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Maximum speed for absorbing photons?

  1. Aug 26, 2013 #1
    1. The problem statement, all variables and given/known data
    A ray of photons coming from a laser with a wavelenght of 589.59nm meets a ray of sodium atoms (A=23) coming from the opposite direction.

    What is the maximum speed the sodium atoms can have in order to absorb photons?



    3. The attempt at a solution
    I thought about viewing this as a kind of photo-electric effect, the work function of sodium being 2.46 eV, but then I realised the problem is about absorbing photons, not about emitting photo-electrons.

    The energy of the photons seems relevant: E = hc/λ = 3.369*10^-19 J
    As this is less than the work function for sodium, I am pretty convinced I shouldn't be viewing this as a photo-electric effect problem.

    I was also thinking the clue might be relativistic energy, viewing the sodium atoms and the photons as two frames of reference. Is there perhaps a kind of maximum (kinetic) energy a sodium atom can have if it wants to absorb a photon?
    Am I perhaps supposed to bring into account different energy levels of sodium with different quantum numbers?
     
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  3. Aug 26, 2013 #2

    mfb

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    A ray of sodium atoms is not a metal, you don't have the photoelectric effect. You can excite electrons in the atoms, or ionize them.

    That is a strange question, as the compton effect and pair production have no upper energy limit.
    I guess the question asks for absorption via the D line. Do you know its wavelength? How fast do sodium atoms travel if they see incoming light at that wavelength?
     
  4. Aug 26, 2013 #3
    Thanks for the reply.

    Absorption via the D-line for sodium occurs at 589.0 and 589.6 nm, though these numbers were not given with the problem.
    I worked it out, taking 589.3 nm as the average wavelength for absorption.

    I used the relativistic Doppler-effect to determine the velocity of the sodium atoms, which would equal 5.64*10^5 m/s.
    That seems like quite a decent speed, but I'm still wondering about some things.

    Why take absorption via the D-line? Is that the lowest possible wavelenght (and thus highest possible energy) at which absorption can occur? Or did you just suggest it because the D-lines are very characteristic for sodium?

    As I understand it, in this approach, we're saying the sodium atoms "see" the approaching fotons at a (slightly) higher wavelength because the sodium atoms are themselves moving fast. The question is thus: "How fast can the sodium atoms move, in order to still observe the photons below a threshold wavelength of 589.3 nm?"
    What bothers me is why this D-line absorption should be the threshold at all...
     
  5. Aug 27, 2013 #4

    mfb

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    There is no upper limit. The wavelength given in the problem statement is basically the D-line, so I guessed that you are supposed to use this line.
    Higher frequency, shorter wavelength, not "higher wavelength".

    Well, above that line there is no allowed transition for a while*, until the energy is sufficient for the next line*.

    *not perfectly true, as spectral lines are not single frequencies, and their distribution has an infinite width.
     
  6. Aug 27, 2013 #5

    vela

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    But would those processes be considered absorption?
     
  7. Aug 28, 2013 #6

    mfb

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    The initial photon is destroyed. If you don't like that: ionization stays possible too, and does not have to produce new particles.
     
  8. Aug 28, 2013 #7

    vela

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    I would interpret absorption to mean that the end state is just an excited atom. There's no second photon, and the electron stays bound to the atom.
     
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