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Hydrogen -Energy State Transitions

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the (algebraic) relationship between the wavelengths of the equivalent transitions (i.e. same n1 and n2) for hydrogen-like ions of atomic number Z and hydrogen itself.

    2. Relevant equations

    I know:

    [tex]h\nu (n_{1} , n_{2} ) = C_{1}Z_{1}^2(\frac{1}{n_{2}^2} - \frac{1}{n_{1}^2})[/tex]

    And

    [tex] \nu = \frac{c}{\lambda}[/tex]



    3. The attempt at a solution

    But that's as far as I can get really. I know putting Z as 1 will give me the simplest case for Hydrogen, but I'm still a bit perplexed at what the question actually wants. I could rearrange for [tex]\lambda[/tex], but I'm still unsure if that's on the right lines?

    Thanks.
     
    Last edited: Oct 13, 2009
  2. jcsd
  3. Oct 12, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    Use lambda = h/v = h^2/(hv) = h^2/(C*Z^2*X)
    where X is the big pair of brackets with the transition numbers in it.
    You want to compare this with the same expression for hydrogen which is h^2/(C*1*X) unless the C is different for hydrogen, too.
    They are the same except for the Z^2 so you'll end up with
    lambda = 1/Z^2 * (lambda for H)
     
  4. Oct 13, 2009 #3
    Sorry, I just realised I've written rubbish:

    [tex] \nu = \frac{c}{\lambda}[/tex] Is what is meant to be there!

    Sorry
     
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