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How does the Compton effect show that photons have momentum?

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A horizontal gradient bar displays the visible light spectrum from violet to red, labeled with corresponding frequency in terahertz, wavelength in nanometers, and photon energy in electron volts. — light When white light is spread apart by a prism or a diffraction grating, the colours of the visible spectrum appear. The colours vary according to their wavelengths. Violet has the highest frequencies and shortest wavelengths, and red has the lowest frequencies and the longest wavelengths.

The Compton effect provides direct evidence that photons possess momentum by demonstrating that light behaves as a stream of particles capable of mechanical collision.12

In this phenomenon, an incident X-ray photon strikes a loosely bound or free electron. By treating this interaction as a collision between two particles, physicists apply the laws of conservation of energy and conservation of momentum. During the collision, the photon transfers a portion of its energy and momentum to the electron, causing the electron to recoil.12

Because the photon loses some of its momentum and energy to the electron, the scattered photon must emerge with a lower frequency and a correspondingly longer wavelength. The specific increase in wavelength, known as the Compton shift, depends on the scattering angle and aligns perfectly with theoretical predictions based on particle-like collisions. This experimental verification confirms that photons, despite having no rest mass, carry momentum and interact with matter as discrete quanta.123