A major objection of Rioux and DeKock (1) is the statement in our earlier paper (2) that electron repulsion is responsible for the relative ionization energies of H and
He. Their work clearly shows that a quantum mechanical treatment of this problem reveals that kinetic energy considerations play a crucial role in these values. However, although their criticism is appropriate in the context of this more sophisticated QM treatment, it does not in any way invalidate our original paper, the goal of which was to provide a model, namely the shell model, for the electronic structure of atoms that is consistent with experimental ionization energies. For this purpose it is not even necessary to discuss the difference in the ionization energies of H and He because it is only the large decrease in the first ionization energy from He to Li, indicating that the third electron in Li is at a much larger distance from the nucleus than are the electrons in He, that is relevant to deducing the shell model. Still, students often ask "Why
is the ionization energy of He not twice that of H?" Within this simple shell model, it would only be twice that of He if the electrons were the same distance from the nucleus as the single electron in H and if there were no repulsion between the two electrons. Repulsion between the two electrons in He would reduce the ionization energy of He to less than twice that of H. This is what was intended by the last sentence of the paragraph quoted by Rioux and DeKock: "The ionization energy of helium is slightly less than twice the ionization energy of hydrogen because of the repulsion between the two electrons in helium" (2).
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Gillespie, Ronald J.; Moog, Richard S.; Spencer, James N. J. Chem. Educ.1998 75 539.
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