The Compton Effect and Photon Momentum
X-rays scattered from electrons come back with a longer wavelength that depends only on the scattering angle, which is what a collision between two particles predicts. The photon therefore carries momentum h over lambda.
What a learner can do afterwards
- Applies conservation of energy and momentum to a photon-electron collision
- Predicts the wavelength shift from the scattering angle and shows it does not depend on the incident wavelength
- Explains why the effect is invisible for visible light on a free electron
1 · Read
In 1923 Arthur Compton aimed X-rays, the same kind doctors use to picture bones, at graphite and measured what bounced off. The scattered rays came back with slightly longer wavelengths, and the shift grew at larger scattering angles. A pure wave scattering off charge should have kept the same wavelength.
The pattern makes sense if each X-ray travels as a packet that collides with one electron the way two balls collide. The photon hands part of its energy and momentum to the electron, so the photon that leaves carries less energy and a longer wavelength. The shift depends only on the scattering angle, never on the starting wavelength. For visible light on a free electron the shift is far too tiny to notice next to the long wavelength, so X-rays were needed to see it.
A photon has no mass yet carries momentum equal to Planck constant divided by wavelength. Short wavelength means high momentum and high energy through E equals h times f. Starlight pushing comet dust away from the Sun is the same momentum at work on a grand scale.
The shift depends only on the scattering angle, never on the starting wavelength. For visible light on a free electron the shift is far too tiny to notice next to the long wavelength. That is why the effect demanded X-rays to be seen.
X-rays scattered off electrons shift with angle, proving photons carry momentum.
The rewritten readings were written for this dataset.
More to read
X-rays reveal photon collisions
Arthur Compton's 1923 experiment sent X-rays into graphite. He found scattered radiation with wavelengths slightly greater than the incident wavelength, with larger changes at greater scattering angles. Classical wave theory predicts unchanged wavelength when light scatters from a stationary charge, so it could not explain the measured shift.
A photon-electron collision explained the results. Each X-ray photon can transfer energy and momentum to an electron, like a collision between balls. The outgoing photon has less energy, so its wavelength increases. For an initially stationary, free electron, the wavelength change depends on scattering angle rather than incoming wavelength. Agreement with the measurements supported the conclusion that light carries momentum.
How light transfers momentum
Although a photon's rest mass is zero, its momentum is Planck's constant divided by wavelength. An X-ray photon therefore carries much more momentum than a radio photon. Absorption transfers photon momentum to matter; reflection can transfer it too.
This transfer produces a push. An atom recoils as it emits a photon, and sunlight's momentum can propel a solar sail. In Compton scattering, the electron's recoil matches the momentum expected from a photon collision.
Photons and the release of electrons
Photoelectric emission gave early evidence that light delivers energy in photons. In the usual single-photon process, a metal releases electrons without a measurable delay only when the light reaches a threshold frequency. Making below-threshold light brighter or waiting longer does not cause emission in this model.
Einstein connected each photon's energy to its frequency. A photon with enough energy can free an electron. Nearly two decades later, Compton used this particle description while accounting for momentum as well as energy.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.