ElectronDiffraction电子衍射.doc

Physics 290Quantum Mechanics10/17/04Electron DiffractionIn this experiment, you will observe the wave phenomenon of diffraction with a beam of particles; an experimental verification of de Broglies postulate. The arrangement is similar to G.P. Thomsons experiment, done in 1927, for which he shared the Nobel Prize with Davisson and Germer. You will make both qualitative observations about the nature of the interference pattern and quantitative measurements of the target structure.The apparatusThe electron diffractometer has three main components: an electron gun, a target, and a viewing phosphorescent screen. All of these are housed in an evacuated glass tube. The power supply that we use provides an accelerating voltage for the gun. The wiring is already done for you; there is no need for you to disconnect and connect cables. Recall how an electron gun operates. A heated filament provides a source of electrons. If the electrons are in the presence of a strong E-field then there is a force on the electrons and they accelerate. In this case, the electrons are accelerated through a potential difference of several kV. Conservation of energy allows us to write down a gun equationeVacc = mv2 = (1)Where e is the charge of an electron, Vacc is the accelerating voltage, m is the mass of an electron, and v (not the frequency n) is the speed with which the electrons leave the gun. We can solve for the speed of the electrons and therefore calculate their de Broglie wavelength in terms of Vacc. Recall (and memorize) that c =hc/2p 200 eV nm (or hc 1240 eV nm) and me = 511 keV/c2.The electron beam passes through a target that is a thin layer of multi-crystalline graphite. Picture the target as many atomic layers of carbon atom diffraction gratings in random orientations. With such a grating the interference pattern becomes a series of concentric circles. We will simulate this in lab with an optical demonstration.The screen where we view the interference pattern is 13.5cm from the target. As electrons hit the phosphor, their energy is converted to visible light that we can see. You will be making measurements on the diameters of the circular interference patterns. As always, think carefully when you record data about the uncertainty associated with every measurement.Qualitative experimentSwitch on the heater supply and allow a minute for it to stabilize. With the room darkened, slowly adjust Vacc between 0 and 4kV. You will see 2 prominent rings about a central spot. These are both first order interference rings. There are 2 of them because there are 2 different atomic spacings in your target. What is the central spot?Observe the rings as you increase and decrease the accelerating voltage. Explain carefully (in your lab notebook) how your observations are qualitatively consistent with de Broglies postulate. Quantitative Experiment:TheoryDerive an equation that relates the de Broglie wavelength ldB to the Vacc.Derive an equation that relates the de Broglie wavelength ldB to: the ring diameter D, the distance between the target and screen L and the atomic spacing d. (To do this, treat the problem as a diffraction grating or a 2 slit interference pattern.) Use the small angle approximation for sin(q).By equating your 2 expressions for ldB, derive an expression that relates D (which you will measure to L (13.5cm), d, and Vacc. This is the working equation for experiment 2.DataMake measurements of ring diameter vs. accelerating voltage for both rings. AnalysisGraph the data is such a way as to produce straight line graphs. Calculate 2 values of d from the 2 slopes. What should happen at infinite voltage? Can you use this to help with your fit?Study the schematic picture of a graphite crystal (next page). Use simple geometry and trig to find the rat