7.2 Compton Scattering

Light acts like a particle

Compton scattering occurs when a photon collides with a loosely bound electron, transferring some energy and momentum to it. The scattered photon emerges with less energy (lower frequency, longer wavelength) than the incident photon. This effect provides strong evidence that light behaves as a particle (photon), not just a wave.

Conservation laws govern the collision

Compton scattering obeys both conservation of energy and conservation of momentum, just like a billiard-ball collision. The photon's momentum is given by p = h/λ. Because the photon loses energy to the electron, its wavelength increases: Δλ = (h/mₑc)(1 − cos θ), where θ is the scattering angle.

Wavelength shift depends on angle

The change in wavelength Δλ depends only on the scattering angle θ, not on the incident wavelength or the material. Maximum wavelength shift occurs at θ = 180° (photon bounces straight back), while θ = 0° gives no shift at all, since no energy is transferred.

Key terms

Compton scattering

The collision of a photon with a loosely bound electron, resulting in a scattered photon with reduced energy and increased wavelength.

Compton shift equation

Δλ = (h/mₑc)(1 − cos θ), giving the increase in photon wavelength based on scattering angle θ.

Photon momentum formula

p = h/λ, where h is Planck's constant and λ is the photon's wavelength.

Why Compton scattering supports particle model of light

The photon exchanges discrete energy and momentum with an electron like a particle collision, which wave theory alone can't explain.

Angle of maximum wavelength shift

θ = 180° (photon backscatters), giving the greatest energy transfer and largest Δλ.

Try an AP-style question

An X-ray photon scatters off an electron. What happens to the photon's wavelength?

1. It stays the same
2. It becomes zero
3. It increases
4. It decreases