We saw the importance of the concept of quantization as a way of solving a large number of problems with which classical physics had struggled without success. Quantization certainly suggested that light—as Einstein had proposed in 1905—is a stream of particles. However, many physicists refused to take quantization as more than an elegant mathematical trick to solve the problems of blackbody radiation, photoelectric effect, and discrete emission lines.
An experiment conducted in 1923 at Washington University in St. Louis by American physicist Arthur Compton finally convinced all but the most die-hard physicists that light is indeed made out of particles. In Compton’s experiment, light (in the form of X-rays) was made to interact with virtually free electrons.
It could be assumed that the electrons were free and at rest, so the solution to the problem shouldn’t be bound by the special cases that needed the “trick” of quantization. Classical physics predicts that the electron should absorb energy from the light wave, and then re-emit the light at the same frequency. However, Compton’s experiments actually showed that light bounces off the electron with lower energy, just as if the light were a stream of particles colliding with the electrons. That is, photons are able to transfer momentum to another particle. That is definitely the signature of a particle! Compton was awarded the 1927 Nobel Prize in Physics for his discovery.
Let’s take a look at the geometry of Compton scattering as shown in Figure 85. A photon of frequency f collides with an electron at rest. Before the collision, the energy of the photon is given by Planck’s formula E = hf. Upon collision, the photon bounces off the electron, giving up some of its energy, while the electron gains momentum. But the photon cannot lower its velocity, so the loss of energy by the photon shows up as a decrease in the photon’s frequency f (or, conversely as an increase in its wavelength λ) since E = hf.
Figure 85 Compton Effect. (a) A photon with momentum pphoton = E/c = hf/c = h/λ approaches an electron at rest. (b) After the collision, the photon transfers momentum to the electron, which results in a proportional decrease in the photon’s frequency.
As we can see, the photon loses some energy after the collision, bouncing off at an angle θ with a new energy E’ and momentum p’, which translate into a decrease in frequency to f’. Of course, the initial photon’s wavelength is λ, and its wavelength after the collision is λ’.
The photon’s momentum is:
So if the change in the photon’s wavelength is Δλ = λ’ – λ, the electron gains the momentum lost by the photon:
Please note that the wavelength shift (but not the frequency or energy shifts) is independent of the wavelength of the incident photon.
The maximum change in wavelength for the photon happens when it transfers as much momentum as possible to the electron. That is, when cos(θ) = −1. The maximum change in wavelength is thus:
Even this maximum shift in wavelength would be insignificant for visible light with λ ≈ 10−7 m, but not for X-rays and gamma rays with λ −10 m. Please note that this is the maximum change, which doesn’t mean that all the photons will recoil at 180° (to give cos (θ) = −1). In fact, most of the photons will bounce at much smaller values of θ.
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