Download Modern Physics Lesson 3

Modern Physics Lesson 3.
The Compton Effect and Photon Momentum
Blue Book § 27-4, 5, 6
The photoelectric effect showed that a photon, or quantum of light, behaves like a
particle, since it has kinetic energy (even though it has no mass). This was a VERY BIG
DEAL since light had always been thought of as a wave before. Einstein proposed that
photons should also have momentum, and then showed that this momentum would equal:
p
h


hf
(since c  f )
c
Note also that
E  hf 
hc

 pc
(for a photon)
This theory was tested in 1922 by A.H. Compton. He directed X-rays (which have short
wavelength, therefore high energy) at a graphite target. The rays were scattered by the
atoms in the graphite. Compton measured that the scattered X-rays had a longer
wavelength, which means they had lost some energy and momentum in the scattering
process.
Unscattered rays (λ)
graphite
X-ray spectrometer
Scattered rays (λ’)
X-ray source
What happened to the “lost” energy and momentum? Compton looked and looked for it,
and found electrons being emitted from the graphite. He tested them and found that they
had the same amount of energy that had been lost by the photons in the X-rays.
It was as though the photon and electron had had an elastic collision (like billiard balls).
This was more evidence for the Quantum Theory. Energy and momentum were
conserved by the photons!!
Conclusion: A photon is a particle of light that has energy and momentum. However,
photons have no mass and travel at the speed of light, c.
deBroglie Wavelength
Louis deBroglie proposed in 1923 that if waves behave like particles, then particles
should also behave like waves! This was the beginning of the idea of WAVE-PARTICLE
DUALITY, the concept that everything has both wave and particle properties.
deBroglie’s calculation of the wavelength of any particle went like this:
p

h

h
p
or  
h
mv
This can obviously only be used for objects with mass (i.e., NOT photons). It is usually
used for electrons and protons, since they are the only objects that display noticeable
wave-like properties. Normal sized objects (like a book or a basketball) also have a
deBroglie wavelength, but it is so small that you could never notice it.
Experiments have backed up deBroglie’s idea – electrons and protons have been shown
to display diffraction patterns, a property that only waves have.
Example. Calculate the deBroglie wavelength of (a) a 1.0 kg basketball traveling at 0.50
m/s, and (b) an electron traveling at 150 m/s.
(1.3 × 10-33 m, 4.8 × 10-6 m)
HW.
Blue Book p. 853 Q13, 16, P27, 36 (3.2 × 10-32 m), 37