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PHY 102: Waves & Quanta Topic 10 The Compton Effect John Cockburn (j.cockburn@... Room E15)

PHY 102: Waves & Quanta Topic 10 The Compton Effect John Cockburn (j.cockburn@... Room E15). Photons: summary so far. Einstein postulated the existence of a particle called a photon, to explain detailed results of photoelectric experiment. Photon has zero rest mass, travels at speed of light

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PHY 102: Waves & Quanta Topic 10 The Compton Effect John Cockburn (j.cockburn@... Room E15)

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  1. PHY 102: Waves & Quanta Topic 10 The Compton Effect John Cockburn (j.cockburn@... Room E15)

  2. Photons: summary so far • Einstein postulated the existence of a particle called a photon, to explain detailed results of photoelectric experiment. • Photon has zero rest mass, travels at speed of light • Explains “instantaneous” emission of electrons in photoelectric effect, frequency dependence. • Further confirmation of the photon picture provided by the COMPTON EFFECT (1922-23)…………………

  3. A little bit about relativity…… • Einstein’s Special Theory of Relativity, 1905: • The laws of physics are the same in every inertial frame of reference (in which Newton’s first law is valid) • The speed of light in a vacuum is the same in all inertial frames of reference, and is independent of the motion of the source. • (corollary: the velocity of light can’t be exceeded) • Many important consequences: length contraction, time dilation effects at high speeds, mass/energy equivalence……

  4. A little bit about relativity…… Momentum and kinetic energy at high speeds…………….

  5. Relativistic expressions for energy and momentum (energy of stationary particle = mc2)

  6. Relativistic expressions for energy and momentum

  7. consequently, particle with zero rest mass (eg photon) has momentum p given by:

  8. The Compton Effect • x-rays scattered from target containing very loosely bound electrons • Wavelength of scattered x-rays found to be different from that of incident X-rays AND to depend on detection angle :

  9. The Compton Effect

  10. photon electron Before pi photon pf After  pe Compton Effect explained by photon model: Treat Compton scattering as a 2-particle collision between photon and initially stationary electron, obeying conservation laws for energy and momentum:

  11. Vector triangle: pf pe  pi Compton Scattering: Conservation of momentum Consider magnitudes of vectors pi, pfand pe:

  12. Compton Scattering: Conservation of energy We are dealing with velocities at, or close to, speed of light so need to use relativistic expressions: Initial energy: Final energy general expression

  13. Compton Scattering: Conservation of energy Divide both sides by c2 (be careful!………)

  14. Compton Scattering: Conservation of energy & momentum Energy momentum

  15. Compton Scattering: Conservation of energy & momentum =

  16. Compton Scattering: Conservation of energy & momentum 

  17. Compton Scattering: Summary The observed experimental result: Is entirely explained by the photon-electron scattering model. Further proof of the validity of the photon concept. • maximum wavelength shift for  = 180°, Δλ=2h/mc • h/mc is known as the COMPTON WAVELENGTH of the electron. • very small (work it out!) so Compton effect only observed for short wavelength radiation (x-rays, gamma rays)

  18. A final word…. We’ve seen that light can be described as a stream of particles called photons, but we don’t have to take this picture too literally. Instead can think of the situation as the electromagnetic wave exchanging energy and momentum with a charged particle in quantised amounts………….

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