Chemical Education Today
Commentary
In Defense of Quantum Numbers by Robert M. Richman
The typical textbook approach to introducing electron configurations of atoms requires that students learn about quantization of energy, rules for allowable quantum numbers in the hydrogen atom, the orbital approximation, the Pauli exclusion principle, removal of degeneracy in polyelectronic atoms, the Aufbau principle, and Hund’s rule (1). Gillespie, Spencer, and Moog have argued that this approach makes introductory courses more abstract, mysterious, and esoteric than necessary (2). They propose an innovative alternative in which the concept of electron shells is naturally introduced to explain first ionization energies, and subshells to explain subsequent ionization energies. From there, electron configurations can be proposed without resorting to the Schrödinger equation. Energy quantization, the Pauli principle, the Aufbau principle, and Hund’s rule must still be introduced, but with experimental justification rather than as the postulates of a theory. I would argue that the strength of this approach is also its weakness. Students taking introductory chemistry courses are generally taking courses in other academic disciplines concurrently, and part of our task is to help them understand what makes chemistry unique. George Gale’s analysis is insightful (3). How do we come to our knowledge? What is our epistemology? One could argue that the sciences have two answers. Present-day strains between theorists and experimentalists date to a divergence since the time of the classical Greek scientists Pythagoras and Aristotle. Aristotle believed that scientific knowledge would come through careful observation. Empiricist epistemology developed from his view that the human sensory system was the only legitimate starting point for scientific knowledge. Today, empiricists also accept as valid experimental evidence the extension of the human senses by instrumentation. Then through the use of inductive logic, experimental results may be generalized into laws. There are some synthetic chemists who reflect this purely empiricist position when they spurn attempts to understand why some reactions occur in favor of cataloguing a large data base of what chemical reactions occur. Pythagoras believed that pure mathematical thought would produce knowledge about the natural world, and a rationalist epistemology developed from the notion that one could start with a set of postulates and use the rules of logic to deduce truths. Geometry is still taught from this strictly rationalistic perspective. Among chemists, theoreticians now come closest to this position. From rationalism come theories. Gillespie, Spencer, and Moog claim that “we should be emphasizing to students that scientific theories and principles are based first and foremost on experiment” (2). To be sure, theoretical predictions must be measured against experimental results in order to be ac-
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cepted by the scientific community. But in fact, theories are based, first and foremost, on postulates. Modern theoretical chemistry, addressing problems that cannot be solved exactly, calls these postulates approximations or assumptions. The goal is to make the least drastic simplification necessary to make the mathematics tractable. While some individual scientists come very close to being pure empiricists or pure rationalists, modern science is based on the interaction of the two epistemologies. General chemistry offers several prototypical examples of this. The ideal gas law correlates experimental results and allows us to predict and control pressure–volume–temperature relationships in new situations. Kinetic–molecular theory allows us to understand and explain why it works at the atomic level. Rate laws correlate kinetics experiments and allow us to predict and control the rate of reaction when we systematically alter concentrations. Mechanisms allow us to understand and explain how we think the molecules are actually reacting. But no more profound example exists in chemistry than the derivation of the periodic law by the empiricist Mendeleev and others with its subsequent explanation based on the theory developed by the rationalist Schrödinger. As sophisticated computer graphics make molecular orbital and mechanics calculations accessible to beginning students, at the same time as scanning tunneling microscopes show us pictures of individual atoms, it becomes ever more important for us to differentiate the theoretical from the experimental while showing students how a seamless integration of the two defines the distinctive nature of how chemists think. When we base our derivation of the periodic table exclusively on the experimental, we miss our best opportunity to do that. Introducing quantum numbers without the benefit of mathematical derivation may indeed be mysterious and abstract to students. But the primary source of this mystery is the anti-intuitive nature of quantum mechanics which makes the topic more, rather than less, appealing for inclusion in a liberal arts education. Literature Cited 1. Zumdahl, S. S. Chemistry, 4th ed.; Houghton Mifflin: Boston, 1997. 2. Gillespie, R. J.; Spencer, J. N.; Moog, R. S. J. Chem. Educ. 1996, 73, 617-622. 3. Gale, G. Theory of Science: An Introduction to the History, Logic, and Philosophy of Science; McGraw-Hill: New York, 1979.
Robert M. Richman teaches in the Department of Science, Mount St. Mary’s College, Emmitsburg, MD 21727; phone: 301/447-6122; email:
[email protected].
Journal of Chemical Education • Vol. 75 No. 5 May 1998 • JChemEd.chem.wisc.edu
