Is the Compton effect more supportive of the photon theory of light than the
I think they are both equally supportive. The Compton effect causes a change in wavelength that can only be explained if the light can also be thought of as a stream of photons with non-zero momentum, some of which is transferred to the target electron.
The photoelectric effect only works if the frequency of the incident radiation is high enough, and is not affected by the intensity. This also suggests that the light is made up of discrete photons - if each one has the required energy to liberate an electron, the number of photons hitting the target per unit time (intensity) makes no difference to whether an effect is observed or not.
In fact, the photoelectric effect can be thought of as a special case of the Compton effect, in which the momentum transferred to the target electron is enough to free it from the surface of a metal.
Actually, no. If you look at the type of momentum spread of a typical photoelectron, it is significantly more than the momentum that the incoming photon can carry.
In this phenomenon, the photon momentum is not significant and is absorbed by the lattice ions. The momentum recoil that occurs when a photoelectron is emitted is taken up also by the lattice ions. So the total momentum here (i.e. looking at just the photon momentum and photoelectron momentum) is not conserved.
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