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Find atomic number from spectral lines

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data
    An atom or ion with one electron has energy levels [itex]E_n=-A/n^2[/itex]. Tw neighboring lines in its spectrum at room temperature have wavelengths [itex]\lambda_1=97.5[/itex] nm and [itex]\lambda_2=102.8[/itex] nm. (Note that [itex]hc=1.240\times 10^{-6}[/itex] eV m).

    (a)What is the constant A?
    (b) Identify the atom.

    2. Relevant equations



    3. The attempt at a solution
    I know that it must be either Hydrogen (line n=3 and n=4 of the Lyman series) or Li++ (which should have frequencies very close to those of the Hydrogen. However, this is a guess and I don't know how to actually prove that.

    Any idea?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 21, 2014 #2

    DrClaude

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    Staff: Mentor

    Which transition in Li2+ are you considering?
     
  4. Jan 21, 2014 #3
    Actually I don't know. I suppose the same ones, but I'm not sure at all.
     
  5. Jan 21, 2014 #4
    To find A, did you consider using the deBroglie relation?
     
  6. Jan 22, 2014 #5

    DrClaude

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    Staff: Mentor

    Do you know the formula that gives the energy levels of hydrogenic atoms?
     
  7. Jan 22, 2014 #6
    It is written in the text of the problem. It's the same but with A=13.6 eV.
     
  8. Jan 22, 2014 #7

    DrClaude

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    No it's not. ##A = 13.6\ \mathrm{eV}## for hydrogen, but not for Li2+. You have a nucleus with three times the charge: surely the Coulomb attraction must be greater.
     
  9. Jan 22, 2014 #8
    You are right. We have an extra factor of [itex]Z^2[/itex] for Hydrogen-like atoms. However, I don't think this solve the problem. What do you suggest?
     
  10. Jan 23, 2014 #9

    DrClaude

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    Staff: Mentor

    I would write the Rydberg formula for each transition, take the difference between the two, and see if, with the value of ##A## for an atom other than hydrogen, it is possible to get two consecutive levels ##n## and ##n+1## to produce those wavelengths.
     
  11. Jan 23, 2014 #10
    That's probably the best thing to do. The point is that you end up with a cubic equation in n, which is quite horrible. However, in principle is exactly solvable so it is probably the right answer. :D
     
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