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It still haunts me that during photoelectric effect, incase the energy ($hv$) of the photons is less than the work function, (ofcourse it doesn't get emitted, heard that a hundered times even after slowly & repeatedly asking my professor) do the electrons still completely absorb that insufficient energy or not absorb it at all?

I was inspired to ask this after seeing this:

*'Prove that it's not possible for a photon to be completely absorbed by an isolated electron.' -Concepts of Physics by HC Verma

Now in case of photoelectric effect I do know that the electron is not an isolated one as it is not loosely bound. And I also have heard that excitation of electrons from one shell to another is PROBABILISTIC PHENOMENON while I was taking a class on Bohr's Atom Model.

But I'm not sure incase of Photoelectric effect if this phenomenon (the one mentioned in the above para) is taking place behind the scenes.

Please kindly help me.

Elizabeth Huffman
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  • This seems like a very good question, but I think there are two basic matters to clear up. Does the idea of work function assume a theory of atom? That is, does the theoritical basis of it depend on bohr theory or QM? Or, is it an experimental observation? Further, I have a strong feeling that this question was asked before. Have you tried searching? – tryst with freedom May 15 '23 at 10:56
  • Before you post a question, I always suggest reading wikipedia. See here. See also Raman Scattering and Compton scattering, or see this question – tryst with freedom May 15 '23 at 11:05
  • @TrystwithFreedom Yes true brother. Wikipedia does clarify my doubt on the photoelectric concept. I had learnt prev abt atomic collisions (hypothetical scenarios for JEE adv) where KE (of the colliding atom and equal to the diff btw energy levels in magnitude) could be partially absorbed. [Partially ineleastic collisions]. That confused me totally. By the way work function assumes the theory of quantum mechanics. – Elizabeth Huffman May 15 '23 at 11:31
  • But I think Im just over thinking too much and should see both of them as 2 separate scenarios as cases of hypothetical ineleastic collisions btw neutron and H atom which causes what I said in the above comment IS "HYPOTHETICAL". So it is not relevant to compare 2 scenarios – Elizabeth Huffman May 15 '23 at 11:33
  • I think Ill delete the post soon. – Elizabeth Huffman May 15 '23 at 11:34
  • Actually you can argue the work function idea using Bohr Theory. For instance, imagine that one of the $n$ is infinity in the Rydberg formula thing – tryst with freedom May 15 '23 at 11:36
  • Let us continue this discussion in chat. – tryst with freedom May 15 '23 at 11:40
  • You can certainly excite the electron into a higher state in the band structure. From there it will rapidly thermalize down through electron-electron and electron-phonon scattering. – Jon Custer May 15 '23 at 12:36

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