What Is Compton Scattering and What Does It Prove About Light?

HL only (E.2 Quantum physics). Compton scattering occurs when a high-energy photon collides with an approximately free electron and is scattered with a longer wavelength. It provides evidence for the particle nature of light because the interaction is explained by photons carrying both energy and momentum.

The Mechanism

An incident X-ray or gamma-ray photon has energy and momentum:

$$E=hf, \qquad p=\frac{h}{\lambda}.$$

The electron is initially approximately free and at rest. During the collision, the photon transfers energy and momentum to the electron, causing the electron to recoil. The scattered photon therefore has less energy, so its frequency decreases and its wavelength increases because $E=hf$ and $c=f\lambda$.

Applying conservation of energy and conservation of momentum gives the Compton shift equation:

$$\Delta\lambda=\lambda_f-\lambda_i=\frac{h}{m_ec}(1-\cos\theta),$$

where $\theta$ is the photon’s scattering angle. The shift depends on this angle, not on the incident radiation’s intensity.

For example, at $\theta=90^\circ$:

$$\Delta\lambda=\frac{h}{m_ec}(1-\cos90^\circ)=2.43\times10^{-12}\text{ m}.$$

Classical wave theory could not account for the angle-dependent wavelength increase. Treating the interaction as a collision between a photon and an electron correctly predicts it, supporting the photon model.

A common misconception is that Compton scattering proves light is only a particle. It does not. Interference and diffraction demonstrate wave behaviour, so the combined evidence supports wave and particle duality: light displays different behaviour depending on the experiment.

Exam Technique

For an IB Explain question, link the wavelength increase to energy and momentum transferred from the photon to the recoiling electron, then conclude that photons possess momentum. For a calculation, distinguish $\lambda_i$ from $\lambda_f$, identify $\theta$ as the photon’s change in direction, and use the equation provided in the Physics data booklet. Do not claim that increased intensity produces a larger Compton shift.