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Spontaneous emission

  1. Apr 24, 2005 #1
    Can someone please explain why an excited electron in an atom decays to the ground state, if energy eigenstates are stationary states.
     
  2. jcsd
  3. Apr 25, 2005 #2

    Claude Bile

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    These stationary states are unstable, and even the slightest pertubation will cause the photon to decay. This is analagous to standing a pencil on its tip: if you balance it dead right it will stay upright (a stationary state), but any slight pertubation (say, a slight breeze) will cause it to fall.

    Claude.
     
  4. Apr 26, 2005 #3
    When you excite an electron via radiation or any wave carrying some threshold energy , the electron absorbs the energy. Initially electron is in an orbit with energy -E , so the electron has also got same energy -E , now when it gains some energy 'K' , its energy becomes -(E+K) which is less than the initial E because of the minus sign. As lower energy levels are more stable and have lesser energy , the electron excites itself from its initial state to a more stable state by gaining certain amount of needed energy from the radiation.
     
  5. Apr 26, 2005 #4

    SpaceTiger

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    You have all this reversed. When an electron absorbs a photon, it gains energy -- meaning the energy would become less negative, -(E-K) -- and gets excited to a higher energy state. In the case that the OP is discussing, the electron is emitting a photon, so it's losing energy, -(E+K). Also, lower energy levels are not always more stable. In general, the lowest energy level is the most stable, however.
     
  6. Apr 26, 2005 #5
    It is not the electron that is excited but the atom to which the electron 'belongs'

    It is important to realize that these electronic energy levels that we all talk about only arise because of the fact that the electron has an interaction with the atomic nucleus. In other words, the energy levels to which electrons will jump when excitation or de-excitation occurs only exist because these electrons are 'part of an atom'

    De-excitation occurs because it lowers the associated potential energy : ie things get more stable...(this is a general formulation and there are those exceptions that confirm this rule)

    marlon

    ps : what did i read about a photon decaying ???
     
  7. Apr 26, 2005 #6

    Astronuc

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    As the name implies, the 'ground state' is the basic state of an atom. Each type of atom has its own unique ground state. With respect to the last electron, all lower energy states are filled with other electrons. An excited electron will exist in upper energy states only briefly before dropping back to the ground state and emitting a characteristic photon. That's just the way it is.
     
  8. Apr 26, 2005 #7

    SpaceTiger

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    If there is only one electron in the atom, don't you think this point is largely semantic? There is some coupling between the electron and the nucleus, but its a very small effect. The wave function is basically that of an electron in a potential well.
     
  9. Apr 26, 2005 #8
    What i wanted to point out is the fact that these energy levels come from the fact that the electron interacts with the nucleus. You mentioned it yourself : an electron in a potential well. Single electrons don't have these energy levels for the obvious reasons. That is just what i wanted to clarify : the energylevels are not inherent to the actual electrons but to the electron-nucleus interaction.

    regards
    marlon
     
  10. Apr 26, 2005 #9

    SpaceTiger

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    But by that definition, it would then be improper to say that a planet could be excited to a higher-energy orbit because, after all, the planet wouldn't be orbiting without the sun. You'd have to say, instead, that the solar system is excited to a different energy state. I have a feeling that dynamicists would look at you strange if you used this terminology.

    I know our argument is largely semantic, and I'm not trying to say that your terms are even incorrect, I just want to defend the terminology of myself and others. I often hear ISM physicists talk in terms of what happens to the "electron" in an atom, rather than always discussing in terms of the atom as a whole. This description is often more helpful for understanding what's going on inside of the atom, even if the language is somewhat imprecise.
     
  11. Apr 26, 2005 #10
    I really don't know why you bring in this analogy. Anyway it is totally wrong because the phenomena we are talking about (electrons in atoms) are totally different compared to celestial motions. I mean, let us not start mixing QM with classical mechanics. That is why this analogy is erroneous.

    It certainly is not. I am just presenting the QM description of an atom and how it is responsible for the specific electronic energy levels.

    It is fundamental that people understand how these electronic energy levels arise. You cannot deny the fact that a Fermi-gass has different behavior then electrons 'inside' atoms. Besides, how else would we describe the "plethora" of atomic spectra that are known to us ???

    regards
    marlon
     
  12. Apr 26, 2005 #11

    SpaceTiger

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    We're discussing the distinguishability of the individual components of the system, not their behavior. An electron does indeed behave differently in an atom than a planet does around the sun, but you haven't properly defended the necessity for combining them into a single conceptual entity. The only reason you've given so far is:

    Thus, my analogy is appropriate, as this fact is also true of planets around the sun.


    I don't see your point. An object will of course behave differently when put under different external restrictions. That doesn't mean, however, that it's inappropriate to consider it as a separate entity.
     
  13. Apr 26, 2005 #12
    Yes we very much are...
    Again, the electronic levels very much explain the actual electronic behavior. You cannot talk about these energy levels without explaining where they came from and why they exist. I challenge you to explain this without bringing in the atomic nucleus.


    Besides this 'distinguishability' does not exist in QM.


    No it is not. You are referring to a classical system. If you would apply this system onto the electrons and the nucleus, you would not even have stable atoms. It is this way of thinking that gives rise to questions like 'why doesn't an electron crash into a nucleus and why doesn't it radiate ???' I have been answering such misconceptions ad nauseum...

    My point was that free electrons are NOT the same as electrons in an atom. You cannot just talk about some electron and its 'possible' energy levels because in the end people will ask : where do these energy levels come from ?

    Separate entity ??? What do you mean ?

    marlon
     
  14. Apr 26, 2005 #13

    SpaceTiger

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    Again, I challenge you to explain the energy of Pluto without invoking the sun. This is beside the point.


    How can you say that? The entire concept of the Pauli Exclusion Principle is based on the distinction between distinguishable and indistinguishable particles.


    You seem to be missing the crux of the analogy, as there is no logical necessity for the above to be true for my argument to work. In case you haven't figured it out yet, I know that classical laws do not describe the electron's wave function in an atom. I know that it doesn't "orbit". Rather, here is what happened:

    1) You said that an electron and proton cannot be considered as separate (distinguishable) when part of an atom.
    2) I asked you to explain why.
    3) You said " the energy levels are not inherent to the actual electrons but to the electron-nucleus interaction".
    4) I gave an example of a system in which the components were considered separate, despite the above being true.

    Note that the classical-quantum distinction does not come into this anywhere, nor do I suggest that electrons should be treated classically. If you think there is some crucial aspect of the quantum nature of particles that supports your argument further and renders my analogy inappropriate, I'm willing to hear it, but most of the things mentioned so far are not relevant to what we're discussing.


    Indeed, their wave functions are different, but we still call them "electrons". We still talk about electrons being ejected from atoms, we still talk about electrons in energy levels, valence shells, etc. It abounds in the literature of many fields. The point is that no essential feature of the atom is lost by characterizing it as an "electron interacting with a nucleus". The only difference is that the electron is now represented by a wave function rather than a point particle with definite momentum and position.


    And you simply answer, "the interaction of the electron with the nucleus".
     
    Last edited: Apr 26, 2005
  15. Apr 27, 2005 #14
    But this is very much the point. I asked you a specific question which you could not answer. Ofcourse not, because it is not possible. I really think that you still are not getting what i am trying to say. My point is that electrons in atoms exhibit their energy levels because of interactions with the nucleus, eg : L-S-coupling or Coulombic-interaction. You cannot just speak about 'exciting an electron' to some higher energy level.


    So when a photon of the right energy hits an atom, it doesn't "excite" an electron, it excites the WHOLE ATOM. The energy states that the electron can occupy is a result of the combination of the nucleus and the electron, not just the electron alone. As a proof : a free electron has no such energy states. This is why i asked you about electrons in ayoms and free electrons.

    So the nucleus plays a significant role in forming those energy states for the electron to occupy. It is the atom that is excited upon photon absorption, not the electron.


    You cannot distinguish between different electrons that make up any Fermi-gass...What is your point ? All electrons obey this very same Pauli principle, so how can it be used to distinguish between electrons.


    But in the example that you gave, isn't there an interaction going on that determins how the bodies move and what energy they exhibit ??? I think so...So i really don't see the justification for your analogy.

    Besides, i never said that electrons and protons cannot be treated as two single entities. Again, what i said is that the energy levels of electrons in atoms are determined by their interaction with the actual nucleus. Why is this so hard to get ??? It's quite elementary if you think about it...

    :) YES, it's better then not being able to answer the actual question isn't it ? Ofcourse if people want a full blown justification of this, then we both know there is only one option.

    regards
    marlon
     
    Last edited: Apr 27, 2005
  16. Apr 27, 2005 #15

    SpaceTiger

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    I assume you're referring to the bit about the challenge to explain the energy levels without the atomic nucleus. Of course you need the nucleus to explain the energy levels, but, as I said in my original post, the nucleus itself is only barely effected by the absorption of the photon. For all intents and purposes, it is only the electron that is excited and the potential well in which it sits is largely unchanged.

    I'm going to reiterate what I said originally; that I think our argument is largely semantic. I don't think it's inappropriate to say that the "atom" is excited, but I also don't think it's inappropriate to say that the electron is excited.


    In my original response to you: "There is some coupling between the electron and the nucleus, but its a very small effect". Again, I'm going to use the analogy of the solar system because I still don't think you've shown it to be inappropriate. In actuality, Pluto does not orbit about the sun, the sun and Pluto orbit about their mutual center of mass (in an idealized two-body system). Thus, the ejection of Pluto from the system would effect the sun, but only a negligible amount. Yet we still talk about "Pluto orbiting the sun" and "Pluto getting excited to a higher orbit". It conveys basically the same information.


    That's not a proof of what you're trying to show. The quantum view of nature does indeed change many things, most notably the quantization of energy levels and the shift from point particles to wave functions. However, it does not change the fact that a much more massive body will be effected less by a given force field than a much less massive one. So it is with the atom, and so it is with the solar system.


    We're not talking about a Fermi gas, that was something you brought up in a separate point. We're talking about an electron and a nucleus, two very distinguishable particles.


    The point of the analogy was to show that, despite the mutual interaction, very little information was lost by talking only about the changes in the much less massive component. The potential well in which it was moving would be almost completely unchanged.


    I'm well aware of what you're trying to show; in fact, I was aware of it from the beginning. I'm trying to show you why it makes no practical difference in the language of atomic physics.
     
  17. Apr 27, 2005 #16

    Claude Bile

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    I think the original poster was confused by the 'spontanaeity' of the spontaneous emission, i.e. where does the time-invariance come into play when one is discussing energy eigenstates. Why does a time-invariant solution suddenly change?

    The explanations offered in this thread that run along the lines of 'It is in a higher energy state, so it wants to decay into a lower energy state' doesn't cut the mustard for me. While I realise it is a standard textbook explanation, not everything decides to shed its potential energy, simply because a lower potential energy state is available to it.

    (If this explanation is used, it begs more questions. Why do energy states have lifetimes? Why doesn't this decay occur instantaneously? Why do different energy levels have different lifetimes?)

    I will quote one case, that of lighting a match. A case more relevant to this thread, is that of metastable states. An atom in a metastable energy state, kept in isolation will not decay into a lower energy state even though there is one available to it because selection rules forbid this from happening.

    External pertubations (such as a collision with another atom) will cause an atom in such a state to eventually decay into a lower energy state.

    Sorry, but I have to go, so apologies if this post seems hastily constructed.

    Sorry, I meant atom, I didn't have time to read over my post (I was being hustled out to lunch).

    Thanks Marlon, for pointing this out.

    Claude.
     
    Last edited: Apr 27, 2005
  18. Apr 27, 2005 #17

    dextercioby

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    Well,Marlon,the photon had tooth decay,of course...

    I'm surprised no one made a reference towards a book where he/she could find the theory of spontaneous emission.

    2 levels:
    *semiclassic (classical radiation,quantum system) which is discribed in every graduate course on QM.
    *quantum (qauntum radiation (photons),quantum system (electrons in atoms)) which is discribed in any serious book on QED.The first is,of course,"The Quantum Theory of Radiation" by W.Heitler (any edition,any language).


    Daniel.
     
  19. Apr 27, 2005 #18

    dextercioby

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    I think you just ruled out spin-spin interaction in the case of electrons (Fermi gas) and a great deal of the theory behind "magnetism"...

    Daniel.
     
  20. Apr 27, 2005 #19

    dextercioby

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    Hyperfine structure due to electron spin-electron spin coupling...? :rolleyes:


    Say what...? :surprised Ever heard of the hydrogen atom,to give the simplest example...? :surprised



    So did I. :wink:

    Daniel.
     
  21. Apr 27, 2005 #20

    dextercioby

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    What energy...?Internal?Rotation around its axis?Translation through an empty space in which only the I-st postulate of Newton would apply...?


    Daniel.
     
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