Physics307L:People/Klimov/eDiffraction

Electron Diffraction Summary

Diffraction is a phenomenon that arises from the interference of waves. Until the early 20th century, diffraction was believed to be an effect reserved to waves, such as light. However, in 1927, an experimental 'accident' by Davidson and Germer led to the discovery that particles, too, could diffract -- that is, particles had some sort of wave nature. Coincidentally, matter waves had been predicted in the doctorate thesis of Louis de Broglie, which was completed several years earlier, in 1924. de Broglie claimed that matter must behave like waves in certain limits to preserve the symmetry often observed in nature. Although the first particles that were observed to diffract were electrons, it has been shown since that essentially anything can diffract, given the correct conditions. Over the course of the century, particle diffraction has become a huge component of various fields of physics and chemistry.

In this experiment, electrons were diffracted through an atomic diffraction grating, a graphite foil. The diameter of the diffraction maxima were then related to atomic spacings in graphite's lattice.

Useful Links:

• Lab Notebook
• Data Analysis

Results

I chose to report two different confidence intervals for reasons that I discuss here

[math]\displaystyle{ d^{actual}_{1} : .123nm }[/math]

[math]\displaystyle{ d^{meas}_{1} (95%C.I.) : .1237(91)nm }[/math]

[math]\displaystyle{ Error = .55 % }[/math]

[math]\displaystyle{ d^{actual}_{2} : .213nm }[/math]

[math]\displaystyle{ d^{meas}_{2} (68%C.I.): .2157(11)nm }[/math]

[math]\displaystyle{ Error = 1.3% }[/math]

Conclusions

• I am very happy with our results, given that they are so close to the accepted values. The first calculated spacing was within the given 95% confidence interval, and the second calculated spacing was roughly two 65% confidence intervals away.
• Systematic errors clearly dominated in this lab and I am actually quite surprised that our results turned out as well as they did. I believe that the main source of systematic error was the width of the diffraction maxima, which made it hard to accurately measure the diffraction rings.
• Potentially incorrect readings of the accelerating voltage could have been another source of error. Unfortunately we did not check this parameter on a secondary device. This source of error had not been considered until I attempted to improve the fit of a least squares line. A solution was to increase the voltage by a magnitude on the order 1kV for each measurement, which would correspond to incorrect voltage measurements by this amount. Although this seems unlikely to me, it is still an unresolved issue. I must also mention that even though this fixed the least squares fit, the corresponding slope corresponded to largely erroneous results. In addition, this voltage shift also introduced large errors into other calculations.
• If I were to redo this lab, I would definitely monitor the accelerating voltage on a secondary device. In addition, it would also help to take multiple measurements for each accelerating voltage, to allow for more statistical analysis.