D

Step 1: The Compton effect refers to the scattering of X-rays or gamma rays by electrons. It demonstrates that light can exhibit both wave-like and particle-like properties.
Step 2: When X-rays collide with free electrons, they impart some of their energy to the electrons, causing the X-rays to scatter at different angles and with reduced energy.
Step 3: This scattering provides evidence that photons (the particles of light) carry momentum, given by the relationship:
$$ p = \frac{E}{c} $$
where $p$ is momentum, $E$ is the energy of the photon, and $c$ is the speed of light.
Step 4: The change in wavelength of the scattered X-rays is also consistent with the conservation of momentum.
Conclusion: Hence, the Compton effect conclusively shows that photons have momentum. Therefore, the correct answer is option D.