Compton Effect

The Compton Effect for Beginners http://www.pdfcoke.com/doc/20246003/Compton-Effect David S. Latchman September 26, 2009 When I was a Physics undergraduate student at the University of the West Indies, the lecturer to my Modern Physics course, a guest professor, often challenged us to explain the concepts of Quantum Mechanics as plainly as possible; if you couldn’t explain it while standing on one foot in thirty seconds, then maybe you needed to study more. What would you say to your grandmother, who supposedly was paying your tuition, if she asked you to explain the Compton Effect? What did the Compton Effect mean and why was it so important? Physicist often find comfort in the language of mathematics, grasping the subtleties of its meaning from the equations they write. But, for the average person, who may have been only too glad to drop that language after high school, may not find the same comfort that we scientists do. If anything, the various equations are an unintelligible mess and left without a Rosetta stone, they often surrender and move on to something else. So I have decided to answer that professor’s challenge (though it is a bit late in coming) and explain the Compton Effect, not to my grandmother (though I am sure she will appreciate it anyway), as plainly as possible and why is it so important. Best of all, those who have been traumatized by their math teachers in high school have nothing to fear. Mathematics will be kept to a minimum; I will introduce two equations and not one more. The Compton Effect describes the effect seen when a monochromatic (single color or frequency) photon, an X-ray in this case, scatters off an atomic target. In this case, we observe a frequency shift as the photon scatters off the atomic particle. If this is still confusing then think of it in this way. Imagine you were playing a game of pool with the 8 ball sitting in the middle of the table. You carefully aim up your shot to sink the No. 2 ball (the blue one) into the pocket but you miss and instead the blue ball hits the 8 ball. As to be expected, the balls hit each other and both fly off in different directions. Hopefully you haven’t sunk the 8 ball and the game goes on. Nothing strange there but in the world of quantum mechanics something strange DOES happen. The 2 ball changes color and becomes red! It still has the number 2 printed on it but only the color has changed. What gives? To explain this, we needed to turn to the new theory (in time of the 1920’s it was new) of Quantum Mechanics. In the 1920’s the particle nature and its possible implications was still being hotly debated after Einstein’s discovery of the photoelectric effect. A. H. Compton, in 1923, performed the decisive experiment of bouncing X-Ray photons off electrons that provided direct evidence of the particle nature of light. One of the puzzling aspects that needs to be grasped, is that the energy of a photon is related to its frequency and not its speed. In fact, the speed of light in a vacuum is constant wherever you go in the Universe. This is quite different from our everyday world of cars and busses. If a car or bus goes faster we can all agree that it has more kinetic energy. In Physics, we write this as 1 (1) E = mv 2 2 where m is the mass of the particle and v is its speed. This works well in our everyday experience but if light moves at a constant speed, does that mean it has constant energy? No, far from it. In fact, the energy of a photon is related to its frequency, or as we said above, its color. We even have an equation for it. It is E = hf (2) where h is Plank’s constant and f is the frequency of our light particle. We won’t focus too much on what h is or what is its value. All you need to grasp is that there is a relationship between E and f for a photon. If f is larger, the photon has more energy and if it is smaller, it has less energy. 1

Now that we have that concept in mind, we can now ask ourselves the question, what happens when a photon “collides” with an atomic particle. Well, if we think about it, when we play pool and one ball hits a stationary ball, the moving ball looses energy and the stationary ball gains energy. A similar thing happens. In the Compton Effect, the photon looses some of its energy upon collision and the particle gains that energy. But we have to keep the photon energy in mind, when a photon looses energy, its color changes; it moves from a higher frequency to a lower one. This is analogous to the color change of blue to red. Of course, X-Rays aren’t blue or red but what is important to realize is that their frequency changes and the speed of the photon always remains the same. It is this observed frequency shift that defines the Compton Effect. And that is the Compton Effect explained as simple as you can get. See? It really wasn’t that hard and once you get the concepts down, any subject becomes easy. As to the importance of this experiment? Well, before Quantum Mechanics came along, the debate between whether light was a particle or a wave was settled; scientists had decided that it was a wave. This model worked remarkably well until we observed and had to explain how light interacted with matter. We simply did not have a model in which light, as a wave, interacted with matter. By treating light as a particle we are able to explain some of the phenomena we see. It is for this reason that A. H. Compton won the Nobel Prize in 1927.

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