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3313 Andrew Brandt 1
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
min
1.24 10hcV 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 )h
mc c
h
mc
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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