The speed of a 𝛾-ray photon after it collides with a free electron and experiences Compton scattering is a) increased, b) decreased, c) equal to zero, d) does not change.
We can start off by drawing a sketch of this photon as it collides with the electron. If we have a stationary unrestricted electron and a photon that comes in and strikes the electron, Compton scattering tells us that both the electron and the photon will start moving in a new direction.
We know from Compton scattering that the wavelength of this photon will change thanks to the collision. But the question is, what will happen to its speed?
The clue we can use is that, both before and after this collision interaction, the object that we’re considering is a photon. A photon will move at the speed of light 𝑐 unless entering a region of a different index of refraction. With no indication of that going on here, we would say then that the speed of the photon is the same before and after the collision. We would choose then option d, that the speed of the photon does not change.