A Simple Model: The multielectron atom is unsolvable, but simple models go a long way. Section 7.8 gives energies and orbit radii for one-electron/hydrogenlike atoms. Let us see how useful these ate by considering lithium,
(a) Treat one of lithium's n = 1 electrons as a single electron in a one-electron atom of Z = 3. 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 roughly 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? (c) Approximately what charge does lithium's lone valence electron orbit, and what radius and energy would it have? (d) Is it reasonable to dismiss the role of the n = 1 electrons in chemical reactions? (e) The actual energies of lithium's electrons are about -98 eV (twice, of course) and -5.4 eV. How good is the model? (f) Why should the model's prediction for the valence electron's energy differ in the direction it does from the actual value?
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