Answer
Yes, this can occur.
Work Step by Step
The new frequency f' is lower than the original frequency f, because the photon has transferred some of its energy to the proton that it scattered from.
However, the proton is some 1800 times more massive than an electron, so it will acquire less kinetic energy from the interaction, and the photon's energy shift is expected to be very small, and harder to measure.
Equation 38.7 can be used to relate the 2 wavelengths, and thus, the 2 frequencies. Because the proton mass is used instead of the electron mass, we see that the wavelength shift is much smaller. As we expected, the Compton effect is much reduced.
