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How did Arthur Compton’s X-ray experiments support the photon model of light?

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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.

Arthur Compton’s 1922 experiments provided critical evidence for the particle nature of light by demonstrating that X-rays behave like discrete particles, or photons, when they collide with electrons.12

Compton treated the scattering of X-rays as an elastic collision between a photon and an electron, similar to the collision of two billiard balls. By applying the conservation laws of energy and momentum to this interaction, he predicted that the photon would transfer some of its energy to the electron, causing the electron to recoil and the scattered photon to emerge with a lower frequency and a longer wavelength.213

The observed shift in wavelength, known as the Compton effect, matched his mathematical derivation:
$λ^{'} - λ = \frac{h}{m c} (1 - \cos θ)$
where $h$ is Planck’s constant, $m$ is the electron's rest mass, $c$ is the speed of light, and $θ$ is the scattering angle. Because this model successfully accounted for the experimental data, it served as powerful evidence that light possesses particle-like properties.123