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Show these wavelengths are consistent with Rydberg formula

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data
    These wavelengths are emitted by a hot gas:
    18.226, 13.501, 12.054 (in nanometres)

    Show that they are consistent with the Balmer series for a hydrogen-like atom.
    Which element do they correspond to?

    2. Relevant equations
    Rearranged Rydberg formula for hydrogen-like atoms:
    ##Z^2 = \frac{hc}{\lambda R}(\frac{1}{n^2}-\frac{1}{4})^{-1}##

    3. The attempt at a solution
    Z is nuclear charge, that's really what I need to find to identify the element, so I rearranged the Rydberg formula to get the above expression.

    The only way I can think of to solve this is by trial and error. So I tried subbing in ##n=3## and the first wavelength, and found that that corresponded to ##Z=6##, then ##n=4## and ##n=5## with the next two wavelengths respectively also gave ##Z=6##. But I'm not sure that really satisfies the condition 'show that they are consistent', because I've just guessed n and it happened to work. Is there a better way to solve this?
  2. jcsd
  3. Oct 12, 2016 #2


    User Avatar

    Staff: Mentor

    Your approach is good.
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