quantum mechanics - Which particle aspect is required to explain photoelectric or Compton effect?

What do we mean when we say that it requires the particle nature of radiation i.e., photons, to explain photoelectric or Compton effect?

I don't understand which particle nature is used to explain these experiments. We cannot say that the momentum and energy are distinctive properties of a particle. Waves, too, have these properties.

So the question is which particle aspect is relevant for explaining the above-mentioned experiments? How do I make it understandable to a High school student?