User:Emran M. Qassem/Notebook/Physics 307L/2010/11/01
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Use the De Broglie relation "wavelength = planks constant / momentum" to measure the inner lattice spacing of the crystalline structure of graphite by sending an electron beam through a thin layer of the material and analyzing the diffraction pattern that it produces on a phosphorus Bulb surface.
Golds Lab manual explains how to setup. Basically do the following:
You will notice that there are two rings glowing green on the white surface of the bulb (see image).
Measure the ring diameter by measuring from the inside edge, as it is unclear where the edge ends on the outside one.
We plotted the Diameter of the inner and outer ring vs one over the square root of the voltage and found a linear relationship. We then calculated the two different lattice spacings "d" by using the slope of the plots and the equation:
The values that we obtained for d were:
This standard error is the average standard error (column SE in the Excel sheet) calculated by the SE divided by the slope, multiplied by the value we obtained for d. The range of values of d we obtained are:
The actual values of d are:
Our results are more than 3 standard errors away from the actual accepted value for both spacings. I would attribute this to our inability to take accurate measurements as it was difficult to hold the calipers steady against the glass bulb as well as systematic error from the curvature of the bulb, which we did not account for. We decided not to include the curvature of the bulb into our calculations as we were having such difficulty getting accurate readings in the first place.
I thank Randy for calculations. I thank Dr. Koch and Randy for helping me understand the what was happening with the electron as it passed through the graphite lattice spacing and why it produced diffraction rings.