PHYSICS 320 LABORATORY

THE DIFFRACTION OF ELECTRONS

OBJECT:

The purpose of this experiment is to demonstrate that electrons have wave properties. Specifically, we wish to show

1. that electrons can produce diffraction effects when scattered from a Carbon target,
2. that the pattern so produced follows the same Bragg equation that applies to x­radiation, and
3. that the results confirm the de Broglie hypothesis - namely, that all material particles have a wavelength which is inversely related to momentum.

BACKGROUND:

The de Broglie wavelength of a material particle is

where h is Planck's constant. For electrons accelerated through a potential difference V, the velocity v can be obtained from the classical expression

and substituted into the de Broglie relation obtaining:

The Bragg condition for diffraction for small angles is

where d = the interatomic spacings, D is the ring diameter, and L is the path length from the carbon target at the gun aperture to the luminescent screen. Combining this with the previous relation,

D and V are the only variables, so the relation can be verified by means of a graph related to these variables.

APPARATUS:

The electron diffraction tube, TEL.555, comprises a 'gun' which emits a narrow converging beam of electrons within an evacuated clear glass bulb on the surface of which is deposited a luminescent screen. Across the exit aperture of the 'gun' lies a micro­mesh nickel grid onto which has been vaporized a thin layer of graphitized carbon. The beam penetrates through this carbon target to become diffracted into two rings.

Connect the tube as shown in the following diagram:

Filament Voltage ( V_F ). . . 6.3 VAC ( 8.0 V max ) from TEL 2813
Anode Voltage ( V_A ). . . . 2500 - 5000 VDC from TEL 2813
External Bias ( V_B ). . . . . . 0 - 50 VDC from TEL 801
Anode Current Meter ( I_A ). . . 0.15 mA at 4000 V ( 0.20 mA max.)

EXPERIMENT:

1. Measure the path length from the Carbon target at the 'gun' exit aperture to the luminescent screen as accurately as possible.
   
2. Switch on the heater supply and wait one minute for the cathode temperature to stabilize.
   
3. While watching the meter which reads the anode current, gradually begin to increase the anode voltage.  The anode current should never exceed 0.2 mA!  The meter on the TEL 2813 unit initially does not read the output voltage.  Press the buttons in the lower right corner of the unit to read kV.   Higher anode voltages can be achieved without exceeding the limit by increasing the external bias control on the TEL 801 which also helps in focusing the electron beam. Set the voltage to 2500 volts for now.

3. Two prominent rings about the central spot are observed. Variation in the anode voltage causes a change in diameter.
   
4. Measure and tabulate the ring diameter, D, for both the inner and the outer rings at different anode voltages, say from 2500 volts up to 5000 volts in steps of 500 volts.

5. Plot a graph of V^-½ versus D for each ring. From the slopes together with equation (5) determine the value of the two spacings d₁₁ and d₁₀ for Carbon which would yield these results.

6. Carbon atoms in a graphite structure are arranged in a hexagonal rather than cubic manner. Using the geometry in the above figure, what is the ratio of the d values?  Compare this theoretical value to your experimental results.  The bond length for carbon graphite is 0.142nm.  Calculate the bond length from your results and compare to the accepted value.

7. Explain why rings, as opposed to discrete points, are observed in the diffraction pattern.