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Compton Scattering : final proof for the existence of photons. In 1923, Arthur H. Compton illuminated graphite (a form of carbon) with X-rays. In 1923, methods of measuring the wavelength of X-rays were already well developed. So, since the frequency is related to
In 1923, Arthur H. Compton illuminated graphite (a form of carbon)
In 1923, methods of measuring the wavelength of X-rays
were already well developed. So, since the frequency is related to
as = c/, Compton knew the values of and of the incident
Compton observed that
the scattered radiation
has a longer wavelength
than the incident radia-
On the grounds of the
wave theory, it is im-
possible to explain
the change of
According to the wave theory, in any conceivable
Scattering process the radiation frequency must
Be conserved! (and thus ).
Compton explained the results of his observations
in terms of Einstein’s photon theory. In 1923, the
photon theory was not yet widely accepted. Many
physicists, including most prominent, still expres-
So, using this theory by Compton was a
Ten years earlier, in 1913, a group of four distinguished German physicists,
(including Max Planck, the father of quantum physics!) wrote in a petition
Recommending Einstein’s appointment to the Prussian Academy of
…That he may sometimes have missed the target in his specula-
tions, as, for example, in his hypothesis of light quanta, can-
not really be held too much against him, for it is not possible
to introduce fundamentally new ideas, even in the most exact
sciences, without occasionally taking a risk.
In 1923 the situation was not muchdifferent.
Compton’s reasoning: in graphite, there is an abundance of weakly
coupled electrons – one can think of them as of “nearly free electrons”
or, with a good approximation, as of “free electrons”.
The photon passes
some part of its
energy to the elec-
tron, and flies away
with less energy.
The energy has to
be Conserved, so
the Remaining part
of the energy is the
kinetic energy of
Momentum also has to be conserved. We assume that the electron is at
rest before the collison, so only the photon momentum matters, and it
has only a component in the x direction, while there is no momentum
in the y direction (of course, it is so because we chose the direction
of the impinging photon as the x axis).
After the collision, the momentum vector of the scattered photon, and the
momentum vector of the electron (now in motion) are both inclined relative
to the x axis. Let’s decompose the two vectors into their x and y components,
as shown in the figure (note that there are two different angles, and , don’t
get them mixed!).
There was no y momentum initially, so the
momentum conservation requires that:
The sum of the x momentum
components after the collision
must be equal to initial
So, we have two momentum
equation that can be rewritten
First, let’s square the
and add them:
(I simply copied
notes, pp. 91-93)
Einstein’s photon theory. After the results became widely known,
no one could express any more doubts that photons really existed!
obtained if Compton also measured the energy and momentum of the
scattered electron, and showed that they also agreed with the theory.
Why didn’t he measure the the electron energies and flight directions?
due to multi-
paths get dis-
Compton’s experiments offered the final proof for the particle-like
nature of EM radiation.
Does it mean that the wave theory of EM radiation was “killed”?
Overall conclusion of the Chapter
“Particlelike properties of light”:
Compton’s experiments did not change the fact that EM radiation
manifests its wave-like nature in many other experiments:
● Young’s double-slit experiments;
● Bragg diffraction from crystals;
● And this is not the end of the list
SO WHAT’S GOING ON?!!!!
to the DUAL NATURE of EM radiation: in some circumstances
light manifests its wave-like nature, and in some other circum-
stances, it behaves as if it consisted of particles…
ABSURD? No! Such is the microworld!
And in the new chapter that we will start right after the present
one we will see that not only light, but also “proper” particles
such as electrons, protons, neutrons exhibit a similar “dual
nature”. That’s simply how the microworld is organized!
About one common misconception: namely, that the photoelectric
effect is a “special case” of Compton scattering, in which the
energy of the scattered photon is simply zero:
Such thinking is absolutely incorrect!
– please read a detailed explanation why it is incorrect
on pages 96 and 97 of the hand-written notes.