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 = mc 2)

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. 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: pipi photon electron Before photon pfpf  pepe After

11. Compton Scattering: Conservation of momentum Vector triangle: pipi pfpf pepe  Consider magnitudes of vectors p i, p f and p e :

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 c 2 (be careful!………)

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

15. Compton Scattering: Conservation of energy & momentum =

16. 

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………….