Physics307L:People/Klimov/eDiffraction

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Electron Diffraction Summary

SJK 03:41, 1 November 2008 (EDT)
03:41, 1 November 2008 (EDT)I put a bunch of comments in your lab notebook.  You did a really great job on this lab--I am very impressed and really enjoyed reading it over!
03:41, 1 November 2008 (EDT)
I put a bunch of comments in your lab notebook. You did a really great job on this lab--I am very impressed and really enjoyed reading it over!

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 graphite's hexagonal 'diffraction grating'. The diameter of the diffraction maxima were measured and then related to atomic spacings in graphite's polycrystalline lattice using the famous Bragg condition.

Useful Links:

Results

SJK 03:39, 1 November 2008 (EDT)
03:39, 1 November 2008 (EDT)I'm not an aficionado of significant figures.  I sort of like the two digits of uncertainty (52) in the first case, though Taylor would say only one is "correct."  However, in the second case, I think three digits (165) of uncertainty is definitely excessive.  That implies an unreasonable precision in the uncertainty :)
03:39, 1 November 2008 (EDT)
I'm not an aficionado of significant figures. I sort of like the two digits of uncertainty (52) in the first case, though Taylor would say only one is "correct." However, in the second case, I think three digits (165) of uncertainty is definitely excessive. That implies an unreasonable precision in the uncertainty :)

I discuss why I chose to report these values here

d^{actual}_{1} : .123nm

d^{meas}_{1}  (95%C.I.) : .1237(52)nm

Error = .55%

 d^{actual}_{2} : .213nm

 d^{meas}_{2} (95%C.I.): .2157(165)nm

Error = 1.3%

Conclusions

  • I am very happy with our results, given that they are so close to the accepted values. Both calculated spacings were comfortably within the reported 95% confidence interval.
  • 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. The fits could be improved by increasing the voltage by 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 resulting slope corresponded to largely erroneous results. However, this would not be known in an original experiment, so I tried to avoid this reasoning.
  • If I were to redo this lab, I would definitely monitor the accelerating voltage on a secondary device. This would help resolve any possible issues stemming from uncertainty in voltage measurements. In addition, it would also help to take multiple measurements for each accelerating voltage, to allow for more statistical analysis.
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