Physics307L F09:People/Ritter/Electrons

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Electron Diffraction

To view the exact procedure for this lab or to learn more about the apparatus follow the given link to last year's lab manual.

Also see lab notebook entries for Monday, November 19 2007.

Purpose

Diffraction patterns are evidence of the wave properties of particles such as electrons. This was first hypothesized by de Broglie. He also stated that the wavelength of the particle is given by Planck's constant divided by the particle's momentum. In this particular experiment we will look at diffraction patterns of electrons passing through a thin piece of graphite.

Equipment and Setup

The setup for this experiment uses an electron diffraction tube that emits a beam of electrons into an evacuated glass bulb. The beam is sent through a thin mesh of graphite screen thus producing a diffraction pattern on the luminescent screen in the form of 2 rings. The diameter of these rings is the experimental data that we are interested in. The actual setup was really very simple and the taking of data was very simple also. The only necessity is complete darkness. As the voltage on the power supply is dropped the rings expand in diameter, but become much more faint as well. The lab manual asked for us to take data from 5kV down to 2.5kV. This was not possible given that the rings disappeared around 3.1kV.

Data Collections

Data collection consisted of .1kV changes of the input voltage and measuring the visible rings with digital calipers. Absolute darkness is a must, but wasn't possible in my case.

Voltage (kV) inner circle (mm) outer circle (mm)
4.9 17.8 35.5
4.8 19.0 36.9
4.7 20.0 38.0
4.6 21.1 41.2
4.5 22.1 42.1
4.4 22.8 42.6
4.3 24.3 43.5
4.2 25.0 43.9
4.1 26.4 44.8
4.0 27.2 45.1

Calculations

The ultimate numbers we are looking for are the lattice spacing (d) as related to the accelerating voltage according to our data and to compare them to the known values of .123 and .213nm. The first step in this process is to determine the extrapolated diameters. From this we can determine the lattice spacing from a plot of the extrapolated diameter versus the the inverse square root of the voltage.

My calculations may be found on the following pages:

File:Inner Ring.xls

File:Outer Ring.xls

The final values of the lattice spacing that we found were .196nm and .207nm

Conclusions

1.) Absence of error - Digital calipers are nice but this was certainly not a very accurate measurement. The mistake we made in our lab was not taking multiple measurements. There was certainly a large amount of error associated with our eyeball method of data taking. What should have been done is several measurements should have been taken at each voltage. The aquired diameters could have then been averaged and error could have been recorded. This, however, was not done. Instead it would seem as though we have good numbers with no real accurate way of reporting any error.