Chemical Education Today
Response to Commentary
Deducing the Shell Model from Ionization Energies and the Use of Models in Introductory Chemistry Ronald J. Gillespie Department of Chemistry, McMaster University, Hamilton, ON L8S 4M1, Canada Richard S. Moog and James N. Spencer Department of Chemistry, Franklin & Marshall College, Lancaster, PA 17604-3003
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). Rioux and DeKock also point out that a previous sentence in this paragraph might give the misleading impression that the two electrons in He are actually at the same distance from the nucleus as the single electron in H. While this interpretation is consistent with our simple model, this conclusion will undergo increasing scrutiny as the model is refined later. At the general chemistry level it is probably sufficient to state simply that the high IE of He with respect to H is due to the greater attraction of the nucleus for the electrons, offset by the repulsion between the electrons. The main thesis of our article was that the derivation of electron configurations from quantum numbers is meaningless to students in the general chemistry course, whereas ionization energies provide easily understandable experimental evidence for the shell model. We do not attempt to explain why the electrons are arranged in shells, as this can only be done by means of quantum mechanics. The point we wished to make was that ionization energies provide experimental evidence for the concept of energy levels in atoms, and the sharp decrease in the ionization energy from a noble gas to an alkali
metal is clear evidence for the existence of shells. Looking into the details a little more we can also find evidence of subshells such as s and p, and thus work towards electron configurations. In this way we make the concept of energy levels in an atom, and the shell model in particular, more understandable and less mysterious to the student than a discussion based on quantum numbers. We put the concrete before the abstract and experimental observations before theory, in accord with scientific method, so that the student does not need to resort to memorization of incomprehensible rules for quantum numbers and is reminded that models and theories are developed to explain observations. In the introductory course we can only use the most simple models even though such models often have serious limitations. Students who proceed to more advanced courses in chemistry will gradually move to more sophisticated and more satisfactory models. In concluding their article, Rioux and DeKock state that the arguments they use are obviously too advanced for introductory students and they raise the question of what we can say to introductory students about the details of the periodicity of physical properties, such as ionization energies, that is both correct and understandable. This is indeed a very general problem, since quantum mechanics is essential for a full understanding of many of the properties of atoms and molecules and of the essential concept of the chemical bond. Clearly we cannot give a full and complete explanation at the introductory level, but we do need to develop approaches and models that—although they will need modification and amplification in later chemistry courses—are nevertheless essentially correct and understandable to students in the introductory course, many of whom will take few, if any, more chemistry courses. Lewis structures and the VSEPR model, as well as the shell model, are examples of approximate models that have proven very useful at the introductory level and are perhaps all that is needed for a discussion of bonding at this level. We believe that it is time the question raised by Rioux and DeKock received some very serious discussion, which we hope will lead to the development of suitable material for the introductory course such as we proposed in the first three parts of our series of articles. Unless we do this and make some real changes to the conventional treatment of topics that require quantum mechanics for a full explanation, chemistry will remain for many freshman students a mysterious and largely incomprehensible subject to be avoided as far as possible. It is to be hoped that subject specialists, in addition to general chemistry instructors and textbook writers, will take part in this discussion so that erroneous and unsatisfactory models are not perpetuated but replaced by correct, never-
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Chemical Education Today
theless understandable, models. The revision of what we teach concerning atomic and molecular properties is one aspect of a much needed reform of the whole content of general chemistry, concerning which there has been much discussion but so far rather little agreement. We would certainly welcome further discussion on all four of our series of articles on demystifying introductory chemistry.
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Literature Cited 1. Rioux, F.; DeKock, R. L. J. Chem. Educ. 1998, 75, 537–539. 2. Gillespie, R. J.; Spencer, J. N.; Moog, R. S. J. Chem. Educ. 1996, 73, 617.
Journal of Chemical Education • Vol. 75 No. 5 May 1998 • JChemEd.chem.wisc.edu
