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Apologies if I have done this wrong, it's my first post.

To my understanding, atoms can be excited by a collision of an electron or photon with sufficient energy to excite the electron into a higher energy level.

With an electron collision, it just needs enough kinetic energy to transfer into the atom for the electron to get into a higher energy level. With a photon collision, it needs exactly the amount of energy as the difference of energies between energy levels in the atom. If it has too little energy, the electron wouldn't be excited and hence the photon wouldn't interact, and the same with if it had too much.

My question is why cant the photon, similarly to the electron collision, collide with the atom with more energy than the difference in energy levels in order to excite the atom and then, to conserve momentum (similarly to how the electron continues with less momentum following a collision), why can't a new photon be emitted with a lower frequency?

Is this because momentarily the system would not conserve energy? If so, why cant a lower frequency photon be emitted instantly when the particles interact, similarly to how an excited electron instantly jumps to a higher energy level?

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  • $\begingroup$ This is when the atom is fully ionised and so the electron can carry the excess momentum? $\endgroup$ Commented Mar 8, 2023 at 20:11
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    $\begingroup$ @EdV I don't think XRF is an answer here. The usual situation in XRF is that the exciting photon ionizes the atom. $\endgroup$
    – John Doty
    Commented Mar 8, 2023 at 22:41
  • $\begingroup$ @JohnDoty You are correct, of course. I read the question too loosely. Thanks! $\endgroup$
    – Ed V
    Commented Mar 8, 2023 at 23:08

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There is an important concept of the oscillator called resonance. For example you can place an energized "c" note tuning fork on the "c" piano string .... and the string will oscillate .... However if you place the fork on the C sharp or B flat string these strings will NOT oscillate.

The photon has energy-frequency and it is pure vibration (wave) in the EM field ... when a suitable electron can resonant at the frequency it can absorb the pure energy. When the photon is at a different frequency-energy the suitable electrons just don't resonate or absorb the energy.

All of quantum mechanics is based on the oscillator model for the atom/electron orbital behaviour.

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  • $\begingroup$ So electrons resonate at different frequencies depending on the energy they require to be excited? $\endgroup$ Commented Mar 9, 2023 at 7:04
  • $\begingroup$ All those fancy orbital/energy diagrams of the electron in hydrogen (s p d orbitals etc)are from the Schrodinger equation ... they represent the electron resonating at various stable/allowable energy levels. So electrons resonate at different frequencies ... period end of story. The energy deltas between levels are where the photon energies must match. $\endgroup$ Commented Mar 9, 2023 at 13:47
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There is fundamental difference between excitation by particle collisions and by photons: in the former case, the energy transferred in the collision not only depends on the particle energy, but also the mass and the impact parameter (look up some text book about Classical Mechanics). Only if the combination of the three is such that the energy transferred matches the energy difference between the two states will an excitation take place. Given that the initial energy is high enough, any transition with a smaller energy can be excited as well, depending on mass and impact parameter. A photon on the other hand can only excite a transition if its frequency exactly matches a transition frequency of the atom.

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