Compton scattering – the momentum of a photon
PhysicsQuantum & Nuclear PhysicsAges 17–18Virtual lab
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An X-ray photon hits an electron at rest and leaves at angle θ with a longer wavelength: λ′ − λ = (h/mₑc)(1 − cos θ). Drag to change the scattering angle and read the wavelength and photon energy before and after, the kinetic energy and direction of the recoil electron, and a vector diagram showing that momentum is conserved: p = p′ + pₑ. The Compton's experiment screen measures the scattered X-ray spectrum with a crystal spectrometer, with an unshifted and a shifted peak; record readings at several angles and plot Δλ against (1 − cos θ) to find the Compton wavelength and the Planck constant.
Lesson: Wave–particle duality: Compton scattering
What it shows
In 1923 Arthur Compton found that X-rays scattered by graphite contain a second, longer wavelength. He explained it by treating the X-rays as photons, each with energy E = hc/λ and momentum p = h/λ, bouncing off free electrons like billiard balls. Conservation of energy and momentum gives λ′ − λ = (h/mₑc)(1 − cos θ), where h/mₑc = 2.43 pm is the Compton wavelength. The shift depends only on the angle, not on the wavelength or the material, so it is large for X-rays and gamma rays but invisible for light. The model treats the electron as free and at rest.
How to use
On Photon–electron collision, set Incident X-ray wavelength λ and drag in the picture or move Scattering angle θ; press Fire photon to watch the collision and Record to add a row to the table. On Compton's experiment, choose the Scattering block and an angle, then drag on the graph or use Spectrometer reading λ′ and its − / + buttons to sit on the shifted peak; press Take reading. Plot Δλ against (1 − cos θ).
Parameters you can change
- Screen Photon–electron collision, Compton's experiment
- Incident X-ray wavelength 2–100 pm
- Scattering angle 0–180 °
- Scattering block Graphite, Aluminium, Copper
- Show momentum diagram
Questions to explore
- Why is the wavelength shift at 90° the same for every incident wavelength?
- At which scattering angle does the recoil electron gain the most kinetic energy, and why?
- Why is the Compton shift easy to detect with X-rays but not with visible light?
