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How did the Compton effect provide evidence that photons have momentum?

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Diagram of a tree leaf illustrating photosynthesis, with arrows showing sunlight, water, and carbon dioxide entering the leaf and sugars and oxygen being produced. A person is shown beside the tree to demonstrate the exchange of oxygen and carbon dioxide between plants and animals. — electromagnetic radiation Diagram of photosynthesis showing how water, light, and carbon dioxide are absorbed by a plant to produce oxygen, sugars, and more carbon dioxide.

The Compton effect provided definitive evidence that photons possess momentum by treating the scattering of X-rays as a mechanical collision between particles.12

When an incident photon strikes a loosely bound electron, it acts like a particle, transferring a portion of its energy and momentum to the electron, which causes the electron to recoil. Because the photon loses energy during this interaction, its frequency decreases and its wavelength increases.12

Arthur Holly Compton successfully derived the observed wavelength shift by applying the laws of conservation of energy and conservation of momentum to these individual collisions. The fact that the experimental results matched these calculations confirmed that light quanta behave as discrete particles with both energy and momentum, serving as a cornerstone of quantum mechanics.21