Final answer:
Compton interactions decrease, but photoelectric interactions increase more rapidly with increasing photon energy. The photoelectric effect relies on the energy exceeding a threshold for electrons to be ejected. Therefore the correct answer is 2) decrease, increase.
Step-by-step explanation:
The correct answer to the statement "The absolute number of Compton interactions _______, but the number of photoelectric interactions ________ much more rapidly" is: 2) decrease, increase.
In X-ray and gamma-ray physics, the probability of the Compton effect (scattering of a photon by a loosely bound outer electron) decreases with increasing photon energy, whereas the probability of the photoelectric effect (total absorption of the photon by binding it to an electron) increases sharply with increasing photon energy, until it reaches a peak and then falls off.
The photoelectric effect is significantly affected by the energy of the photons. If the energy of the photons is above a certain threshold, then according to the photoelectric effect, electrons will be ejected from the material.
However, if the frequency of the incoming light is not high enough, no electrons will be ejected, no matter how high the intensity is.