- #1

strangequark

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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.

## Homework 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]

## 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 doesn't 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.