More Fodo Effects

The graph below shows electrons ejected from the surface of a metal by photons in two distinct processes represented by the gray and blue line.  The ejected electrons follow two distinct KE profiles.  The resulting profile is represented by the red lines.

As the stopping voltage increases, the number of electrons from each process stopped before being collected increases.  The process with an associated higher work function ejecting electrons with lower KE will stop first as the stopping voltage increases. But which of the two processes has a lower work function?  If we assume that the lower rated process, also produces less energetic electrons then at point A,  all electrons from the gray process are completely stopped and the resultant red profile adopts a new gradient, which is the gradient of the blue process.  What makes the gray and blue processes distinct is that the number of electrons ejected with a certain KE is different. In both cases, the KE vs numbers graphs, are linear.  But we know that photons of different frequencies eject electrons with similar KE profile.  In the typical graph shown below, the red, green and blue curve represent illumination of different frequencies

All have a similar downward drop.  One possible conclusion is, on the metal side of the issue, two similar processes are contributing electrons.  Each producing electrons at a different rate.  The one with a lower rate is "switched off" by the stopping voltage first.  It is proposed that the production differences in the two processes are of two parts, a small work function part and a dependency on the incident photon \(r\) compared to the electrons orbital radius \({r}_{e}\) part.

A plot of corresponding electron productions as opposed to being stopped is shown below.

Some photons frequencies not producing a split curve suggest that electrons around a nucleus may not be simple concentric shells.  Otherwise, once a split occurs at a lower frequency, similar split should also be seen at all higher frequencies, because \(r\) is small enough to interact with all orbits \({r}_{e}\) of higher values if the orbits are entirely inside another.

It is also possible that the photons do not interact with electrons in orbits too large compared to its radius of circular motion.  That photons interact mostly with electrons in orbits of radius near its circular motion radius.  And so photons interact with at most two close adjacent orbits and there are only two observed \(KE_{max}\).

We could also be looking at different electrons orbiting in the same shell.  Although the energy difference seem too large for this scenario.