- #1
Antonija
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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: r2 is distance from second electron to nucleus, r12 is distance between first and second electron.
The Attempt at a Solution
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Potential is sum of Coulomb potential between one electron and nucleus, and potential between 2 electrons themselves:
Φ(r2)= -e/(4πε0) * 1/r2 + e/(4πε0) ∫ (Ψ1s(r1))2 /r12 d3r1
I know 1s wavefunction for hydrogen so when I write it, it is proportional to exp(-r1/a0)I can put it into my potential but I don't know how to solve integral with wavefunction, as I have r12 in denominator, which is equal to Ir1-r2II 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...