[worlov (OP)]

The energy of the Hydrogen 1.4GHz resonance is 5.8 μeV.The energy of the photoelectric work function is typically around 3-5 eV.

I mentioned Hydrogen 1.4 GHz resonance as an example. The whole treatment concerns the solids. And I get the frequencies that are in the order of the work function and even more. I use a very simple model. Considering the interaction with the neighboring atoms, the frequencies will sink and then even fully agree with the experimental results. Qualitatively I see no problem for the resonance hypothesis of the photo effect. A photon counter counts the photons less often at low light intensity. And so it would be expected in a resonance phenomenon: it takes more time to spin up the electron with less light intensity for the necessary kinetic energy.

[alancalverd]

Wrong, wrong, wrong.

You need to distinguish between photon energy and beam intensity. The photoelectric effect is observed with single photons above the work function energy. A photon counter counts photons less often at low intensity because they are arriving less often.

[Bored chemist]

The electron is a negatively uniformly charged ball and the metal ion is a positively uniformly charged ball. The two are about the same size

That is probably the most wildly wrong assertion ever made.
"According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic" (from WIKI)
https://en.wikipedia.org/wiki/Classical_electron_radius

So, the metal ion has a finite size and the electron is infinitely smaller.
Yet you say they are about the same size.
Which makes you infinitely wrong.

[evan_au]

we're getting to Hooke's Law. Therefore, we have for the spring constant...

Quantum events are not like a classical analogue spring (which follows Hooke's Law).
- An analogue spring can collect energy near its resonance frequency, increasing amplitude over time until something breaks.
- Quantum interactions only take on specific energies;
      - if an incoming photon has this specific energy, it can interact
      - if an incoming photon has insufficient energy, it will pass through
      - if an incoming photon has excess energy, it will often interact, but the excess energy has to go somewhere

In the case of the photoelectric effect, this specific energy is the work function.
- In case of excess energy, it goes into the velocity of the emitted electron. This velocity is not a quantum thing, but is a classical velocity which can take on all values of energy.
- Hence, the photoelectric effect does not exhibit a resonance, but a threshold
- Above this work function threshold, the emitted electron shows the relationship that photon energy is proportional to frequency (via Planck's constant)

[worlov (OP)]

A photon counter counts photons less often at low intensity because they are arriving less often.

Yes, it can be explained this way and that. And the sensitivity curves of the photon detectors speak also for the resonance. They look like the damped resonance curve (figure below).

So, the metal ion has a finite size and the electron is infinitely smaller.Yet you say they are about the same size.

The metal ion is immobile. The electron, on the other hand, is very fast. In its chaotic movement around the metal ion, it blurs into a sphere.

[esquire]

Your conductingelectron.png triggered a memory of an article I had read circa 2010. The article and an accompanying png, resembled your conductingelectron.png. On a quick perusal of your post, several buzzwords further sparked my attention. Although your post focused on a quantum aspect of a photoelectric effect, the theory in the article I had read, focused on a real world  practical aspect of propulsion for naval vessels. A quick search of the internet lead me to the magnetohydrodynamic drive. As I mentioned above, a very similar theory and the same keywords/buzzwords are employed to explain your photoelectric effect as resonance effect, with practical variation implemented

en.wikipedia.org/wiki/Magnetohydrodynamic_drive

en.wikipedia.org/wiki/Variable_Specific_Impulse_Magnetoplasma_Rocket

[alancalverd]

A photon counter counts photons less often at low intensity because they are arriving less often.

Yes, it can be explained this way and that. And the sensitivity curves of the photon detectors speak also for the resonance. They look like the damped resonance curve (figure below).

No. There is no explanatory and predictive classical mechanism for the photoelectric effect, which (along with the ultraviolet catatstrophe) is why we use quantum physics that also predicts a whole lot more and doesn't involve absurdities like orbiting electrons.

I have a moustache and white hair. On a windy day I could look like Einstein, but it wouldn't make me a genius.

[Bored chemist]

Yes, it can be explained this way and that. And the sensitivity curves of the photon detectors speak also for the resonance. They look like the damped resonance curve (figure below).

Those are not the same thing.
For what it's worth, absorption spectra generally look rather like damped resonances- because the maths looks pretty similar, but this is the model they use, rather than a ball on a spring
https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)#Time-dependent_perturbation_theory

A quick search of the internet lead me to the magnetohydrodynamic drive. As I mentioned above, a very similar theory and the same keywords/buzzwords are employed to explain your photoelectric effect as resonance effect, with practical variation implemented

Those really have practically nothing in common.

[Bored chemist]

The metal ion is immobile. The electron, on the other hand, is very fast. In its chaotic movement around the metal ion, it blurs into a sphere.

A chaotically moving charged particle like an electron would emit radiation and stop moving.
Also, that's not what you said earlier.
You said it was the same size as an atom, and that's infinitely wrong.

[korosten]

worlov,
I just stumbled upon your idea and I think it makes a lot of sense - I recently had a similar discussion on another forum and I was wondering about the same thing.

If it were due to resonance, then one would expect that a change in intensity would merely change the probability of an event, which is indeed observed (lower intensity would mean that on average it takes longer for an event to occur). I would be interested to see if there is any correlation between intensity and the time it takes for an electron to be emitted.
There have been a few papers recently that determined the amount of time it takes for different atoms, which is in the order of attoseconds (so it is not "immediate" as it is sometimes claimed).
Here are some references that might be relevant:

"Time-delayed photoelectric effect "
"....We describe here photoelectric emission (PE) experiments using very low-intensity nanosecond light pulses with energies near the PE threshold. Signal correlated, time-delayed pulses of emitted electrons were observed for single light pulses incident on a photosensitive material."

(I am not able to post links, so here are just the titles)
"Controlling the Photoelectric Effect in the TimeDomain"

"Photoemission and photoionization time delays and rates"

Maybe this one: "Absolute timing of the photoelectric effect" ?

It seems to me, if resonance is indeed the cause then we would expect a slight delay for ultra low intensities. I am not sure if this experiment has been done yet or not and how to compute the expected delay? Does anyone know?

Best wishes,
Chantal