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Unformatted text preview: Ex pe rim e nt MP-2 El e c tro n D i ffrac ti o n o ff G rap h i te
Educational Objective To study wave-like properties of massive particles (i.e. electrons). Experimental Objective To measure the deflection of an electron beam due to diffraction by virtue of its de Broglie wavelength; also, to measure the interplanar spacing of carbon atoms in graphite. Apparatus One Tel-Atomic CRT tube containing: an electron gun, an evacuated clear glass bulb on which is deposited a luminescent screen, and a target of graphitized carbon. Voltage and current meters to: monitor the potential on the reversed-bias field, and monitor the current in the high voltage supply; not to exceed 0.2 mA. the atoms in the target (i.e.graphitized carbon). By plotting the accelerating voltage vs. the diameter of the rings, one can determine the interplanar spacings of the target. Theory Connect the tube as shown in Fig. 1, switch on the heater supply (i.e. the 6-Volt supply) and wait one minute for the cathode heater to stabilize. Slowly adjust the HV supply to about 2000 Volts. As the high voltage increase be careful to not allow the central spot on the luminescent surface of the evacuated bulb to become too bright. As you increase the high voltage slowly turn up the reversed-bias by adjust the 50-Volt supply. Two prominent rings should appear around the central spot (see figure 2). An increase in the high voltage causes a decrease in the ring diameter while a decrease in high voltage results in an increased ring diameter. This is in accord with de Broglie's suggestion that wavelength increases with a decrease in momentum. This experiment demonstrates the wave-like properties of the electron, thus revealing its dual nature. The de Broglie wavelength of a matter particle is 1. 2. 3. 1. 2. Method By varying the potential in the electron gun, one can vary the momentum (i.e. the de Broglie wavelength) of the electrons. Secondly, one can adjust the intensity of the electron beam by varying the reversed-bias potential on the Cathode can (see figure 1). This can be done by varying the potential on the 50Volt supply. Use this adjustment to keep the HV (high voltage) current less than 0.2 mA. There's no reason to have the HV current exceed 0.1 mA. Two rings are formed on the luminescent screen whose radii are determined by the de Broglie wavelength and the interplanar spacing of l= h mv (1) where h is Planck's constant, m is the mass, and v is the velocity. The velocity can be obtained from the classical expression: eV = 12 mv 2 (2) where V is the potential of the high voltage supply and e is the charge of the electron. Substituting equation (2) into equation (1) we find: l= h = mv h 1. 23 nm = 2 meV V (3) and so from equation (3) we have È 1. 23( nm) 2 L ˘ 1 D= Í ˙V Î d ˚ (7) A calculation using de Broglie's equations shows that electrons accelerated through a potential difference of 4 kV have a wavelength of about 0.02 nm. Interference and diffraction effects, as studied in physical optics, demonstrate the existence of waves, where for a simple ruled grating, the condition of diffraction is Using the slope of the lines recorded in the table in figure 3a and equation (7), the interplanar spacing, d, can be calculated. l = d sin J , (4) Procedure (1) (2) Turn on the ammeters and voltmeters resting next to the power supplies. Turn on the 6-Volt supply which is connected to the heating element inside the evacuated tube. A dull red-orange glow should appear in the electron gun. Making sure that the high voltage coarse and fine knobs are turned down to their respective minimum values, turn on the high voltage power supply and the 50-Volt supply. Increase the high voltage by turning the coarse knob clockwise. As you do make sure that you control the current in the high voltage supply by increasing the voltage on the 50-Volt reversed-bias supply. Protection of the Carbon Target. The graphitized carbon through which the electron beam is confined to pass is only a few molecular layers in thickness and can be punctured by current overload. The purpose of the "reversed-bias voltage" is to reduce the likelihood of damage to the target due to accidental user-abuse. The total emitted current passes through the resistor R; increase in the current causes the cathode-can (see figure 1) to become more negatively biassed, so reducing the emitted current. where d is the spacing of the grating and where for small angles sin q = q. The best man-made gratings are ruled at 2,000 lines per mm and with a wavelength of 0.02 nm, the angle q will be less than one second of arc or only 0.5 mm at 10 m from the grating. If electron diffraction is to be observed in our evacuated tube with a path length of 140 mm, the spacing between 'rulings' to produce a first order of interference at 14 mm from zero degrees (i.e. sin q = 0.1), must be 0.2 nm. In 1912, Prof. Max von Laue had suggested, in connection with X-ray studies, that if fine gratings could not be made by man because of the basic granularity of matter, then perhaps this very granularity might provide a suitable grating. Sir Lawrence Bragg used the cubic system of NaCl (i.e. salt) to calculate interatomic spacings and showed them to be of the right order for X-rays. This salt, like most salts is not suitable for sealing into an evacuated tube; however carbon is vacuumstable and can be formed in many different ways. The condition for diffraction for small angles using equation (4) above is (3) l = dJ (5) where the small angle q can be calculated from the geometrical relationship of Figure 2 as D J= 2 L (6) 2 Practical Precautions. Current overload causes the target to become overheated and to glow dull-red. It is good practice to inspect the target periodically during an experiment and especially at switch-on when at least one minute should be allowed for the cathode temperature to stabilize before applying the high voltage. As an additional safeguard, the anode (high voltage) current should be metered and never allowed to exceed 0.2 mA. Larger high voltages can be achieved without exceeding this limit by reducing the heater voltage. (4) Figure 3a shows the table that needs to be filled with the data from this experiment. In particular the inner and outer diameters of the rings observed on the luminescent screen need to be recorded for different high voltages, labelled Va. Figure 3b shows a typical plot of the 1/ V vs. the diameter of the two rings (meters). You should plot similar lines using the data you collect in the table in figure 3a. Figure 4 shows geometrical relationship between the interplanar spacings corresponding to the two different diffraction gratings in graphitized carbon. The two different slopes in figure 3b correspond to the two d values, d10 and d11. d10 (inner) = 0.213 nm d11 (outer) = 0.123 nm Note: Graphical Construction The convention of proportionality has been inverted for the purposes of this graphical construction in order to facilitate the calculation of d11 and d10 from the slopes of the respective lines. The accuracy of these calculations depends on the length of the line and the caliper measurement of the ring diameters. Note: Measurement of ring diameters For maximum accuracy the ring diameter should be extrapolated as in figure 5 in order to compensate for both the curvature and the thickness of the glass envelope. (5) (6) 3 ...
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