Photoelectric Effect under cutoff frequency

[Djinn Ming]

I understand the concepts of photoelectric effect where an electron will be emitted when a photon with sufficient energy collides with it.

There are two parts to this question,

1. What happens during the collision?
Is the photon absorbed by the photoelectron wholly as energy?

2. If so, what happens if photon is under the cutoff frequency?
If energy is absorbed, wouldn't a second collision cause a release of photoelectron.

 

[BvU]

Hello Djinn,

1.

an electron will be emitted

an electron can be emitted . The maximum kinetic energy of the electron is $h\nu$ minus a material-dependent energy (usually called the work function)

2.
The electron that may have picked up some extra energy quickly loses it again on its journey through the metal. The chance that it picks up more energy by being hit again are very small (odds related to 1/the Avogadro number I suppose).

 

[vanhees71]

If you are under the "cutoff frequency", i.e., the photon has a lower energy than the binding energy of an electron, the photon cannot kick the electron out, and it's simply scattered.

What happens "during the collision" is a question that cannot be anwered so easily. In relativistic QFT such socalled transient states are usually not interpretable. That's why one usually calculates S-matrix elements, which describe transition rates from one asymptotic free state to another asymptotic free state. In the case of the photoeffect you have an atom (say in the ground state) and a photon as the initial state and an ionized atom and an electron in the final state.