![]() Note that conservation law (I) (conservation of momentum) is a landmark equation in the history of physics. Multiply by 2π and use that (1-cos θ) = 2 (sin θ/2) 2 Substitute this into (II) and divide through by cℏ,īring mc/ℏ to the left-hand side and square the equation, Noting that v = 0 gives p = 0 and E = mc 2, one has the energy (scalar) equation with on the left-hand side the energy of the system (electron plus photon) before scattering and on the right-hand side the energy of the system after scattering: (I) Conservation of momentum (a vector equation):Īnd (II) conservation of energy. ![]() So that the relativistic energy of a particle with rest mass m and magnitude of momentum p is,Ĭompton's derivation is based on two conservation laws. It is convenient to express the energy E in terms of p (the modulus of p). After scattering it has non-zero velocity v and corresponding energy and momentum. The energy of the incident photon is ℏck, where c is the speed of light.Ī relativistic particle, such as an electron, with velocity v and rest mass m has kinetic energy E and momentum p,īefore scattering the electron has velocity v = 0 and hence energy After scattering the photon has wave vector k′ and wavelength λ ′. The electron is hit by a photon of momentum ℏ k, where k is the wave vector and ℏ is Planck's constant divided by 2π,Īnd λ is the wavelength of the incident light. ![]() Without knowing about the uncertainty relation between momentum and position, Compton considers a free electron at rest positioned at certain point in space. It is, however, based on Einstein's theory of special relativity. The derivation of equation (1) by Compton predates the new quantum mechanics of Heisenberg, Schrödinger, Dirac and others. Electrons having wave character is also a form of wave-particle duality. The particle and wave points of view being simultaneously true is known as wave-particle duality.Ĭompton received the Nobel in Physics in 1927 for "his discovery of the effect named after him." His discovery came almost simultaneous with the discovery of Louis de Broglie that particles, such as electrons, have wave character. Compton's observation implies that light can be seen as a stream of corpuscles as well in agreement with Isaac Newton's view (ca. Later it was shown that this holds for electromagnetic radiation of all wavelengths, including X-rays. It was known since the 19th century that visible light consists of waves. Compton's work showed that (X-ray) photons not only have energy, but also momentum, just like ordinary (nonzero rest mass) particles. Already in 1905 Albert Einstein had proposed that electromagnetic radiation, such as X-rays, consists of energy parcels (photons). The scattering was observed and theoretically explained in 1922 by Arthur Holly Compton (1892-1962) who gave his name to the effect. The quantity h/(mc) is known as the Compton wavelength of the electron it is equal to 2.43×10 −12 m. The Compton effect showed for the first time that the photon has a momentum with a well-defined direction, a vector. Where h is Planck's constant, m is the rest mass of the electron and c is the speed of light. Noteworthy is the fact the energy transfer depends on the angle θ between the incident and scattered ray: During the scattering some energy of the photon is transferred to the electron with the consequence that the wavelength λ′ of the scattered X-rays is longer by an amount Δλ than of the incident X-rays. ![]() The Compton effect is the scattering of an X-ray photon off a free, or nearly free, electron. Incident ray of wavelength λ scattered by free electron (black sphere) that receives momentum (black arrow) Δλ = λ′−λ > 0.
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