# Physics307L F09:People/Gonzalez/Electron Diffraction

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## Electron Diffraction

SJK 16:15, 11 October 2009 (EDT)
16:15, 11 October 2009 (EDT)
This summary is pretty much of the right scope--important missing things are noted below (discussion of whether measurement is consistent with accepted value, for example).

Using Bragg diffraction we can measure the atomic spacing within a sheet of graphite. Using an electron gun we can accelerate a free electron by applying a potential through an anode, the resulting magnetic fieldelectric will propel the electron. To minimize interference from air the electron is sent traveling through a vacuumed sealed tube. The electron then strikes the end of the tube, where a diffraction pattern can be seen.

Once the pattern was observed (which takes the form of a ring) I simply measured it's diameter and recorded it along with the potential needed to create that particular size of ring. The data is collected and using the relation:

$\lambda =h/p=\frac{h}{\sqrt{2mE_{k}}}=\frac{2\pi \hbar}{\sqrt{2m_{e}V_{a}}}$

where λ = Rd / L and R=d/2, is true for small angles, we get:

$Rd/L=\frac{2\pi \hbar}{\sqrt{2m_{e}V_{a}}}$$=d=\frac{4\pi \hbar L}{D\sqrt{2m_{e}V_{a}}}$

We can then calculate the lattice spacing within the graphite by measuring the difraction rings created on the electron gun tube.

### Data analysis

SJK 16:11, 11 October 2009 (EDT)
16:11, 11 October 2009 (EDT)
I am guessing that 0.106nm(1) means 0.106 +/- 0.001 nm? If so, the better way of writing it is 0.106(1) nm. So, it is good that you included an uncertainty on your measurement. However, I cannot determine where that uncertainty came from? Standard error of the mean? It's not even clear from your primary notebook, since I didn't have access to your excel sheet. As for the plot, that is very nice (though the error bars do look a little funky--we can discuss that). I think it'd be better to plot the spacing versus voltage, because that would be more likely to reveal systematic problems. Finally, in this section in your summary you'd definitely want to state what the accepted latice spacings are, and then discuss whether your measurements along with uncertainty are consistent with the accepted value. In your case, it looks like definitely not, and thus you'd want to discuss why your measurements are not consistent.

Using my data from day two I came up with a mean of :0.106nm(1) and 0.190nm(1) for the spacings within the graphite. The following picture is a chart plotting both the inner and outer lattice spacings along with the error bars for one standard deviation.

## Conclusion

I learned a lot from this lab, including the importance of taking time for careful measurements, my errors were mostly due to difficulty seeing the diffraction rings especially at lower potentials. My day 2 results were used because I noticed that I was measuring my first results at different angles leading to inconsistencies.