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Helium radius

  1. Feb 27, 2008 #1
    b]1. The problem statement, all variables and given/known data[/b]
    Given the observed spectrum of helium, estimate the distance between two electrons in a helium atom (a) in the ground state and (b) in the first excited state. Neglect the exchange energy.

    2. Relevant equations
    [tex]E_{1}=-78eV[/tex]
    [tex]E_{2}=-58eV[/tex]

    Given in my textbook,
    "Hartree theory predicts that the radius of the n=1 shell is smaller than that of the n=1 shell of hydrogen by approximately a factor of [tex]\frac{1}{Z-2}[/tex]"

    [tex]r~\frac{r_{hydrogen}}{Z-2}[/tex]

    3. The attempt at a solution

    I'm confused by the text above. Doesn't [tex]Z_{helium}=2[/tex], and hence [tex]Z-2=0[/tex]?

    Another source I found says that,

    [tex]E_{n}=\frac{n^{2}(-13.6eV)}{(Z-2)^{2}}[/tex]

    and,

    [tex]r~\frac{a_{0}}{Z-2}[/tex]

    I can solve the first eq. for Z-2, but again this doesnt really make sense to me because I get Z-2=2.39 (for ground state) which would imply that Z=4.39? Also using this, I don't get the answers that are in the key.

    Please point me in the right direction... thanks.
     
  2. jcsd
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