Compton scattering is the change in wavelength that occurs when a high-energy photon, such as an X-ray, collides with a nearly free electron. The scattered photon leaves with a longer wavelength and lower energy, while the electron recoils and carries away kinetic energy. This effect matters because it showed that light behaves like particles called photons, not only like waves.
It was one of the key experimental proofs that photons carry momentum.
Key Facts
- Compton wavelength shift: Δλ = λ' - λ = (h/m_e c)(1 - cos θ)
- Electron Compton wavelength: h/m_e c = 2.43 x 10^-12 m
- Photon energy: E = hf = hc/λ
- Photon momentum: p = h/λ
- The scattered photon has lower energy because λ' > λ for any nonzero scattering angle θ.
- The maximum wavelength shift occurs at θ = 180°, giving Δλ_max = 2h/m_e c = 4.86 x 10^-12 m.
Vocabulary
- Compton scattering
- Compton scattering is the collision of a photon with an electron that causes the photon wavelength to increase and the electron to recoil.
- Photon
- A photon is a particle-like packet of electromagnetic radiation with energy E = hf and momentum p = h/λ.
- Scattering angle
- The scattering angle is the angle θ between the incoming photon direction and the outgoing photon direction.
- Recoil electron
- A recoil electron is the electron that moves away after gaining energy and momentum from the scattered photon.
- Compton wavelength
- The Compton wavelength h/m_e c is a constant that sets the scale of the photon wavelength shift when scattering from an electron.
Common Mistakes to Avoid
- Using the incoming photon wavelength instead of the wavelength shift is wrong because the Compton formula gives Δλ = λ' - λ, not λ' directly.
- Forgetting that θ is the photon scattering angle is wrong because the formula depends on the angle between the incoming and outgoing photon directions, not the electron recoil angle.
- Assuming the photon keeps the same energy is wrong because the scattered photon has a longer wavelength, so E = hc/λ shows its energy decreases.
- Treating the electron as completely fixed is wrong because conservation of momentum requires the electron to recoil and carry away kinetic energy.
Practice Questions
- 1 An X-ray photon scatters from a nearly free electron at θ = 90°. Calculate the wavelength shift using h/m_e c = 2.43 x 10^-12 m.
- 2 A photon with initial wavelength 7.00 x 10^-11 m is scattered through 180°. Find the scattered wavelength λ'. Use h/m_e c = 2.43 x 10^-12 m.
- 3 Explain why Compton scattering supports the idea that photons carry momentum, using conservation of energy and momentum in your answer.