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Atomic physics

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data

    A line of wavelength 1093 nm is observed in the hydrogen spectrum. Identify the transition that leads to this line.

    2. Relevant equations

    where n refers to the upper state and n' to the lower state.

    1/lamda = R (1/n' - 1/n) -----1

    Ei - Ef = hc/lamda ------2

    3. The attempt at a solution

    i am not very sure with my answer... please help along thanks.

    basically i see this as a simultaneous equation with two unknown.
    i put lambda = 1093nm in equation 1
    hence i get,

    0.083401374 = 1/n' - 1/n -------3

    this is the part i am not so sure. using the equation 2.

    Ei - Ef = hc/lamda

    (- 13.606ev / n ' ) - (- 13.606ev / n ) = hc/1093nm

    13.606 ev (1/n' - 1/n) = 1.81855 x 10^-19 ------4

    If i put eq 3, 1/n' = 0.083401374 + 1/n into eq 4

    it will become zero.

    Where did i go wrong?
     
  2. jcsd
  3. Oct 12, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member


    No, the equations

    [tex]\frac{1}{\lambda}=R\left(\frac{1}{n'^2}-\frac{1}{n^2}\right)[/itex]

    and

    [tex]E_i - E_f =13.606\text{eV}\left(\frac{1}{n'^2}-\frac{1}{n^2}\right) \frac{hc}{\lambda}[/tex]

    (You forgot to squares the "n"s! ) both give you exactly the same information (since [itex]\frac{R}{hc}=13.606\text{eV}[/itex] )

    So you only really have one equation and two unknowns. However, you also know that both [itex]n[/itex] and [itex]n'[/itex] are positive integers, so this should provide you with enough additional information to answer the question.
     
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