[sparkle123]

So we are given the Bohr energy formula and we calculate that the ground state energy of a hydrogen atom is -13.6 ev.

The question is:
H– is a two-electron atomic system. Assuming that the Bohr energy formula is valid for each electron with nuclear charge Z replaced by Zeff, calculate Zeff for H–.

The solution is:
Zeff = –13.6 + 27.2*(Zeff)^2 = 0.7

I don't understand the solution... I see that 27.2 comes from 13.6 X 2, and I believe that the -13.6 accounts for the second ionization and the 27.2*(Zeff)^2 is trying to account for the first ionization, and the Zeff is changed due to the repulsion of the two electrons.

I have no idea when 27.2*(Zeff)^2 is has a plus sign, or why we can just add the two values to get our Zeff, or why Zeff would be represented by -13.6 in the first place, because it seems more like the value for "energy" (i.e. E=-13.6*Zeff^2/n^2). Also it seems like the solution gives a quadratic...