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 radiation. Compton observed that the scattered radiation has a longer wavelength than the incident radia- Ion. On the grounds of the wave theory, it is im- possible to explain the change of wavelength! 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 Science: …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 much different.

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 electron.

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).

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 (5)

Compton scattering (6) The sum of the x momentum components after the collision must be equal to initial momentum: So, we have two momentum equation that can be rewritten as:

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 )

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- less. In condensed Matter, fast electrons very quickly loose their energy due to multi- ple collisions with atoms. Also, their paths get dis- torted (zic-zac-like)

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”? NO!!! 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?!!!!

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.