# Physics307L:People/Josey/Electron Diffraction

Steve Koch 03:01, 21 December 2010 (EST): Love your primary lab notebook & description of problems you encountered.

## Electron Diffraction

For this experiment, my lab partner, Kirstin, and I used the diffraction of electrons to measure the spacing between carbon atoms in graphite. The electrons were able to diffract, like light passing through slits, because they have wave properties in addition to their particle properties. To get their wave properties, we accelerated the electrons across several different potential differences. The electrons then traveled through some graphite, and were diffracted before hitting a fluorescent screen. This screen allowed us to see the diffraction rings, which we then measured with digital calipers. The diffraction pattern were made out of rings, while the crystal lattice of graphite is hexagonal. The reason for this is that there are several layers of graphite overlappingSJK 02:50, 21 December 2010 (EST)
02:50, 21 December 2010 (EST)
moreover, it's a powder, so all orientations present across the width of electron beam
, that averages out to rings. Here is a picture of the diffraction pattern:

## Data and Results

From our measurements, we were able to plot the measured diameters of the rings as a function of the inverse square root of the acceleration potential. From this slope, we were able to determine the spacing distance, in nanometers, but using this formula:

$d = \frac{\frac{2hL}{\sqrt{2me}}}{Slope}$

Using this formula, we were able to determine two values for the spacing. The first value had a best estimate of 0.245 nm, with a confidence interval between 0.242 nm and 0.246 nm. This closely estimated the known value for one of the spacings of 0.213 nm. Our best estimate was off by only 15%. The second value we determined had a best estimate of 0.139 nm, and a confidence interval of 0.136 nm to 0.140 nm. Again, this was close to the accepted value of 0.123 nm. Our value was off by about 13%.

While our values for both of the spacings in the graphite lattice were close, they were also off by a real margin. This is likely caused by the curvature of the glass diffraction tube. The screen that we measured the diameters from was curved while our measurements assumed that it was flat. This of course through off our measurements, and generated the error in our final results. If we were to repeat this experiment, we would have to account for the curvature of the glass a little better. My notebook for this experiment can be read here. Kirstin's work can also be read here for her notebook and here for her summary.