Photoelectric effect – What is the probability of a photon absorbtion by an electron? Is it correct that 

each photon above threshold frequency is absorbed by an electron

What is the probability of a photon absorbtion by an electron?
Can a quantitative example be given?
 A: There are two steps to photoemission:


*

*an electron absorbs a photon. This produces an electron moving in the same direction as the original photon i.e. down into the bulk of the metal

*the electron either backscatters off other electrons in the lattice or it transfers its energy to other electrons. Either way this produces an electron moving in the opposite direction i.e. towards the metal surface and ultimately out of the metal
The yield for step 1 is almost 100%. We can measure this experimentally because exactly this principle is used in a photomultiplier tube. In a PMT a very thin sheet of metal is used so when an electron absorbs a photon it travels right through the metal sheet and out the other side. This design means no scattering is necessary for the original electron to escape. PMT efficiency can approach 100% in ideal conditions.
The yield for step 2 is absolutely awful. Experiment shows that only one in $10^5$ to $10^6$ photons produces a photoelectron. This shouldn't be surprising since the scattering of an electron headed down into the bulk of a metal is a random process and the probability of it producing an electron headed in the opposite direction with enough energy to escape is very low.
