The idea of the experiment is straightforward: Monochromatic X-rays with wavelength λ λ are incident on a sample of graphite (the “target”), where they interact with atoms inside the sample they later emerge as scattered X-rays with wavelength λ ′. The schematics of Compton’s experimental setup are shown in Figure 6.11. The explanation of the Compton effect gave a convincing argument to the physics community that electromagnetic waves can indeed behave like a stream of photons, which placed the concept of a photon on firm ground. The Compton effect has a very important place in the history of physics because it shows that electromagnetic radiation cannot be explained as a purely wave phenomenon. To explain the shift in wavelengths measured in the experiment, Compton used Einstein’s idea of light as a particle. Compton and his collaborators, and Compton gave its explanation in 1923. This classically unexplainable phenomenon was studied experimentally by Arthur H. Contrary to this prediction of classical physics, observations show that when X-rays are scattered off some materials, such as graphite, the scattered X-rays have different wavelengths from the wavelength of the incident X-rays. By classical theory, when an electromagnetic wave is scattered off atoms, the wavelength of the scattered radiation is expected to be the same as the wavelength of the incident radiation. The Compton effect is the term used for an unusual result observed when X-rays are scattered on some materials. We can verify that the magnitude of the vector in Equation 6.22 is the same as that given by Equation 6.18. Notice that this equation does not introduce any new physics. The magnitude of the wave vector is k = | k → | = 2 π / λ k = | k → | = 2 π / λ and is called the wave number. The propagation vector shows the direction of the photon’s linear momentum vector. Vector k → k → is called the “wave vector” or propagation vector (the direction in which a photon is moving). In Equation 6.22, ℏ = h / 2 π ℏ = h / 2 π is the reduced Planck’s constant (pronounced “h-bar”), which is just Planck’s constant divided by the factor 2 π. According to the theory of special relativity, any particle in nature obeys the relativistic energy equation For example, how can we find the linear momentum or kinetic energy of a body whose mass is zero? This apparent paradox vanishes if we describe a photon as a relativistic particle. From the point of view of Newtonian classical mechanics, these two characteristics imply that a photon should not exist at all. In a vacuum, unlike a particle of matter that may vary its speed but cannot reach the speed of light, a photon travels at only one speed, which is exactly the speed of light. Unlike a particle of matter that is characterized by its rest mass m 0, m 0, a photon is massless. This idea proved useful for explaining the interactions of light with particles of matter. A beam of monochromatic light of wavelength λ λ (or equivalently, of frequency f) can be seen either as a classical wave or as a collection of photons that travel in a vacuum with one speed, c (the speed of light), and all carrying the same energy, E f = h f. Beyond 1905, Einstein went further to suggest that freely propagating electromagnetic waves consisted of photons that are particles of light in the same sense that electrons or other massive particles are particles of matter. Two of Einstein’s influential ideas introduced in 1905 were the theory of special relativity and the concept of a light quantum, which we now call a photon. Describe how experiments with X-rays confirm the particle nature of radiation.By the end of this section, you will be able to:
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