User:Darrell Bonn/Notebook/307L Lab book/lab 3 diffraction Summary

Electron Diffraction Lab Summary

Lab Partner: None

Procedure/Comments

Procedure followed was not precisely that found in our Lab Manual. Please check my lab notes for variations.

The purpose of this lab was to use the de Broglie relationship lambda = h/p to measure the spacing of the molecular lattice of a very thin carbon film. To do this a simple electron gun mounted in a vacuum tube is used to accelerate electrons to strike the carbon film. Electron diffraction pattern is then visible on the phosphorescent coated end of the tube. By de Broglie's relationship the electron beam will exhibit diffraction a predictable pattern.

There are a few difficulties with this lab, the most prominent of which is the difficulty of obtaining accurate measurements. The diffraction pattern is very dim and not always regular. This is compounded as the accelerating voltage of the electron gun is varied. At most accelerating voltages only one or the other of the primary or secondary diffraction rings are clearly visible. The measurements were made with a pair of digital calipers, but the inherent inaccuracy of measuring the size of these rings by using calipers held across a barely visible light ring is very high. To counter this measurements were repeated 10 times in hopes that the random distribution of measurement error would be able to reduce inaccuracy.

Another error in these calculations arises from the fact that the work function of the cathode for releasing electrons via thermionic emission is not known for this device, and I did not consider trying to measure it during data acquisition. Therefore the values for p are underestimated. However, I expect this error is small compared to the other measurement errors presented above.

Analysis

Analysis was carried out via matlab. The m-file loads the experimental data into arrays, calculate estimates for measured diameters and with these calculates the lattice value along with error bars. Error bars in this plot were calculated from the standard error of the diameter measurements propagated through the calculations.

From these values the final estimates for the lattice spacing are Inner ring lattice value: 0.191(5) nm Outer ring lattice value: 0.114(3) nm Clearly, these errors are insufficient to explain the variances in the data. And as the mean of these lines produce values that are only 90% of the expected value for the inner ring and 93% of expected value for the outer ring, the error bars as plotted do not in any instance overlap the expected values. Consequently the error present is due to other acquisition errors. The primary candidate for this is simply bad measurement technique. Although the data was repeated with fair accuracy, this does not necessarily indicate that it was correctly done. I expect that I measured the rings consistently too large. As noted above, the work function of the cathode is also unaccounted for in this analysis. However, this should also be insignificant as the work function should be on the order of a few eV.

The code is available here: File:Edifraction.m. Some of the variables used in the matlab file reference the following diagram.