Physics 241 Modern Physics I

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Physics 241Modern Physics I

• Chapter 3
• The particlelike Properties of Electromagnetic
  Radiation
• Section 3.4, 3.5

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The Compton Effect

• Another way of radiation interaction with atoms.
• In Compton effect, radiation scatters from
  loosely bound, nearly free electron.
• Part of the radiation energy is transferred to
  the electron and the remainder of the energy is
  reradiated as EM waves.

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The Compton Effect
Scattered photon
Incident photon
E, p
Ee , pe
E, p
Scattered electron
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The Compton Effect
Conservation of Energy Einitial Efinal
E mec2 E Ee
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The Compton Effect
Conservation of Momentum (x-component)
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The Compton Effect
Conservation of Momentum (y-component)
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The Compton Effect
Squaring and adding
The relativistic energy,
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The Compton Effect
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The Compton Effect
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The Compton Effect
Using
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The Compton Effect
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The Compton Effect
Compton wavelength of the electron
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The Compton Effect
X ray Source
Detector
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The Compton Effect
Detector
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The Compton Effect
Detector
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The Compton Effect
Detector
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The Compton Effect
Detector
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The Compton Effect
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The Compton Effect
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The Compton Effect
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The Compton Effect
?-Ray
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X-Ray
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75
74
5
Slope 2.4 x 10-12 m
73
4
Slope 2.4 x 10-12 m
72
3
71
70
2
0
1
2
0
1
2
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The Compton Effect
Example What is the maximum wavelength shift for
a Compton collision between a photon and a free
proton?
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The Compton Effect
Example Show that ?E/E, the fractional loss of
energy of a photon during a collision with a
particle of mass m, is given by
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Other photon processes
Bremsstrahlung and X-ray Production
V
C
A
X-ray photon
h?
Electron
K
K
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Other photon processes
Bremsstrahlung and X-ray Production
h?
X-ray photon
Electron
K
K
Maximum photon energy when the electron loses all
its energy.
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Other photon processes
Bremsstrahlung and X-ray Production
Relative Intensity
0
0.10
0.02
0.04
0.06
0.08
Wavelength (nm)
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Other photon processes
Bremsstrahlung and X-ray Production
In Bremsstrahlung process electron ? electron
photon
Reverse processes
In photoelectric effect electron photon ?
electron
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Other photon processes
Pair Production (????? ???????? ???????)

• IDEA
• Another process when photons encounter atoms.
• The photon loses all its energy and a pair of
  particle is created an electron and a positron.
• The photon energy is converted into the
  relativistic total energies E and E- of the
  positron and the electron

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Other photon processes
Pair Production
Photon
Electron
E mec2 K-
E mec2 K
E h? E gt 2mec2
Positron
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Other photon processes
Pair Production
Electron
Photon
E- mec2 K-
E mec2 K
E h? E gt 2mec2
Positron
photon ? electron positron
h? E E- (mec2 K) (mec2 K-)
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Other photon processes
Pair Annihilation (???? ???????? ???????)
electron positron ? photon
(mec2 K) (mec2 K-) E1 E2
Conservatin of momentum requires that the two
photons to have equal energies of mec2 ( 0.511
MeV)
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Other photon processes
Pair Production
Photon
E h? E gt 2mec2
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Other photon processes
Example A beam of 35.0 keV electrons strikes a
molybdenum target. What is the cutoff wavelength?
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What is a Photon?
They move with the speed of light They have zero
rest energy They carry energy and momentum Eh?,
ph/? They can be emitted and absorbed They can
have particlelike collisions
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What is a Photon?
Wave
They move with the speed of light They have zero
rest energy They carry energy and momentum Eh?,
ph/? They can be emitted and absorbed They can
have particlelike collisions
Particle
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What is a Photon?
Wave
They move with the speed of light They have zero
rest energy They carry energy and momentum Eh?,
ph/? They can be emitted and absorbed They can
have particlelike collisions
Particle
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What is a Photon?
Laser
B
Mirror
Splitter
A
Switch
Splitter
Mirror
Interference pattern
Detector
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What is a Photon?
Laser
B
Mirror
Splitter
Wave property detection
A
Switch
Splitter
Mirror
Particle property detection
Interference pattern
Detector
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What is a Photon?
An incident photon can be reflected from one atom
(particlelike property) of form both atoms
(wavelike property). The reflection can be
detected using the polarizer (P)
Incident light
Ion trap
L
P
D
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What is a Photon?
Wave-particle dulaity No single experiment can
detect both particle and wave properties of a
photon.
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Summary

• The Photoelectric Effect h? Kmax F
• Blackbody Radiaton
• Steafans law ?max a 1/T
• Wiens disp. law ?maxT 2.898x10-3 m.K
• Rayleigh-Jeans R(?) (8p/?4) (kT) (c/4)
• Planck R(?) (c/4) (8p/?4) (hc/?) (ehc/?kT-1)-1
• Compton Effect ? - ? (h/mec) (1-cos ?)
• Wave-particle duality