INTRODUCTION:

BEFORE LAB:

- Look up both "electron diffraction" and "double-slit interference" in either your Modern Physics text or an Introductory Physics text. Take good notes. Read these instructions before class as well.
- Find library resources that tell you more about the role of Louis deBroglie, Clinton Joseph Davisson and Lester Germer, and George Paget Thomson in the history of this experiment. Be sure to include this in your Introduction, as well as some discussion of “particle-wave duality”.

THE EXPERIMENT:

(There are other rings, but they will be too dim and at angles too large for us to observe.) Measuring the relation between accelerating voltage and diffraction ring diameter will allow us to determine the interatomic distances in the carbon foil inside.

To pull those distances out of our raw data, we will need to start with the deBroglie wavelength of a particle, λ = h/p. For non-relativistic electrons (KE << mc

Question 2: In this experiment, the accelerating voltage is limited by our power supply and multimeter to no more than 5kV. Can we ignore relativity? Why?

The diffraction rings follow the same physics as the interference maxima in a two-slit or multiple-slit interference pattern. Find the equation -- in a physics textbook -- in terms of the slit distance, d, the angle, θ, of the "nth" interference maximum, and the wavelength, λ. Note that for small angles, sinθ = D/2L.

Connect the tube into the circuit shown in Figure 2, paying special attention to the precautionary notes. Do not turn on the power supply until your circuit has been checked by an instructor, and when you do turn it on, let the filament warm up for 1 minute before increasing V

Measure the inner diameters of the two most visible rings, D

ANALYSIS:

Graphite consists of two-dimensional sheets loosely bound to other parallel two-dimensional sheets. Within each sheet, the atoms are arranged in a hexagonal lattice. (Fig. 4 & 5.) Your first task is to locate the planes. Take the attached sheet with the hexagonal lattice on it and find two different sets of planes. Notice that the distance between planes has to repeat itself exactly. Most likely you have found the "(10)" and the "(11)" planes, which differ by a factor of 1.732 in size. Measure these two interplanar distances , d

Finally, calculate the two "d"s from your data, using the slopes you calculated from your raw data. Don't forget to calculate the uncertainties. From these, calculate the closest distance between two atoms in the graphite. You can estimate the approximate spacing of carbon atoms in the crystal knowing that 12 grams of carbon contain 6 x 10

THE HEXAGONAL LATTICE: