The wave properties of matter

Before discussing these ideas, we look briefly look at the classical mechanics of particles, reviewing some simple concepts that form an essential background to the quantum theory of matter. 

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In this chapter, you learned about the electronic structure of the atom in terms of the older Bohr model and the newer quantum mechanical model. You learned about the wave properties of matter, and how to describe each individual electron in terms of its four quantum numbers. You then learned how to write the electron configuration of an atom and some exceptions to the general rules. 

Matter is classically particulate in nature, but it also manifests wave character. The wave property of matter is related to its particle nature by de Broglie s relation A = hip, where A is known as the de Broglie wave length. 

For what sizes of particles must one consider both wave and particle properties Summarize some of the evidence. supporting the wave properties of matter. 

The periodic nature of the properties of atoms and the nature and chemistry of molecules are based on the wave property of matter and the associated energetics. Concepts including the electron-pair bond between two atoms and the associated three-dimensional properties of molecules and reactions have served the chemist well, and will continue to do so in the future. 

The discovery of the wave properties of matter raised some new and interesting questions. Consider, for example, a ball rolling down a ramp. Using the equations of classical physics, we can calculate, with great accuracy, the ball s position, direction of motion, and speed at any instant. Can we do the same for an electron, which exhibits wave properties A wave extends in space and its location is not precisely defined. We might therefore anticipate that it is impossible to determine exactly where an electron is located at a specific instant. 

The major part of this book will be concerned with the wave properties of matter, but it will be helpful, at the outset, to spend a little time looking at the particle properties of electromagnetic radiation because similar concepts apply in both cases. 

Note that this conclusion is based on the assumption that no 4n-mem-bered rings are present. If they are, resonance theory fails because the parallel between numbers of resonance structures and NBMO coefficients no longer holds. Consider, for example, styrene (48) and cyclooctatetraene (49). There are in each case two possible classical structures yet styrene is aromatic, while cyclooctatetraene is antiaromatic. This situation is quite general. Thus one can write four classical structures for biphenyl (50), corresponding to the Kekule structures for each benzene ring, but for biphenylene (51), where there is an additional quinonoid structure (52). This should imply that the central ring in biphenylene is aromatic in fact, it is antiaromatic. Thus resonance theory should not be allowed to survive even as a poor substitute for the PMO method since there are cases where it leads to qualitatively incorrect results. The reason for the failure of resonance theory in these cases stems from the fact that resonance theory has no firm foundation in the wave properties of matter. 

The wave properties of matter form the foundation for a theory called wave mechanics, which serves as the basis of all current theories of electronic structure. The term quantum mechanics is also used because wave mechanics predicts quantized energy levels. In 1926 Erwin Schrddinger (1887-1961), an Austrian physicist, became the first scientist to successfully apply the concept of the wave nature of matter to an explanation of electronic structure (Brady et al. 2000, p. 290, original emphasis). 

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