Range of Different Photoelectron Kinetic Energies?: Photoelectric Effect

[PhysJs]

First of all, I would like to apologize if this question is in the wrong section of the forums. I'm not sure if the photoelectric effect should go into "Quantum Physics", "Classical Physics" or even "Homework & Coursework Questions"

Descriptions of the photoelectric effect commonly states the fact that ,provided the frequency of the light incident on the metals surface is more than the threshold frequency, the photoelectrons emitted have a range of kinetic energies, below and up to the maximum kinetic energy.

Question
My question is, why does the electrons have a range of kinetic energies? I am confused because I have heard 2 separate explanations of why there is a range of kinetic energies for the photoelectron:

Explanation 1): The electrons in the atom of the metal occupy different energy levels, thus have different minimum energy required to be "ejected" from the atom. So if two electrons occupying different energy levels absorb energy from a photon of the same frequency, the electron occupying a higher energy level in the atom will have a higher kinetic energy, while the electron occupying the lower energy level will be emitted with lower kinetic energy since it required more energy to be "ejected" from the atom.

Explanation 2): The electron might not be emitted from an atom at the surface of the metal, rather it could be somewhere within the metal. Therefore, the emitted electron has to pass through some portion of the thickness of the metal to exit the metal. In the process, it loses energy (Maybe because it bumps into/repelled by the electrons in the other atoms?)

Which, if any, is the correct explanation as to why emitted photoelectrons have a range of different kinetic energies?

Possible explanation?: "An electron to which kinetic energy has been imparted in the interior of the body will have lost some of this energy by the time it reaches the surface."-paragraph 3, no.8, pg13 of the document ,http://www.esfm2005.ipn.mx/ESFM_Images/paper1.pdf"
The above extract from a English translation of Albert Einstein's "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light" seems to suggest Explanation 1). EDIT: Sorry typed wrongly when I posted this. seems to support Explanation 2), not 1).

Thank you for the attention,
PhysJs

EDIT:restored a spacing that I accidently removed when quoting "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light". And I type the wrong possible explanation.

 

[mathman]

Non-expert opinion. Explanation 1 is always valid. There may be an additional effect due to explanation 2.

 

[PhysJs]

Mathman, yeah I was thinking that there might be another explanation: that both explanations are true.

But I have so far found no direct evidence that both must be true or that only either one is true.

 

[mathman]

I am not sure what you mean by direct evidence. There must be many papers describing the experiments with the photoelectric effect. Einstein got his Nobel prize for explaining it.

 

[ZapperZ]

First of all, I would like to apologize if this question is in the wrong section of the forums. I'm not sure if the photoelectric effect should go into "Quantum Physics", "Classical Physics" or even "Homework & Coursework Questions"

Descriptions of the photoelectric effect commonly states the fact that ,provided the frequency of the light incident on the metals surface is more than the threshold frequency, the photoelectrons emitted have a range of kinetic energies, below and up to the maximum kinetic energy.

Question
My question is, why does the electrons have a range of kinetic energies? I am confused because I have heard 2 separate explanations of why there is a range of kinetic energies for the photoelectron:

Explanation 1): The electrons in the atom of the metal occupy different energy levels, thus have different minimum energy required to be "ejected" from the atom. So if two electrons occupying different energy levels absorb energy from a photon of the same frequency, the electron occupying a higher energy level in the atom will have a higher kinetic energy, while the electron occupying the lower energy level will be emitted with lower kinetic energy since it required more energy to be "ejected" from the atom.

Explanation 2): The electron might not be emitted from an atom at the surface of the metal, rather it could be somewhere within the metal. Therefore, the emitted electron has to pass through some portion of the thickness of the metal to exit the metal. In the process, it loses energy (Maybe because it bumps into/repelled by the electrons in the other atoms?)

Which, if any, is the correct explanation as to why emitted photoelectrons have a range of different kinetic energies?

Possible explanation?: "An electron to which kinetic energy has been imparted in the interior of the body will have lost some of this energy by the time it reaches the surface."-paragraph 3, no.8, pg13 of the document ,http://www.esfm2005.ipn.mx/ESFM_Images/paper1.pdf"
The above extract from a English translation of Albert Einstein's "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light" seems to suggest Explanation 1). EDIT: Sorry typed wrongly when I posted this. seems to support Explanation 2), not 1).

Thank you for the attention,
PhysJs

EDIT:restored a spacing that I accidently removed when quoting "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light". And I type the wrong possible explanation.

The range of KE of the emitted photoelectrons is made full use of in photoemission spectroscopy to investigate subtle interactions of the electrons in a material.

So why is there a range of energies? When photons greater than the work function enters a metal, in can excite electrons not only at the Fermi level, but also those below the Fermi level. Depending on how energetic it is and the difference between its energy and the work function, it can, in principle excite and liberate quite a range of electrons below the Fermi level.

The most energetic photoelectrons will be those emitted from the Fermi level (assuming temperature is very low and the thermal broadening is negligible). This will provide the largest number of photoelectrons. It will then taper off as a Lorentzian distribution towards lower KE.

In photoemission spectroscopy, this energy distribution at a particular momentum is called the energy distribution curve (EDC), and is often the main spectrum obtained in experiments such as angle-resolved photoemission spectroscopy (ARPES).

There are, of course, "higher order" complexities in this phenomenon that I haven't touched yet (such as inelastic scattering of the photoelectrons that can cause it to lose energy in the Spicer's 3-step model of photoemission). But this I think should answer your question.

Zz.

 

[PhysJs]

Thank you ZapperZ, that is truly a lot of information, I will have a lot to read up. It definitely answers my question.

So Explanation 2 is not valid?

 

[ZapperZ]

Thank you ZapperZ, that is truly a lot of information, I will have a lot to read up. It definitely answers my question.

So Explanation 2 is not valid?

There's nothing wrong with Explanation 2 because it depends on the penetration depth of that light. Note that for a metal, the "skin depth" is quite small due to the presence (and shielding) of the conduction electrons. But this length scale doesn't have a direct impact on the energy distribution, i.e. you simply can't use that explanation alone to explain this.

Note also that in the standard photoelectric effect (as opposed to core level photoemission), you are emitting off the conduction band, not electrons attached to a particular atom. There are no conduction electrons in atoms. There are, however, conduction electrons in metals where the many-body effects have produced such continuous band of energy and states.

Zz.

 

[PhysJs]

Thank you ZapperZ. I believe all the issues are now resolved.