# Physics307L F09:People/Gonzalez/Electron Diffraction

## Electron Diffraction

^{SJK 16:15, 11 October 2009 (EDT)}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 field~~electric 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:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda =h/p=\frac{h}{\sqrt{2mE_{k}}}=\frac{2\pi \hbar}{\sqrt{2m_{e}V_{a}}}}**

where
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda =Rd/L}**
and R=d/2, is true for small angles, we get:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Rd/L=\frac{2\pi \hbar}{\sqrt{2m_{e}V_{a}}}}**
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle =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)}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.