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Which of the following postulates regarding the photoelectric effect is considered to be INCORRECT according to the quantum mechanical model we currently understand?

(A) Increasing the intensity of light does not change the energy per photon.

(B) The energy of a photon which ejects an electron from a metal surface must be equal to the binding energy (a.k.a. work function) of the electron plus the KE of the electron.

(C) Increasing the frequency of a photon can allow that lone photon to eject multiple electrons from a metal surface.

(D) Some electrons in a metal are easier (require less energy) to eject than others.

Please see question above and the teacher also supplied us with answers, so I know that answer is C. Now, I am trying to reason why C is an answer, and A seems to be reasonable from what I read in my book. D looks somewhat good even though books keep mum about it. But I am puzzled about answer B. I looked at every AP Chemistry source I could get, and I am not sure where I can find formula for energy of photon, which would be equal binding energy + KE of electron. I can imagine this might exist outside of AP Chemistry, but within a subject? I found the equation in Wikipedia, for example:

The energy of a photon causing the photoelectric effect is found through E = hf = KE + w, where h is Planck's constant, 6.626X10^(-34) J*s, f is the frequency of the electromagnetic wave, KE is the kinetic energy of the photoelectron and w is the work function for the metal.

Any help on this matter would be highly appreciated. Desirably, reference to AP Chem book with page number. Thank you so much in advance!

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I think the teacher pointed out that (c) is the correct answer because the postulate is generally regarded as incorrect according to the normal convention of photons behaving as individual packets of energy.

However what I think is interesting is that more than one electron can be ejected provided the photon is sufficiently energetic (this information will not be useful during an examination, so I suggest forgeting about this when you take an exam or do your homework, but if interested read on). For more information you can search for "multielectron ejection in auger spectroscopy" which provided references [1] and [2] below. Reference [2] opens up with the following statement:

Absorption of an energetic photon by a target should in first approximation lead to the ejection of one electron only, as this interaction is purely mono-electronic. However it is well established that sometimes several electrons can be ejected. This can happen in valence multiple ionization or after innershell ionization when secondary electrons are emitted sequentially (cascade Auger decays) or simultaneously (direct double Auger decays). Such processes and especially the ‘one-step’ or direct ones (direct double ionization or direct double Auger decay) are extremely interesting to investigate as they revealthe strongelectron correlation phenomena which are at their origin.

Not sure what Einstein would have thought of this in any case.

An Auger process does not violate the principle that intramolecular electronic transitions are quantized and therefore that the energy required to eject electrons is quantized, irrespective of the number ejected. So the first two postulates are still correct.

References

  1. P. Lablanquie, M.A. Khalal, L. Andric, J. Palaudoux, F. Penent, J-M Bizau, D. Cubaynes, K. Jänkälä, Y. Hikosaka, K. Ito, K. Bučar, M. Žitnik, Multi-electron coincidence spectroscopy: Triple Auger decay of Ar 2p and 2s holes, Journal of Electron Spectroscopy and Related Phenomena, Volume 220, 2017, Pages 125-132, https://doi.org/10.1016/j.elspec.2017.04.003.

  2. https://pure.mpg.de/rest/items/item_737492/component/file_737491/content

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  • $\begingroup$ Isn't Auger always a 1-photon -2 electron effect? One photon would knock out the signal electron and the remaining events would be dependent on the other "electron"? Spectroscopy is always interesting. $\endgroup$ – M. Farooq Sep 22 at 21:55
  • $\begingroup$ @M.Farooq I guess not: one of the references states "The Auger decay of Ar innershell holes by emission of three Auger electrons is studied." But multiple emissions can be "simultaneous" (the exact meaning of simultaneity here I am not sure about). In the context of the question I thought this more of a curiosity worth mentioning. $\endgroup$ – Buck Thorn Sep 23 at 6:09
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(C) Increasing the frequency of a photon can allow that lone photon to eject multiple electrons from a metal surface.

I am glad that you gave a second thought to your teacher's "correct C" answer. Einstein might be turning in his grave. Photoelectric effect is one photon to one electron ejection phenomenon. Answer "C" is fundamentally wrong. Otherwise, increasing the intensity of a photon of the right frequency, the photo-current would not be a linear function of light intensity.

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    $\begingroup$ It might have been less clear in a previous edit, but the question does ask for which of the options is incorrect. $\endgroup$ – Tyberius Sep 22 at 23:55
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Answers A and D are both correct. Increasing the intensity of light just means there are more photons hitting the surface. Indeed some electrons in a metal are easier to eject than other.The band gap of the electrons of 1s subshell are harder to leave the nucleus than the electrons of a 2s subshell.C seems to be incorrect.Photons are small packets of energy absorbed/emitted by 1 electron.Also they are absorbed/emitted as a particle which makes it impossible to be emitted by 2 different electrons.

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