1. Feb 27, 2008

### strangequark

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
$$E_{1}=-78eV$$
$$E_{2}=-58eV$$

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 $$\frac{1}{Z-2}$$"

$$r~\frac{r_{hydrogen}}{Z-2}$$

3. The attempt at a solution

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

Another source I found says that,

$$E_{n}=\frac{n^{2}(-13.6eV)}{(Z-2)^{2}}$$

and,

$$r~\frac{a_{0}}{Z-2}$$

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.