Four vector derivation of compton effect12/11/2023 ![]() ![]() I won’t go over how we derive them, because I’ve done it more than once. And you guys should be really on top of those two marvelous equations, because all the stuff we are doing is a consequence of that. Professor Ramamurti Shankar: Let me remind you that everything I did so far in class came from analyzing the Lorentz transformations. \boldsymbol backward on the car.Fundamentals of Physics I PHYS 200 - Lecture 14 - Introduction to the Four-VectorĬhapter 1: Recap-Consequences of the Lorentz Transformations (See Figure 2) He won a Nobel Prize in 1929 for the discovery of this scattering, now called the Compton effect, because it helped prove that photon momentum is given by Energy and momentum are conserved in the collision. This phenomenon could be handled as a collision between two particles-a photon and an electron at rest in the material. Around 1923, Compton observed that x rays scattered from materials had a decreased energy and correctly analyzed this as being due to the scattering of photons from electrons. Some of the earliest direct experimental evidence of this came from scattering of x-ray photons by electrons in substances, named Compton scattering after the American physicist Arthur H. Momentum is conserved in quantum mechanics just as it is in relativity and classical physics. We expect particles with mass to have momentum, but now we see that massless particles including photons also carry momentum. Not only is momentum conserved in all realms of physics, but all types of particles are found to have momentum. Gas atoms and molecules in the blue tail are most affected by other particles of radiation, such as protons and electrons emanating from the Sun, rather than by the momentum of photons. Evidently, photons carry momentum in the direction of their motion (away from the Sun), and some of this momentum is transferred to dust particles in collisions. The dust particles recoil away from the Sun when photons scatter from them. Comet tails are composed of gases and dust evaporated from the body of the comet and ionized gas. What most people do not know about the tails is that they always point away from the Sun rather than trailing behind the comet (like the tail of Bo Peep’s sheep). Navy, via Wikimedia Commons)įigure 1 shows a comet with two prominent tails. ![]() ![]() The blue ionized gas tail is also produced by photons interacting with atoms in the comet material. Particles of dust are pushed away from the Sun by light reflecting from them. Dust emanating from the body of the comet forms this tail. The tails of the Hale-Bopp comet point away from the Sun, evidence that light has momentum. Figure 1 shows macroscopic evidence of photon momentum. In fact, photon momentum is suggested by the photoelectric effect, where photons knock electrons out of a substance. (Maxwell and others who studied EM waves predicted that they would carry momentum.) It is now a well-established fact that photons do have momentum. Despite photons having no mass, there has long been evidence that EM radiation carries momentum. Particles carry momentum as well as energy. Massive quanta, like electrons, also act like macroscopic particles-something we expect, because they are the smallest units of matter. A photon interacts as a unit in collisions or when absorbed, rather than as an extensive wave. The quantum of EM radiation we call a photon has properties analogous to those of particles we can see, such as grains of sand. Account qualitatively for the increase of photon wavelength that is observed, and explain the significance of the Compton wavelength.Relate the linear momentum of a photon to its energy or wavelength, and apply linear momentum conservation to simple processes involving the emission, absorption, or reflection of photons. ![]()
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