Physics307L:People/Andrego/Electron Diffraction

ELECTRON DIFFRACTION LAB SUMMARY

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Please note that Anastasia Ierides was my lab partner for this lab. You can find her lab summary by following this link.

Brief Overview

The purpose of this lab was to study and verify the de Broglie hypothesis that electrons act as waves and particles with the application of the de Broglie equation of [math]\displaystyle{ \lambda=\frac{h}{p}\,\! }[/math]. Through investigation of the electron diffraction through a thin layer of graphite (carbon), which acted as a diffraction grating, creating two rings, one inner and one outer ring. By taking measurements of the diameters of both the inner and outer rings at different accelerating voltages, we were able to calculate the "d", the separation between the carbon atoms, also referred to as the lattice spacing of carbon. By graphing the linear relationship between the diameters of the rings and 1 over the square root of the voltage we were able to use the excel Linest Function to determine the slope of the linear relationship and relate it back to "d".

Data Results

For the inner rings we calculated the following

[math]\displaystyle{ d \simeq0.177 nm\,\! }[/math]

[math]\displaystyle{ d_{min} \simeq0.154 nm\,\! }[/math]

[math]\displaystyle{ d_{max} \simeq0.206 nm\,\! }[/math]

For the outer rings we calculated the following

[math]\displaystyle{ d \simeq0.0893 nm\,\! }[/math]

[math]\displaystyle{ d_{min} \simeq0.0821 nm\,\! }[/math]

[math]\displaystyle{ d_{max} \simeq0.0979 nm\,\! }[/math]

Error

^{SJK 18:32, 15 December 2009 (EST)}

18:32, 15 December 2009 (EST)
Better than just calculating percent error would be comparing the distance from the accepted value relative to your range of uncertainty.

For ALL RECORDED accounts of error in our experiment methods and procedures please see the Notes about Our Uncertainty section in our Electron Diffraction Lab Notebook.

The percentage error of our average measured value relative to the accepted value of [math]\displaystyle{ d_{inner}=0.123 nm \,\! }[/math] from Professor Gold's Manual was calculated as:

[math]\displaystyle{ \% error=\frac{d_{inner}-d_{measured, average}}{d_{inner}}\,\! }[/math]

[math]\displaystyle{ \% error=\frac{(0.213 nm-0.177 nm)}{0.213 nm}\,\! }[/math]

[math]\displaystyle{ \simeq16.9%\,\! }[/math]

The percentage error of our average measured value relative to the accepted value of [math]\displaystyle{ d_{outer}=0.123 nm \,\! }[/math] from Professor Gold's Manual was calculated as:

[math]\displaystyle{ \% error=\frac{d_{outer}-d_{measured, average}}{d_{outer}}\,\! }[/math]

[math]\displaystyle{ \% error=\frac{(0.123 nm-0.0893 nm)}{0.123 nm}\,\! }[/math]

[math]\displaystyle{ \simeq27.1%\,\! }[/math]

Conclusions

In this lab I am fairly disappointed with our out come and final error percentiles. I feel as though we probably could have made some fine tune adjustments to the circuit set up to try to minimize the otherwise large systematic and random error we observed in our data. It was very odd to me that in order to make the diffraction rings visible that we needed to wire the circuit through the low voltage bias supply, but we never needed to even turn the supply power on for the low voltage bias. I believe that this in some way could have an adverse effect on our data. There is no logical reason as to why we needed to run the circuit in this manner, our connections and cables were in good working condition and our set-up was checked many times in relation to the circuit diagram described and shown in our lab notebook. This lab proved to be most interesting with the discovery of the strange standing wave diffraction pattern observed in both bulbs in the upper left hand corner. I would like to know what caused this strange pattern, and why our experimentation was the only occurrence of it in the lab.^{SJK 18:31, 15 December 2009 (EST)}

18:31, 15 December 2009 (EST)
I want to know too! Other students have seen it, but it never seemed as distinct as with your experience. Also, as for the mysterious need for the power supply: that indicates some kind of grounding problem. Grounding issues can be extremely complicated and I'm often confused by them.