Letter pubs.acs.org/jchemeduc
Replace Band Theory in Introductory Chemistry Stephen J. Hawkes* Department of Chemistry, Oregon State University, Corvallis, Oregon 97331-4003, United States ABSTRACT: Band theory is less helpful than the Mott−Hubbard theory of combined electron excitation and delocalization for explaining conductivity and semiconductivity for introductory students. KEYWORDS: First-Year Undergraduate/General, Curriculum, Physical Chemistry, Textbooks/Reference Books, Conductivity, Electrochemistry, Metalloids/Semimetals, Theoretical Chemistry
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and theory is used in introductory texts to explain conductivity and semiconductivity but it is not adequate for this purpose. Band theory offers no explanation for the increase in conductivity when a substance is compressed.1 It does not explain what happens when an electron is excited to the conduction band or why it then assists conduction. It does not explain why insulators are in the top right corner of the periodic table or why metallic allotropes of an element have higher densities than their nonmetallic allotropes.1 The Mott−Hubbard model2,3 succeeds where band theory is inadequate. Electrons dissociate from their parent atoms and form a nonlocalized system with the dissociated electrons of other atoms. Such a nonlocalized system contributes to conductivity in the same way that the nonlocalized system of graphite makes it a conductor. Multiple excited atoms cause more delocalizations and greater conductivity. Even more excitations create an “electron sea” as in a metal. The “band gap” posited by band theory is the energy necessary to excite the electrons (with the help of delocalization energy). This model also accounts for the existence of insulators and their position in the periodic table. Two conditions must be fulfilled for a substance to be a conductor. An electron must be easily dissociated (i.e., the substance must have a low ionization potential) and the atoms must be packed together closely enough that a dissociated electron is in close contact with an electron of another atom and can form a delocalized system with it. Sulfur, for example, and other elements at the top right of the periodic table, have neither criterion under normal conditions, so they are insulators. Increasing the temperature of semimetals and nonmetals aids the release of the electron so that conductivity increases with temperature. Increasing the temperature of metals decreases the density and hence the conductivity. Extending the theory beyond what is described above or making it quantitative requires a better understanding of physics than is usual among introductory students. This is described in refs 2 and 3. Band theory should be eliminated from introductory texts and replaced by the Mot−Hubbard model, which is more comprehensible and more useful at this level. The band model is more useful for theoretical development, which is also described in refs 2 and 3. © 2012 American Chemical Society and Division of Chemical Education, Inc.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
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REFERENCES
(1) Hawkes, S. J. J. Chem. Educ. 2009, 86, 431. (2) Edwards, P. P.; Johnston, R. L.; Rao, C. N. R.; Tunstall, D. P.; Hensel, F. Philos. Trans. R. Soc. London, Ser. A 1998, 356, 5. (3) Edwards, P. P. What, Why and When is a Metal? In The New Chemistry; Hall, N., Ed.; Cambridge University Press: Cambridge, 2000; pp 108−109.
Published: March 6, 2012 694
dx.doi.org/10.1021/ed100850g | J. Chem. Educ. 2012, 89, 694−694
