Wave properties of matter

1 De Broglie Waves and Low-energy Electron Diffraction (LEED) 

In 1924, Louis de Broglie proposed that all matter has wave properties and that the wavelength of the associated wave is related to the momentum, p, of the particle by the expression already derived for photons, namely  

In 1927, Davisson and Germer demonstrated that electrons can be diffracted from the surface of a nickel crystal, a result which can be explained only if electrons have wave-like properties. By applying the de Broglie relationship they were able to calculate the interatomic spacing between the nickel atoms, and their result agreed with the value obtained from X-ray diffraction measurements. 

54 V electron beam striking surface at normal incidence 

Defracted beam leaving surface at an angle of 50° to the normal 

The concept that matter possesses both particle and wave properties was first postulated by de Broglie in 1925. He introduced the equation A = hlmv, which indicates a mass (m) moving with a certain velocity (v) would have a specific wavelength (A) associated with it. (Note that this v is the velocity not v the frequency.) If the mass is very large (a locomotive), the associated wavelength is insignificant. However, if the mass is very small (an electron), the wavelength is measurable. The denominator may be replaced with the momentum of the particle (p = mv). 

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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. 

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