Anyone can help? A question about Compton Effect.?

Question

I was taught in school that electron can only accept certain amount of energy, therefore corresponding wavelengths are required, and a photon will give all of its energy to an electron once it hits an electron.

But in Compton Effect an X-ray photon may not give all its energy to an electron, it only gives some of its energy, and therefore the frequency after collision is decreased. But what decides whether a photon will give all of its energy or not? Why there is a difference between the photons in photoelectric effect and the photons in Compton Effect?

Does the electron still only accept certain value of energies in Compton Effect? I think so but I'm not so sure.

Answer 1

From: http://physics.bu.edu/~duffy/semester2/c...

Convincing evidence that light is made up of particles (photons), and that photons have momentum, can be seen when a photon with energy hf collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved in this elastic collision. After the collision the photon has energy hf/ and the electron has acquired a kinetic energy K.

Conservation of energy: hf = hf/ + K

^ The energy and momentum of the photon are conserved, this can be expressed as p1 + p2 =0 or p1=p2. The conservation of momentum gives p1 = p2 +p_e

Answer 2

It's to conserve momentum.  Process will continue as long as photon has enough energy left to give.