Physics 3313 - Lecture 6

1. Physics 3313 - Lecture 6 Wednesday February 11, 2009 Dr. Andrew Brandt • What is Light? • X-Rays • Compton Effect • Pair Production 3313 Andrew Brandt

2. What is Light? • Both wave and particle theory needed. • Quantum theory: light has individual photons… but frequency is a wave phenomenon • Two different interpretations of intensity • Wave theory average magnitude of EM wave over a complete cycle • Photon description I=Nh • Both descriptions must give the same intensity if they are valid so • Consider double slit experiment: for large N observer looking at screen would see a double slit interference pattern (continuous distribution) • However, for small N, see a flash of light as one photon at a time goes through either slit (quantum phenomena), but if you wait a long time you would see an interference pattern • How can photon interfere with itself ? (sounds vaguely immoral) 3313 Andrew Brandt

3. What is Light (2)? • Must conclude that is the probability of finding a photon at a certain place and time—each photon has a wave associated with it; the intensity of wave a given place on the screen determines the likelihood that a photon will arrive there • Light travels as a wave, but deposits and absorbs energy like a particle (or a series of particles) • Wave-particle duality: need both pictures (outside of our everyday life experience!) • It not a wave nor a particle…it’s a WARTICLE 3313 Andrew Brandt

4. X-Rays • 1895 Roentgen found that when fast moving electrons strike matter a highly penetrating unknown radiation (X-Ray) is produced. He found certain characteristics of X-Rays: they 1) travel in straight lines 2) are unaffected by E+B fields (what does this imply) 3) can pass through opaque materials 4) can expose photographic plates • He also observed that faster electrons yield more penetrating X-Rays and that increasing the number of incident electrons yields higher intensity X-Rays 3313 Andrew Brandt

5. More X-Rays • Soon it became obvious that X-Rays are EM waves • Accelerating charges produce EM waves (basis for radio transmitters) • How does an electron produce X-Rays? • What happens as an electron interacts with matter? • It decelerates: bremsstrahlung (“braking radiation”) • Higher atomic number nuclei cause more energetic brem. (energy loss is more important for light particles like electron—NLC) 3313 Andrew Brandt

6. Measuring X-Ray Wavelength • Scattering of X-Rays off Crystal (draw) • Use crystals as a diffraction grating (need crystals since d must be on order of a wavelength () for diffraction effects to be observed and  is very small (0.01 to 10 nm) for X-Rays. • Small wavelength implies large , so if X-Ray has several orders of magnitude smaller wavelength than light, it has several orders of magnitude higher energy 3313 Andrew Brandt

7. Inverse P.E. Effect • X-Ray production is an inverse photoelectric effect: electron in/photon out, instead of vice-versa • Small wavelength implies large , so if X-Ray has several orders of magnitude smaller wavelength than light, it has several orders of magnitude higher energy • For photoelectric effect: • For X-Rays can neglect binding energy, since X-Ray is so energetic: where V is the accelerating potential of X-Ray machine and the frequency is maximum when the electron gives all of its energy to a single photon • Duane-Hunt formula for X-Ray production: 3313 Andrew Brandt

8. Compton Effect • Can photon be treated like a particle when it interacts with an electron? • Consider conservation of momentum and energy, and also have an additional constraint that the loss in photon energy yields an equivalent gain in electron KE: 3313 Andrew Brandt

9. Compton Effect • some math occurs on blackboard yielding: • where is called the Compton Wavelength, and has a value of 2.4 pm for electrons • this is largest when? • Compton scattering is the main way that X-Rays lose energy when passing through matter; visible light has long wavelength so small wavelength shift is less noticeable • Experimentally Compton effect initially not verified! • The problem was that electrons in matter are not free—some are tightly bound and if whole atom recoils the large mass implies a small wavelength shift (when this is corrected for, the Compton picture is validated) 3313 Andrew Brandt

10. Pair Production • In pair production a photon of sufficient energy can create an electron/positron pair. • How much energy? • Charge conserved, for energy and momentum conservation need the nucleus (Ex. 2.5) • Opposite of pair production is annihilation 3313 Andrew Brandt

11. Energy Loss in Matter 3313 Andrew Brandt

12. Photons and Gravity for v=c effective mass of photon, implies light affected by gravity Black hole—so much gravitational force that photons cannot escape 3313 Andrew Brandt