The Compton Effect

The Compton Effect The beginning of the 20th century saw the classical theory of electromagnetism challenged by Einstein's discovery of the photoelectric effect, which introduced the idea of light being a stream of particles. But for the physics community to adopt this revolutionary idea, further experimental evidence needed to be brought forward. Enter Arthur Compton. In 1922 Compton performed an experiment in which he shot x-ray beams towards a graphite target. These beams were then scattered from the graphite towards a detector, which was placed at an angle theta with respect to the direction of the incident beam. Compton placed the detector at various angles, measuring the intensity of the scattered beams as a function of wavelength. Throughout the experiment, he kept the wavelength of the incident beam constant, but he found that there were intensity peaks in the scattered beam corresponding to two different wavelengths. What's more, the difference between these two wavelengths was getting larger and larger as the angle of scattering increased. This result was surprising, because classical electromagnetism predicts no wavelength shift between the two beams. But the experiment clearly showed larger wavelengths in the scattered beam. Compton used Einstein's photon model of light to explain his findings. He considered each beam of x-rays as a stream of high-energy photons, which each collided with an electron from the In this collision, the photon transferred some of its energy to the electron and scattered at an angle theta with respect to its initial direction. So the scattered photon had lower energy than the incident photon. But what does that say about its wavelength? From the Planck-Einstein relation, we know that each incident photon has energy equal to Planck's constant times the frequency. Since frequency is equal to the speed of light divided by the wavelength, we can easily arrive to this, and see that the energy of a photon is inversely proportional to its wavelength. This means that the scattered photon must have a larger wavelength if it loses some of its energy, which is in perfect agreement with the experiment. By assuming the collision was elastic, Compton used the principles of conservation of momentum and conservation of energy to derive an equation for the amount by which the wavelength increased, now known as the Compton shift. What's interesting to note is that the wavelength shift only varies with the angle of scattering, because all the other quantities in the equation are constants. By plugging in different values for the angle theta, we can see that the Compton shift increases, much like in the experiment discussed earlier. Nevertheless, the photon model of light is able to explain the appearance of the second peak at lambda prime. But what about the first one? As you can see on the graph on the right, there are two peaks at different wavelengths. But how does this occur? The second peak occurs due to Compton scattering, as explained before, and shown here. The first peak occurs because the photon strikes an inner electron, and since it's an inner electron, it will usually have a binding energy greater than the energy of the incident photon. This means that the electron does not escape the atom, therefore the result is that the photon scatters off the entire atom. So the photon still transfers momentum, however, this time to the entire atom rather than just an electron. The momentum is however so small in comparison to the atom that it hardly moves. The incident photon and the scattered photon still have different wavelengths. However, because it's being scattered off the much heavier atom, the change in wavelength is tiny, and therefore the scattered photon essentially has the same wavelength as the incident photon. This effect is shown here. Applications of Compton scattering. The first application is Compton scattering imaging, which is used a lot in research. It uses spectral scattered radiation to gain information about the material we want to test, and we can easily tell where the material has flaws. Like in this diagram, we can shoot a ray into the test spaceman, then the detector will receive information from the defined volume V, and after a series of calculations, we will get the information for the entire spaceman. These are some other applications of Compton scattering. The imaging technique can be used for security purposes. For instance, airport security can check whether you have brought a bomb with you to blow up the airplane. It is also commonly used in agriculture and food processing. You can detect impurities in food and make sure you do not have any pieces of glass, for example, in your rice. Medical uses like radiotherapy, osteoporosis testing, and lung function testing are also possible thanks to Compton scattering.