What does classical wave theory incorrectly predict about the Compton effect? I saw a video clip demonstrating how ionizing ray emits from a radioactive source is scatter by object, an aluminum rod and the experimenter thus position the angle of the detector to measure the electrons being knocked out. The experimenter then use the result to calculate the shift in the frequency of the scattered xray and mentioned something about how classical wave theory cannot explain such a phenomenon. Does the experimenter meant in wave theory light acts like a standing wave and the energy of the incident and refracted light must then be equal which is clearly not the case? I need to know what the classic wave theory predicts and got wrong in this compton scattering experiment NOT how the compton effect prove the light is quanta, thanks.  
 A: In the classical wave picture, the electromagnetic field of an incoming wave accelerates an electron via the Lorentz force, but does no work upon it. The electron oscillates at the same frequency as the incoming wave and then re-emits (scatters) light at that same frequency  as a classical oscillating electric dipole. This is an elastic process and no net energy is given to the electron.
What is found experimentally is that if the frequency of light is high enough, that the scattered light has a frequency that is lower than the original light, and that the frequency depends on the scattering direction. This behaviour is not found to be dependent on the light intensity (i.e. the electric field amplitude in the classical picture).
The explanation is that this is not an elastic process and is described in the photon picture in terms of conservation of momentum and energy. The photon gives some of its momentum and energy to the electron and hence the scattered photon is of lower energy and frequency.
The classical picture works reasonably well until the photon energy becomes a non-negligible fraction of the electron rest-mass energy (511 keV). Up until this point the transfer of momentum to the electron can be considered negligible. In practice this means up until photons at X-ray wavelengths.
A: In a nutshell:

Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light. However, the effect will become arbitrarily small at sufficiently low light intensities regardless of wavelength. Light must behave as if it consists of particles to explain the low-intensity Compton scattering. Compton's experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

Bold mine.
Compton effect experimentally:

As described in the quote above, the classical Thomson scattering does not change wavelength unless the intensity of the beam introduces a doppler shift due to the large energy transfer to the electron. Compton scattering persists for low intensity when it should be zero by classical calculations.
