Physics Lecture 6 2/11/ Andrew Brandt Wednesday February 11, 2009 Dr. Andrew Brandt 1.What is Light? 2.X-Rays 3.Compton Effect 4.Pair Production

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) 2/11/ Andrew Brandt2

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 2/11/ Andrew Brandt3

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 2/11/ Andrew Brandt4

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) 2/11/ Andrew Brandt5

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 2/11/ Andrew Brandt6

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: 2/11/ Andrew Brandt7

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: 2/11/ Andrew Brandt8

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) 2/11/ Andrew Brandt9

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 2/11/ Andrew Brandt10

2/11/ Andrew Brandt11 Energy Loss in Matter

2/11/ Andrew Brandt12 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