Of Photons and Electrons

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Of Photons and Electrons

• Compton Effect, Pair Production and X-Rays

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What Is a Photon?

• Massless particle
• Travels with speed of light c 3.0x108 m/s
• Has momentum p E/c
• But E hf
• p E/c hf/c h/l l h/p

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Photon Interactions With Matter

• Photoelectric Effect photon knocks electron out
  of atom and disappears
  
• Compton Effect photon scatters off electron and
  loses energy (frequency)
  
• Atomic excitation electron takes all of
  photons energy and goes to higher energy state
  
• Pair Production photon disappears, electron and
  positron created

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Compton Effect

• Used in astronomy to detect violent events in
  distant galaxies
  
• Used in nuclear medicine to treat cancer

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Compton Effect is a Collision Between Photon and
Electron Resulting in a Lower Energy Photon
Courtesy OSHA http//www.osha-slc.gov/SLTC/radiof
requencyradiation/rfpresentation/ionizinglectur/sl
idepresentation/mainpage.html
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Question

• What happens to the wavelength of a photon after
  it Compton scatters?
  
• (a) increases
• (b) decreases
• (c) remains the same

Dont forget Wavelength and frequency are
inversely related
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Wavelength Increases

• l l (h/moc)(1 - cos f)
• f is angle of scattered photon with incident

e- after collision
Incident photon
f
Scattered photon
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Compton Effect in Astronomy
The Imaging Compton Telescope (COMPTEL) utilizes
the Compton Effect and two layers of gamma-ray
detectors to reconstruct an image of a gamma-ray
source in the energy range 1 to 30 million
electron volts (MeV).
Graphics courtesy NASA Goddard Spaceflight Center
Lab for High Energy Astrophysics
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What the Compton Telescope Sees the Gamma Ray
Universe
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Cobalt 60 Gamma Ray Irradiation for Cancer
Treatment
Radiologists must understand how gamma rays
interact with tissues in the body.
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Pair Production

• Involves creation of antimatter
• Minimum energy photon is 2mec2

e
photon
e-
2 x 9.11x 10-31 kg x(3.0x108 m/s)2 1.64x10-13 J
1.02 MeV
Rest Energy of one electron is 0.51 MeV
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What Happens to the Positron?

• It annihilates electron at rest positron and
  electron rest mass converts to photon energy
  
• Produces two photons of energy 0.51 MeV each
• Photons must be emitted back to back to
  conserve momentum

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Find Wavelength of 1.02 Mev Photon

• l

h/p hc/E
(6.6 x 10-34 J-s)(3.0 x 108 m/s)/(1.64x10-13 J )

1.2 x 10-12 m
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X -Ray Production

• When high speed electrons (30 150kV)slam into a
  metal target (usually tungsten)x-rays are given
  off
  
• X-Rays are EM
• radiation with
• wavelength about
• 10-2 - 1 nm

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Wavelength of an X-Ray

• Find the wavelength of the maximum energy x-ray
  that can be produced by 100 kV electrons
  

h 6.63 x 10-34 J-s
l c/f hc/hf hc/E (6.63 x 10-34 J-s)(3x108
m/s)/(100 keV)x(1.6 x 10-16 J/keV) 0.012 nm
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X-Ray Emission by Atoms

• Atoms become excited higher energy state
• Give off x-rays when they decay to ground
  state
  
• Inner electrons are involved- much higher energy
  than outer electrons
  

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X-Rays Applied

• CAT scan of dinosaur egg

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X-Ray Diffraction

• Like visible light x-rays diffracts when it hits
  small objects
  
• Produces circular rings
• Effect is pronounced for atomic spacings around
  10-10 m
  
• Used to study complex organic molecules such as
  DNA

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X-Ray Diffraction Image Courtesy Nonius B.V.
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Particle or Wave?
Niels Bohr 1885-1962

• Young 2 Slit - WAVE
• Photoelectric and Compton Effect PARTICLE
• Light has DUAL nature
• Bohr principle of complementarity- to understand
  any given experiment use wave theory or photon
  theory not both
  

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What Equation Links the Wave and Particle
Properties?

• E hf
• E is energy of a particle
• f is frequency of a wave
• You cannot have a visual picture of light which
  is correct for all situations

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Wave Nature of Matter

• De Broglie (1923) Deep symmetry of nature
  requires that if l h/p for photon, particles
  have a wavelength
  
• l h/p h/mv
• Called De Broglie wavelength

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Wavelength of a Baseball

• Find the wavelength of a 0.20 kg baseball
  traveling 15 m/s

H6.6 x 10-34J-s

• h/mv (6.6 x 10-34 J-s)/(0.20 kg)(15 m/s)
• 2.2 x 10-34 m

Too small to have observable effects
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Wavelength of an Electron

• Find the wavelength of a 100 eV electron

v (2eV/m)1/2 (2 x 1.6 x 10-19 J/eV x 100V /
9.1 x 10-31 kg)1/2
5.9 x 106 m/s
l h/mv (6.6 x 10-34 J-s)/(9.1 x 10-31
kg)/(5.9 x 106 m/s) 1.2 x 10-10 m
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What If Electron Wavelength is Comparable to
Interatomic Spacings?

• Crystal spacings about 10-10 m
• Could electrons diffract like x-rays?
• YES, according to Davisson Germer experiment
  (1927)

Typical Electron Diffraction pattern from a
crystal. Courtesy http//www.matter.org.uk/diffr
action/electron/electron_diffraction.htm
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Davisson- Germer Experiment
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Set-up for Electron Diffraction by
Back-Scattering(reflection)
Courtesy http//www.chem.qmw.ac.uk/surfaces/scc/s
cat6_2.htm
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Transmission Electron Scattering of Germanium
Courtesy Northwestern University Materials
Science Dept.
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What is an Electron?

• Particle or wave?
• Use wave model when it works
• Use particle model when it works
• Electron is merely its measurable properties, a
  logical construction.

Cathode Ray Tube used by J.J. Thompson in his
discovery of the Electron. Photos courtesy
American Institute of Physics