In 1923, in his doctoral dissertation, Louis de Broglie proposed that all forms of matter have wave as well as particle properties, just like light. The wavelength, , of a particle, such as an electron, is related to its momentum, , by the same relationship as for a photon:
where is Planck’s constant. The wave properties of electrons are illustrated in this experiment by the interference, which results when they are scattered from successive planes of atoms in a target composed of graphite micro crystals. The spacing between successive planes is obtainable from the interference pattern.
For a single crystal, strong reflection of waves occurs when the Bragg condition is met:
In the graphite target, there are very many perfect micro crystals randomly oriented to one another.
Therefore the strongly emerging beam will be of a conical shape of half-angle as shown in Fig. 3. If this beam falls on a phosphor-coated screen, rings of light will be formed.
The apparatus is shown in Fig. 4. Electrons emitted by thermionic emission from a heated filament (4) inside the cathode are accelerated towards the graphite target (9) of the anode by a potential difference, between the cathode and anode. A focusing electrode (8) is located in front of the target to focus the electron beam in order to provide a sharp interference pattern on the screen (11).
Their kinetic energy, , on reaching the target is equal to their loss of potential energy:
Connect the power supplies and micro-ammeter to the vacuum tube as shown in Fig. 5
HAVE THE CIRCUIT CHECKED BY YOUR INSTRUCTOR BEFORE TURNING ANYTHING ON.
Adjust the voltage controls on the power supplies to zero and then turn them on. Wait a few minutes for the filament to warm up. Set the focusing/intensity voltage to 30 V and then slowly increase the accelerating voltage to 3 kV. Monitor the electron beam current to ensure that it never exceeds 0.2 mA. A bright central spot and two rings should be observable on the screen. The rings are due to first order (n = 1) diffraction from two different sets of atomic planes having different spacings. Adjust the focusing/intensity voltage until the rings are as sharply defined as possible and then measure their diameters. Obtain sets of values of D for different accelerating voltages, Va, over as wide a range as possible, but not exceeding 5 kV. For each voltage, re-adjust the focusing/intensity voltage as necessary.
The geometry for the vacuum tube is shown in Fig. 6.
The value of can be obtained from
here and . The structure of graphite is shown in Fig. 7. The two possible layers are indicated by dashed lines. Using these parameters together with your measured voltages and the associated diameters, determine the two different spacings between the planes. Make a plot of your result as a function of the voltages. Include all error bars. Determine the average values and their uncertainty.