THE WAVE BEHAVIOR OF MATTER

As it turns out, the Bohr model was only an important step along the way toward the development of a more comprehensive model. What is most significant about Bohr s model is that it introduces two important ideas that are also incorporated into our current model  

Electrons exist only in certain discrete energy levels, which are described by quantum numbers. 

Energy is involved in the transition of an electron from one level to another. 

We will now start to develop the successor to the Bohr model, which requires that we take a closer look at the behavior of matter. 

De Broglie suggested that an electron moving about the nucleus of an atom behaves like a wave and therefore has a wavelength. He proposed that the wavelength of the electron, or of any other particle, depends on its mass, m, and on its velocity, v  

Because de Broglie s hypothesis is applicable to all matter, any object of mass m and velocity v would give rise to a characteristic matter wave. However, Equation 6.8 indicates that the wavelength associated with an object of ordinary size, such as a golf ball, is so tiny as to be completely unobservable. This is not so for an electron because its mass is so small, as we see in Sample Exercise 6.5. 

Analyze We are given the mass, m, and velocity, v, of the election, and we must calculate its de BiogUe wavelength, A. 

Plan The wavelength of a moving particle is en by Equation 6.8, so A is calculated by inserting the known quantities h, m, and v. In doing so, however, we must pay attention to units. 

Solve Using the value of Planck s constant, we have the following  

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THE WAVE BEHAVIOR OF MATTER We recognize that matter also has wave-like properties. As a result, it is impossible to determine simultaneously the exact position and the exact momentum of an electron in an atom (Heisenberg s uncertainty principle). 

We believe that such reconciliation Is not adequate. Moreover, we believe that the thermodynamic behavior of matter is due to quantum uncertainties of the same nature but broader than those associated with wave functions and invoked in the uncertainty principle. 

WAVE BEHAVIOR OF MATTER (SECTION 6.4) De Broglie proposed that matter, such as electrons, should exhibit wave-like properties. This hypothesis of matter waves was proved experimentally by observing the diffraction of electrons. An object has a characteristic wavelength that depends on its momentum, mv A = h/mv. 

A class of partial differential equations first proposed by Erwin Schrodinger in 1926 to account for the so-called quantized wave behavior of molecules, atoms, nuclei, and electrons. Solutions to the Schrodinger equation are wave functions based on Louis de Broglie s proposal in 1924 that all matter has a dual nature, having properties of both particles and waves. These solutions are... 

Quantum Mechanics theory that explains the behavior of matter using wave functions to characterize the energy of electrons in atoms... 

Figure 3.9. The Fourier transform of spectra of Fig. 3.8 Projection PK(a>) of the pure excitonic state on the eigenstates of the coupled system of an exciton K and the effective photon continuum in a 2D lattice, for various values of the wave vector K (KXd). The vertical peak represents a discrete state, whose weight is represented by a rectangle (a-d). For an exciton with K < K0, the continuum band (matter-contaminated photons) dominates the spectrum, with a quasi-lorentzian resonance (a,/). For K > K0, the discrete state dominates (d,e). In the intermediate region (b, c) the spectrum reflects the complicated behavior of its Fourier transform cf. Fig. 3.8. 

In investigating the highly different phenomena in nature, scientists have always tried to find some fundamental principles that can explain the variety from a basic unity. Today they have shown not only that all the various kinds of matter are built up from a rather limited number of atoms but also that these atoms are composed of a few basic elements or building blocks. It seems possible to understand the innermost structure of matter and its behavior in terms of a few elementary particles electrons, protons, neutrons, photons, etc., and their interactions. Since these particles obey not the laws of classical physics but the rules of modem quantum theory of wave mechanics established in 1925, there has developed a new field of quantum science which deals with the explanation of nature on this basis. 

The key new ideas of qnantnm mechanics include the quantization of energy, a probabilistic description of particle motion, wave-particle duality, and indeterminacy. These ideas appear foreign to ns because they are inconsistent with our experience of the macroscopic world. We have accepted them because they have provided the most comprehensive account of the behavior of matter and radiation and because the agreement between theory and the results of all experiments conducted to date has been astonishingly accurate. 

In the present section we shall discuss another aspect of the behavior of matter in an electromagnetic field. We shall analyze by means of statistical-mechanical methods the propagation of electromagnetic waves through a fluid. We shall assume that our system consists of optically isotropic, electrically neutral molecules... 

Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the fi eld of quantum mechanics, which examines the wave nature of objects on the atomic scale. In 1926, Erwin Schrddinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom. The model describes an atom that has certain allowed quantities of energy due to the allowed frequencies of an electron whose behavior is wavelike and whose exact location is impossible to know. 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

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