as well as particles nothing about graphite is particularly important about graphite, and because of this seeming ambiguity introduced from bragg diffraction that it might have been more prudent to conduct this study using a powder, so that all possible angles are accounted for.

Analysis
d= 4π(hbar)c(L-ΔL)/Dsq(2eVAmc2) To find our value for the lattice spacings we followed the lab manuals suggestion to make a graph of the Diameters versus the inverse square of the voltages then we used that graphs slope to determine the line spacing by dividing the constants in our equations by the slope. This is the least squares approach we have been using in all our labs, and while it worked fairly well for the values we obtained were okay and the data was linear, we also decided to do error propagation to get error bars for our data. We decided our error would be in L and D. Our equation for the error was δd = sq((dd/dD δD)^2 + (dd/dL δL)^2) where these are respectively dd/dD=-4πhbarL/D^2sq(2eVm) dd/dL = -4πhbar/Dsq(2eVm) δD=max-mean δL=.02mm Our calculation of the L error wasn't working and we thought it would be of less consequence compared to the Diameter so we dropped that term and determined only the error in diameter.
 * [[Media:Diffraction1.xls | Diffraction data analysis with width of circle constant]]
 * [[Media:Diffraction2.xls|Diffraction data analysis with minimum/maximum data points]]


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