Energy and Orbit Radius for Multielectron Atoms: Lithium's N=1 Electrons

[aznkid310]

Homework Statement

Treat one of lithium's n=1 electrons as a single electron in a one-electron atoms of z=3.

a) Find the energy and orbit radius.

b) The other n=1 electron, being in the same spatial state, must have the same energy and radius, but we must account for the repulsion between these electrons. Assuming they are one orbit diameter apart, what repulsive energy would they share, and if each claims half this energy, what would be the energies of these two electrons?

Homework Equations

I am stuck at part b. How should i proceed?

The Attempt at a Solution

a) r = [(n^2)a_0]/z = a_0/3 = 1.76E-11, where a_0 is the bohr radius

E = -[(z^2)(13.6eV)]/(n^2) = -(9*13.6)/2 = -112.4 eV

 

[SporadicSmile]

What force is providing the repulsion?
Decide on your force, and then calculate the energy caused by this force.
Then simple to calculate the shift in enegry.

 

[aznkid310]

U = k(q1*q2)/d = 41eV where d = 2r

What if each claims half this energy?