Compton Scattering
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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

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Compton Scattering : final proof for the existence of photons

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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

 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 scattering (2)

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-

serious doubts.

So, using this theory by Compton was a

courageous act!

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 scattering (3)

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

the scattered


Compton scattering (3)

Compton scattering (4)

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).

Compton scattering (5)

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:

Compton scattering (6)

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


Compton (7): We will now solve the equations. It’s a pretty tedious job, but

rather straightforward.

First, let’s square the

monemtum equations

and add them:

(I simply copied

the handwritten

notes, pp. 91-93)

Compton’s experiments offered extremely strong support for

Einstein’s photon theory. After the results became widely known,

no one could express any more doubts that photons really existed!

But you may ask: even better confirmation of the photon theory would be

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?

Answer: such

results would

be meaning-


In condensed

Matter, fast

electrons very

quickly loose

their energy

due to multi-

ple collisions

with atoms.

Also, their

paths get dis-



Compton effect – conclusions:

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


Well – all those experiments and facts we have reviewed point

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.

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