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This question involves two cases: electrons bound to a nucleus and free electrons.

Bound electrons

Let's consider the hydrogen atom for simplicity. As far as I know, to be able to excite the electron, the energy of the photon should be in discrete values corresponding to the difference between energy levels inside the hydrogen atom. By the way in this link, the answer states that it is not the electrons that absorbs the photon but the atom in general, which makes sense to me (please correct or clarify if wrong).

The question is how long does the electron stay in that excited state, i.e. how quickly is the photon emitted back? Is it the same for all energy levels and all conditions like particle density (when many atoms together), temperature, presence of electric field, nucleus structure (neutron count) etc?

Free electrons

Again, according to the same link, free electrons do not absorb photons, which means they only undergo Compton scattering. Is this correct? If not, how long does it take for the photon be emitted back? Is the energy gain permanent?

Xfce4
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2 Answers2

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the answer states that it is not the electrons that absorbs the photon but the atom in general,

That is true, the system nucleus-electrons absorbs the energy. In the usual approximation of a nucleus at rest (due to its much larger mass a good approximation) one talks of the electron changing orbitals going to a higher energy level.

The question is how long does the electron stay in that excited state, i.e. how quickly is the photon emitted back?

The question is answered by the width of the spectral line by the energy-time uncertainty , although to get the correct number one must study the general broadening that can exist.

which means they only undergo Compton scattering.

This is correct, although I would include all kinds of scatterings, (Compton is high energy ).

anna v
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  • If it's the system nucleus-electrons that absorbs the energy, then it's this same system that changes energy level, not just an electron. – Ruslan Oct 03 '21 at 08:07
  • @Ruslan yes, but i, because the nucleus is so tiny and so much heavier, we talk of electrons in orbitals as if the nucleus is at rest, its orbitals confined in such small radiii – anna v Oct 03 '21 at 14:13
  • My point is that in the first part of the sentence you talk about nucleus-electrons system, and in the second you silently assume fixed-nucleus approximation, invalidating the quote being answered and the first part of your sentence. – Ruslan Oct 03 '21 at 14:26
  • @Ruslan I have clarified – anna v Oct 03 '21 at 14:44
  • @annav In your answer you wrote 'the electron's mass is fixed, and if it were able to absorb a photon - at the electron's center of mass - the mass would have to change, which contradicts observations'. But in this link you provided it writes 'The measurement of the mass energy of an unstable particle a large number of times gives a distribution of energies called a Lorentzian or a Breit-Wigner distribution'. How do we observe distribution if electron mass is constant? – Xfce4 Oct 10 '21 at 16:13
  • @Xfce4 The electron is stable as far as our measurements can detect so th comment does not apply to it. The distribution of a stable particle is a delta function https://en.wikipedia.org/wiki/Dirac_delta_function , which means that in an experiment measuring the electron mass we would just get the experimental error distribution. – anna v Oct 11 '21 at 04:08
  • @annav Ok but if the distribution is just due to an experimental error, how can we use such a distribution to determine how long the electron stays in the excited state? – Xfce4 Oct 11 '21 at 07:18
  • @Xfce4 I am talkaing about experimentes measurint themass ot the electron. The transition energies are in atoms are much larger than the experimental errors in measuring the mass of the electron. see https://arxiv.org/abs/1406.5590 . In atomic mass units =0.000 548 579 909 067(14)(9)(2) see the publication for the errors ( the numbers in parenthesis) equation 5) . – anna v Oct 11 '21 at 08:26
  • @annav The question is "How soon does an electron emit the absorbed photon back?" In your answer, you provided this link. I don't understand how this link will help us if the mass of the electron is always constant. – Xfce4 Oct 12 '21 at 09:16
  • @Xfce4 The fixed mass of the electron ( and the nucleus) is used in calculating the spectra for example for hydrogen , the width is due to the reasons given here http://www-star.st-and.ac.uk/~kw25/teaching/nebulae/lecture08_linewidths.pdf , not a variation in masses but in the probability space envelope given by the HUP. – anna v Oct 12 '21 at 09:26
  • @annav Oh, the distribution does not imply that the mass changes, even though it is expressed as $E_0=m_0c^2$. The distribution is to find the amount of uncertainty in the energy. From that we deduce the uncertainty in time and that gives an idea about average time the electron returns to the ground state I suppose. Thank you. – Xfce4 Oct 12 '21 at 10:34
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An isolated atom in a' excited state woul remain there forever. However, the atom necessarily interacts with electromagnetic field, other atoms, etc., which would cause it to reemit the photon. Some of these processes, such as spontaneous emission are independent on temperature and other conditions. Others, such as stimulated emission or relaxation due to collisions with other atoms can be temperature dependent.

Roger V.
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  • An isolated atom in an excited state would remain there forever. However, the atom necessarily interacts with ... That part is so cool. Looking at the QM interpretation of orbitals this is what I would expect. Because once the WF of the electron fits into an orbital (like particle in a 1-D box), why would it change its state without disruption. If it was mandatory for electrons to drop into lower orbitals without an environmental factor, wouldn't they always act the same and drop at the same duration? But still, are you sure about the correctness of that statement? – Xfce4 Oct 03 '21 at 17:22
  • Yes. But normally atom is coupled to electromagnetic field, even if it is in vacuum. This is why it eventually spontaneously emits a photon. It is called natural lifetime of an excited state – Roger V. Oct 03 '21 at 17:44
  • ...normally atom is coupled to electromagnetic field, even if it is in vacuum. Is this statement from quantum field theory about the fields covering the whole universe or do you mean the classical electromagnetic field between the electron and the proton? – Xfce4 Oct 03 '21 at 17:58
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    It is quantum statement - with classical em field spontaneous emission cannit be derived. – Roger V. Oct 03 '21 at 18:45