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Physics 3313 - Lecture 6

2/11/2009

Wednesday February 11, 2009Dr. Andrew Brandt

1. What is Light?2. X-Rays3. Compton Effect4. Pair Production

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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)

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2

0I cE

2N E

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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

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2E

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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

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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)

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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

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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:

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maxeV hv

6

min1.24 10hc V m

eV V

h max 0KE eV

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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:

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hv hv KE

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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)

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(1 cos )hmc

chmc

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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

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22 .511 2em c MeV

e e

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Energy Loss in Matter

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Photons and Gravity

hpc

hmvc

2

hvmc

E pc h

for v=c

effective mass of photon, implies light affected by gravity

Black hole—so much gravitational force that photons cannot escape