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Line spectra

  1. Jul 7, 2006 #1
    I need help on this problem that asks me to solve for [tex]n_1[/tex] and [tex]n_2[/tex] (the initial and final quantum numbers).

    This is the given information (the line spectra for Hydrogen):

    color red known wavelength: 656.4 nm
    color turquoise known wavelength: 486.3 nm
    purple wavelength: 434.2 nm
    purple wavelength: 410.3 nm

    [tex]n_1[/tex] and [tex]n_2[/tex] are unknown for each one.

    I've tried using this equation, the Rydberg Equation, to solve for [tex]n_1[/tex] and [tex]n_2[/tex]:

    [tex] \frac {1}{\lambda} = (R_H)(\frac {1}{n^2_2} - \frac {1}{n^2_2})[/tex]

    where [tex]\lambda[/tex] is the wavelength, [tex]n_1[/tex] and [tex]n_2[/tex] are the initial and final principal quantum numbers, with the initial one being larger than the final one. [tex] R_H[/tex] is Ryberg's constant.

    I've plugged in the numbers and (for the color red) I got
    [tex]\frac {1}{656.4} = \frac {R_H}{n^2_1} - \frac{R_H}{n^2_2}[/tex]

    I still can't find n1 and n2. Am I using the right formula? I just couldn't understand how to solve a problem with 2 variables.
     
  2. jcsd
  3. Jul 7, 2006 #2

    Astronuc

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    Staff: Mentor

    Well n2 > n1, so pick n1 = 1, then solve for n2, which must be an integer.

    If that doesn't work, then try n1 = 2, and solve for n2.

    Alternatively, one can select n1=1, and then using n2 = 2, 3, 4, . . . solve for the wave lengths.

    What value is one using for Rydberg's constant.

    Try this reference - http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html

    Hint - the visible lines are in the Balmer series.
     
  4. Jul 8, 2006 #3

    GCT

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    Science Advisor
    Homework Helper

    Also, consider the selection rules as well as the determination of the ionization energy.
     
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