# Electron diffraction

## Objective

We hope that by sending electrons through a diffraction grating their wave properties will be exhibited by an interference pattern of some sort being produced. Louis de Broglie predicted that every particle has a wavelength that can be determined by the ratio of Planck's constant and the relativistic momentum of the particle. We will examine how the electrons diffract through thin graphite layer, which will act as the diffraction grating.

## Equipment

Electron Diffraction Apparatus
• Cathode ray tube, model TEL2507, with heater and bulb and phosphor screen, sitting upon Universal Stand. This fires the electrons into the diffraction grating and projects the diffracted electrons onto the screen, making an image.
• Small bar magnet that was taped onto the tube, used to center what we saw on the screen.
• Multimeter to see that we had the right currents
• Calipers to measure the actual size of the diffractions
• One power source (up to 5kV) to accelerate the electron in the CRT
• Another power source that powered the heater on the CRT
• Alternate power source that gave the lab manual does not require, but without which the experiment does not really work

## Setup

There is a circuit diagram from the previous course manual, but its not really that useful. We made our own. We hooked up the power supplies and the CRT and had it all work one week, but not the next. We did the best we could, following the diagram, but had to take the multimeter out of the equation. I don't think it was setup optimally, because we kept shocking ourselves; implying that we had an open circuit somewhere. Dr. Koch was shocked twice and I was shocked once, Bradley escaped like one of Tesla's assistants.

## Procedure

We fired everything up and set our alternate power source at about 50 V, this gave us our clearest and largest diffraction pattern. On our main source we had to stay min the range of when we could see multiple rings on the screen (~2.5 kV) to less than the maxed out level of 5 kV. We had our setup set so we were always much below .25 mA, for more than that and we risked destroying the grating. Once we could see the rings distinctly, at about 2.5V, we measured the radius of each the inner and outer rings (there are only two rings!). The rings were not clear or discrete; more of a blurry distribution, like a false color Gaussian distribution. I tried to measure from the center of the ring to the brightest area in the ring. We'd take a measurement and incrementally increase the current and repeat. Bradley took some measurements but they were just awful.

2.5 .0167 0.0292
3.0 .0137 .0262
3.2 .0135 .0245
3.4 .0133 .0229
3.6 .0127 .0220
3.8 .0125 .0212
4.0 .0121 .0203
4.2 .0121 .0208
4.4 .0110 .0201
4.6 .0104 .0198
4.8 .0103 .0192

## Analysis

Since what we are really looking for is the lattice spacing, which I call d1 and d2. All the necessary calculations were performed in my excel file here: Image:E dif.xls

and my Maple file here: Image:Electroniff.mw

You can see from here that the slope is m1=1.0575 +/-.0004, which correlates to a d1=.150+/-.0004) nm

And the slope here is m2=1.8266 +/-.0006, which correlates to a d2=.0877+/-.0006 nm

My error on both, once I propagated it, was greater than the values I found by at least three orders of magnitude.SJK 02:56, 10 December 2007 (CST)
02:56, 10 December 2007 (CST)
I don't understand what you mean here.
I assumed I did it incorrectly. Looking at possible error sources I found several:
1. We could have been reading bizarre currents, because our multimeter was not successfully hooked up.
2. We are trying to measure a glowing beam about a centimeter thick, as its projected onto curved glass, and say where the center of it is. Thats says too much right there.
3. We may have not hooked the whole setup up correctly, we assumed that we thought we did. We assumed that because it was working, just not terribly well.

## Conclusion

We have our lattice spacings of .150+/-.0004 nm and .088+/-.0006 nm. The error on these is not a significant amount, and it is interesting that d2 is smaller than d1.

Once we set up the cathode ray with the multimeter and the two power supplies we turned it all on and were getting the green image on the phosphor screen. Once the voltage was turned up past 2.6 kv the multimeter made a screeching noise. Whether or not the multimeter was on, it made the noise. Regardless of the second power supply being on, the noise still occurred when the voltage was increased.