Photons
 Compton effect
 Dual nature of EM radiation
 Photons and matter: X-rays production,
electron-positron pairs
 Problems
Photons
Photons:
Electromagnetic energy is quantized into
localized bundles moving with velocity c and
having energy proportional to the frequency
and momentum inversely proportional to the
wavelength
E ph  h
p  k  h 
These particlelike bundles are called photons
Compton effect
Experimental arrangement:
Compton effect
Classical predictions:
em
waves incident on electrons should:
Have
radiation pressure that should cause
the electrons to accelerate
Set the electrons oscillating
Oscillating
electrons should emit in the
same frequency
Compton effect
Results:
• Compton’s experiments showed
that, at any given angle, one
additional frequency of radiation is
observed
Compton effect
Results:
h
 '0 
(1  cos  )  C (1  cos  )
me c
C  2.43 10 12 m
Dual nature of EM radiation
• To explain all experiments with EM radiation
(light), one must assume that light can be
descried both as wave (Interference, Diffraction)
and particles (Photoelectric Effect, Compton
Effect)
• Experimentally, it can be concluded that the
“shorter” the wavelength of light, the harder to
observe its wave properties
– For instance, wave properties of X-rays were observed
only when solids were used as diffraction grating
• Thus, as result of the observations, we have to
accept both models as true
Dual nature of EM radiation
• Wave and particle models of light
compliment each other
• Neither model can be used to exclusively
explain all properties of the light
• The wave and particle models relate to each
other via relationship between the
wavelength/frequency of light and the
momentum/energy of photon
E ph  h
ph 
Photons and matter
X-rays production:
Electrons are emitted
thermally from a heated
cathode and accelerated
toward the target. After
electrons hit target, xrays are emitted.
h  K  K '
Photons and matter
X-rays production:
h  K  K '
K  eV
If K’ = 0,
min
Number of
electrons
Accelerating
potential
Material
hc

eV
Photons and matter
Electron-positron pairs:
h  E  E  2m0c  K   K 
2
Problems
X-rays with a wavelength of 120 pm undergo
Compton scattering. (a) Find the wavelength
of the photons scattered at angles of 30°, 60°,
90°, 120°, 150°, and 180°. (b) Find the energy
of scattered electron in each case. (c) Which of
the scattering angles provides the electron
with the greatest energy?
Problems
After 0.8 nm x-ray photon scatters from a free
electron, the electron recoils at 1.4·106 m/s. (a)
What is the Compton shift in the photon
wavelength? (b) Through what angle is the
photon scattered?
Problems
Determine the maximal wavelength shift in
the Compton scattering of electrons and
protons.
Problems
Determine the Plank’s constant h from the
fact that the minimum x-ray wavelength
produced by 40 keV electrons is 3.11·1011 m
Problems
A particular pair is produced such that the
positron is at rest and the electron has a
kinetic energy of 1 MeV. Find the energy of
incident photon.