Scattering of light
Physics 123
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Lecture XI
1
Test #1
• March 8- in lecture class (12:30-1:45pm)
• Equation sheet will be provided with the test
– Review it in advance – available on the web
• HW#6 is based on Chapters 33-37 to help you
prepare for the test
• Lecture #14 – review, send requests (e.g.
homework problems)
• HW#7 – light and conceptual, but more work
after spring break
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Lecture XI
2
Electron and EM wave
• Prediction from classical EM
• Electric field exerts a force on an electron 
acceleration electron radiates EM wave
• Oscillating electric field (frequency f) on
electron forced oscillator with the same
frequency  radiation at the same frequency f
• An electron will scatter EM wave frequency f,
wavelength l in all directions without changing
its frequency and wavelength.
• Rayleigh scattering
1

E
-
l4
• Blue-violet light gets scattered more than redorange  than is why the sky is blue
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Lecture XI
3
Photons – particles of light
• Photon= particle of light = quantum of light = gamma(g)-quant
• Each photon carries energy proportional to the frequency of the
EM wave:
Eg=hf=hc/l
• Photon has zero mass m0=0, it is always (and in any inertial frame
of reference) moving at the speed of light v=c
• Photon’s momentum can be calculated from relativistic formula
pg=h/l
E  p c m c  p c
2
2 2
2 4
0
2 2
E  pc
p  E/c  h/l
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Lecture XI
4
Collisions: Compton effect
• EM wave – collection of photons
• Light particle – photon scatters
of electron at rest:
Eg=Eg’+KEe
• Electron gets some energy 
photon looses energy
• Eg goes down  f goes down 
wave length l goes up:
l’>l
• Expect maximum change
(longest l) for back scattering
(fp)
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Lecture XI
KEe
Eg
Eg’
5
Compton effect
• Calculate wavelength of scattered
photon as a function of angle with
respect to its initial direction f
• Energy and momentum is conserved
Eg  Ee  me c  Eg '
Energy-momentum

 
pg  pe  p'g
conservation
Ee
Eg
2
E  pe c  me c
2
e
2 2
Eg  pg c
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2 4
Eg’
“Dispersion” equations
Relate energy, momentum and mass
Lecture XI
6
Compton effect
Ee  Eg  me c 2  Eg '



pe  pg  p'g
Ee
Eg
E  pe c  me c
2
e
2 2
2 4
Eg  pg c  hc / l
Eg’
( Ee  Eg  me c 2  Eg ' ) 2  Ee  Eg  me c 4  Eg '2 2( Eg  Eg ' )me c 2  2 Eg Eg '


 2 2
2
2
( pe  pg  p'g )  c  pe c 2  Eg  Eg '2 2 Eg Eg ' cos 
2
2
2
Ee  pe c 2  me c 4  2( Eg  Eg ' )me c 2  2 Eg Eg ' (1  cos  )
2
2
2
me c 4  me c 4  2( Eg  Eg ' )me c 2  2 Eg Eg ' (1  cos  )
2
2
( Eg  Eg ' )me c 2  Eg Eg ' (1  cos  )
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Lecture XI
7
Compton effect
Eg  pg c  hc / l
Ee
Eg
( Eg  Eg ' )me c 2  Eg Eg ' (1  cos  )
 hc hc (hc) 2 1
 ll '
 

(1  cos  )  
2
 l l ' me c ll '
 hc
h
l 'l 
(1  cos  )
me c
Eg’
h
l' l 
(1  cos  )
me c
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Lecture XI
8
Compton effect
h
l' l 
(1  cos  ) Always positive change
me c
Ee
Eg
f  0  cos   1  l '  l No change
~no interaction
2h Max change
f  p  cos   1  l '  l 
me c Back scattering
h
f  p / 2  cos   0  l '  l 
me c
Compton wavelength
Eg’
Note how small!
h
hc
1243eV  nm
3
lC 



1
.
4

10
nm  1.4 pm
2
6
me c me c
0.5 10 eV
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Lecture XI
9
Pair production
• A piece of antimatter Positron –
antipartner of electron – same
Emass, opposite charge
• When matter and antimatter meet
Eg
(positron and electron collide)
they annihilate – produce light
• It can go in the opposite direction
e+ after
as well
collision
• A photon can create matter, such
as the production of a positron
E+
and electron pair.
• Minimum energy of the photon
for pair production from energy
hc 1243eV  nm
conservation:
12
l



1
.
2

10
m
6
2
Eg=2mec =2 0.5MeV=1MeV
E
110 eV
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Lecture XI
10
Light interaction with matter
Eg
• Rayleigh scattering
• Photoelectric effect –
photon is absorbed and an
electron is knocked out
• Excitation – absorbed by
atoms that go to an excited
state. Atom goes to ground
state and emits a photon.
• Compton scattering –
wavelength is increased
• Electron-positron pair
production
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l
1-100 eV
500-10nm
~1-10 eV
~500nm
1-20 eV
500-100nm
0.5MeV
2.43pm
>1MeV
<1.2pm
Lecture XI
11
Light interaction with matter
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Lecture XI
12