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I am currently watching a series of lectures on Nuclear Physics. One of the topics covered is the emission and absorption of X-Rays. This got me thinking about some of the physical chemistry I took as an undergraduate, in particular, about the way photons interact with electrons.

My basic photon/electron understanding: Electrons absorb photons that are at energies equivalent to the energy gap between different orbitals. Also, an electron emits a photon at an energy equal to the energy gap of the transition the electron undergoes between orbitals.

My question is what governs the absorption of a photon by an electron when the energy of the photon doesn't correspond to a transition state, ie when the electron is ejected from the material.

NOTE: This is not a duplicate question. Answers to similar questions so far have been about whether or not this type of process is allowed. I am not confused that it is allowed. I am curious to know how one would go about understanding what goes into figuring out which electrons in an atom are more likely to absorb an incoming photon given that it exceeds the work function of the material.

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"Electrons absorb photons" is not accurate. Atoms, and in general bound states( molecules, lattices), absorb photons by an electron going to a higher quantized energy orbital.

Note that the photoelectric effect appears easily in metal lattices. Metals are quantum mechanically described well with the band theory of solids. In conductors the electrons are bound to the whole lattice, so their allowed energy levels are practically continuous. This means that a photon of higher energy than the lattice conduction band bound states, will "ionize" the lattice by giving it enough energy to get the electron out of the band, the excess becomes the kinetic energy of the ejected electron. The electrons are bound in the conduction band , that is why a minimum frequency/energy photon is needed so that the lattice can be ionized.

The study of the effect in insulators is active, for example this link, if you have access. Due to the higher binding energies it is not as simple as the effect in metals.

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  • $\begingroup$ But how does the energy of the photon and the initial energy level of the electron affect the probability of absorption by the bound state? $\endgroup$ Jun 4 '20 at 6:06
  • $\begingroup$ it is a scattering problem : photon +lattice it has to be computed a) an elastic part b) an inelastic part that due to the quantum mechanical nature will describe what I state in words.From the experimental curves, the function is linear in energy , until the energy gets too small to eject a conduction electron from its energy level. $\endgroup$
    – anna v
    Jun 4 '20 at 6:27
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Take the simpler case of hydrogen atom. It has a discrete spectrum that is bound above. Beyond that energy, the electron is no longer bound to the proton. But note that this still is an allowed energy state of the system, but in this case we’ll have two independent states, ie the interaction energy is low.

So to get probabilities, one can calculate in the exact same way one does for transitions between bound states. However, the same information is present in the experimental spectra.

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