PURPOSE : The purpose of the experiment is to investigate the wave property of the electrons using De Broglie's hypothesis.
EQUIPMENT : Tel-atomic model 555 tube, tube mount, high voltage power supply, digital ammeter, lamp, connecting wires and ruler with sliding calipers.
THEORY: De Broglie's relation, electron wavelength l = h/p (1)
Kinetic energy, K = eV = p2/2m (2)
So that, l = h/(2meV)1/2 = 1.23 V-1/2 nm (3)
From Bragg's diffraction formula, 2dsinf = nl (4)
d is the spacing between two adjacent Bragg's planes, f is the angle of diffraction, n is an integer.
In the experiment, n=1 and, the measured angle is twice the angle(f=2q) in equation (4).
sinf Å f = 2q = (D/2)/L = D/2L small angle approximation (5)
D is the diameter of the circle on the screen and L is the distance from the target to the screen. It can be shown that the spacing d is,
d = (2.46)(L/D)V-1/2 nm (6)
Draw a diagram and derive the equation (6), using equations (1) through (5). Show that it can be reduced to an equation of a straight line with suitable variables D and V. What are the slope and intercept of the graph of lnD versus lnV?
EXPERIMENT : Read the relevant sections of the text on Bragg plane and electron diffraction. This experiment uses an evacuated glass tube. It has an electron gun that sends a narrow beam of electron that strikes a target made of graphite (a form of carbon). The thin layer of carbon is obtained by vaporizing and depositing it on the surface of a micro-mesh nickel grid. The electron gun is made of an indirectly heated oxide coated cathode that emits electron. The electron beam from the target is received at the luminescent screen painted on the inner wall of the spherical glass tube. The diffracted electron beam forms two well-defined circles at the screen corresponding to two sets of Bragg planes in the carbon structure (see figure 1). The measurements of the experiment will make it possible to determine the inter-atomic space in the crystal lattice from the knowledge of electron energy and, diameter of the circle created by diffracted electron beam.
CAUTION : Use extreme care while working with High voltage power supply and evacuated glass tube under high atmospheric pressure. After the completion of the experiment, bring the high voltage down, turn off all the switches and unplug the electrical connection. Current in the Ammeter MUST NOT exceed 2 mA (milliampere) or else the tube will be damaged.
ELECTRIC CIRCUIT PREPARATION : Draw the circuit diagram of the experiment. DO NOT turn the high voltage on unless the circuit is checked by the instructor. Heater connection for the electron gun is made by two wires at the back of the glass tube. The two terminals of the heater are connected to the 6.3 volts AC source on the power supply. The high voltage for electron acceleration is obtained by connecting a wire from the side of the tube to the high voltage source terminal +2500 volts. A lead wire from the -2500 volts terminal is connected to the ammeter (note proper polarity) and then from the ammeter to the ground terminal on the power supply. The other terminal at the back of the glass tube is connected to the ground on the power supply. Show your circuit to the instructor.
PROCEDURE : Complete the electric connections and have the circuit checked by the instructor. The table lamp should be turned on, when the room lights are off. Turn the High voltage Power supply on. Notice the light inside the tube. The hot filament produces electrons by thermionic emission. Slowly turn the high voltage to about 3000 volts. The two circular traces of the diffracted electron beam on the tube's end, should be visible at this point. If not, seek help.
1. Measure each of the diameters of the two circles with a ruler and Vernier calipers, for 2500, 3000, 3500, 4000, 4500 and 5000 volts. Voltage should be read off the upper scale of the voltmeter.
2. The most intense part of the beam trace should be considered for recordings. Take two readings of diameter at inner edge and middle of the circle. Use the average value of the diameter to calculate d for each circle. Use L = 14cm in the formula.
3. Use the set of data for 3500 volts, to calculate value of d for each circle. Known values of d are 0.213 nm for inner circle (d1) and 0.123 nm for outer circle (d2).
4. Draw a graph of lnD versus lnV for each circle on the same graph. Record the slope and intercept for each circle. Find d values from the intercepts. Slope should be -0.5. Find the percent error of your experimental results.
5. Complete the lab write up with at least one page of discussion.
Updated: 09/23/2002
Contact person: M. Azad Islam