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•• The ground state of sodium (Z = 11) has two electrons in the 1s level, two in the 2s, six in the 2p, and one in the 3s. Consider an excited state in which the outermost electron has been raised to a 3d state (but all of the inner electrons are unchanged). Because the 3d wave function is not very penetrating, you can treat the outer electron as if it were completely outside all the other electrons. (a) In this approximation what is the potential-energy function U(r) felt by the outer electron? (b) In the same approximation, what should be the energy of an electron in a 3d state? Compare your answer with the observed value of −1.52 eV. Why is the observed value lower than your estimate?
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