- #1

Antonija

- 18

- 0

## Homework Statement

The negative H− ion is a two-electron system like the He atom. How large is the binding energy of the second electron?

## Homework Equations

For hydrogen-like atoms we can use hydrogen wavefunctions so I did it here. First there is potential to be found and then, multipled with charge, it gives energy. Symbols: r

_{2}is distance from second electron to nucleus, r

_{12}is distance between first and second electron.

## The Attempt at a Solution

[/B]

Potential is sum of Coulomb potential between one electron and nucleus, and potential between 2 electrons themselves:

Φ(r

_{2})= -e/(4πε

_{0}) * 1/r

_{2}+ e/(4πε

_{0}) ∫ (Ψ

_{1s}(r

_{1}))

^{2}/r

_{12}d

^{3}r

_{1}

I know 1s wavefunction for hydrogen so when I write it, it is proportional to exp(-r

_{1}/a

_{0})I can put it into my potential but I don't know how to solve integral with wavefunction, as I have r

_{12}in denominator, which is equal to Ir

_{1}-r

_{2}II can use cosine law but still can't solve integral. I don't know how to behave with this in integral. Sorry if my equation writing is bad, I'm posting for the first time so still learning...