37.1 - The Compton effect
Compton effect: Considering x-rays as
composed of particles explains why their
frequency diminishes as they are scattered by a
material.
Einstein stated that light was composed of indivisible packets of energy. His theory was
rooted in experiment. By treating light as a particle he could explain the photoelectric
effect and make successful predictions: Calculating the energy of the photons that
make up light of a particular color allowed Einstein to predict whether shining that color
light on a given material would cause it to emit electrons.
This opened up another question: Did light have other particle properties, such as
momentum? In 1916, Einstein derived an equation quantifying a photon’s momentum.
As shown in Equation 1, the momentum equals Planck’s constant divided by the
photon’s wavelength. However, it remained to be shown experimentally that photons
actually had momentum. Some scientists believed that the photoelectric effect might be
explained by updating the wave theory of light, but if light could be shown to have
momentum then it would be hard to deny its particle-like nature.
Physicists such as W.H. and W.L. Bragg í a famous British father-and-son pair í had
been using x-rays to analyze the structure of matter, particularly crystals. The small
wavelengths of x-rays, compared to the atomic spacing in the crystals, meant that the
scattered radiation would exhibit diffraction patterns, that is, the radiation would be
strong in particular directions. The diffraction pattern could be used to analyze the
regular, periodic layout of atoms within crystals, and this technique was later used to
deduce the double-helix structure of DNA. Since diffraction is a property only of waves,
you might think that x-ray diffraction experiments could not provide any support for a
particle view of electromagnetic radiation í but as it turned out, they did.
Scientists experimenting with x-rays scattering from target materials started to observe
some disturbing data. To explain their discomfort, we first have to explain what they
expected.
Their expectations were based on the view of light as an electromagnetic wave,
consisting of oscillating electric and magnetic fields. In this classical picture, when an
electromagnetic wave encounters an atom, it causes the atom’s electrons to oscillate at
the same frequency as the wave. Accelerating charges emit radiation, so these
oscillating charges then radiate their own electromagnetic waves. This process is called
scattering; some waves would be re-emitted in the same direction as the initial wave,
while others would be re-emitted in other directions.
The critical point to focus on is the frequency of the re-radiated waves. Classical
electromagnetic theory, used by scientists like the Braggs, predicted that the outgoing
waves should have the same frequency as the incoming waves. Scattering would
change the direction of the incoming radiation, but scientists were confident that it
should not change its frequency.
Alas, observations did not accord with theory. Scientists observed that atoms being
subjected to x-rays were re-emitting radiation of lower frequency than the initial
radiation, and the effect depended on the angle at which the radiation was scattered.
Something was diminishing the frequency (and the energy) of the scattered radiation.
At first, the data were not taken seriously. However, in 1923 the American physicist A.
H. Compton published two papers that argued conclusively that if radiation were
quantized, one should expect the frequency to be reduced. The problem was not with
the experimental data; the problem was with a theory that regarded light solely as a
wave.
How did Compton explain the discrepancy? He assumed that the electromagnetic radiation was made up of photons that had momentum. He
proposed that instead of picturing a light wave shaking electrons up and down, scientists ought to picture the interaction as akin to a collision
between two particles, a photon and an electron. Like Einstein, he was asking his peers to expand their conception of radiation to include
properties usually associated with particles, such as momentum.
He then used classical mechanics, applying the laws of conservation of energy and momentum to the collision. He applied the same principles
that would be applied to a collision of two billiard balls. (His analysis had to be more complex than that for two balls, because he had to relate
the quantized photon energy to wavelength and frequency, and relate its energy and momentum.)
Compton stated that when the photon in question collides with an electron belonging to an atom in the target, the electron gains some kinetic
energy from the collision. Energy must be conserved, and the photon loses that same amount of energy. The energy of a photon equals hf, the
product of Planck’s constant and its frequency. When its energy is diminished in the scattering process, so too is its frequency.
Electromagnetic radiation as
wave
When an x-ray met a crystal:
·Scientists anticipated its frequency
would stay the same
·They were wrongCompton effect
Consider x-ray as a photon (particle)
A photon “collides” with an electron in
the crystal
Photon loses energy in collision
Less energy means lower frequency (E
=hf)