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•• The ground state of lithium (Z = 3) has two electrons in the 1s level and one in the 2s. Consider an excited state in which the outermost electron has been raised to the 3p level. Since the 3p wave functions are not very penetrating, you can estimate the energy of this electron by assuming it is completely outside both the other electrons. (a) In this approximation what is the potential-energy function felt by the outermost electron? (b) In the same approximation write the formula for the energy of the outer electron if its principal quantum number is n. (c) Estimate the energy of the 3p electron in this way and compare with the observed value of −1.556 eV. (d) Repeat for the case that the outer electron is in the 3d level, whose observed energy is −1.513 eV. (e) Explain why the agreement is better for the 3d level than for the 3p. Why is the observed energy for 3p lower than that for 3d?
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