Electron as particle

We are used to thinking of electrons as particles. As it turns out, electrons display both particle properties and wave properties. The French physicist Louis de Broglie first suggested that electrons display wave-particle duality like that exhibited by photons. De Broglie reasoned from nature s tendency toward symmetry If things that behave like waves (light) have particle characteristics, then things that behave like particles (electrons) should also have wave characteristics. 

We need ways to visualize electrons as particle-waves delocalized in three-dimensional space. Orbital pictures provide maps of how an electron wave Is distributed In space. There are several ways to represent these three-dimensional maps. Each one shows some important orbital features, but none shows all of them. We use three different representations plots of electron density, pictures of electron density, and pictures of electron contour surfaces. 

The mathematical treatment of the Rutherford-Bohr atom was especially productive in Denmark and Germany. It led directly to quantum mechanics, which treated electrons as particles. Electrons, however, like light, were part of electromagnetic radiation, and radiation was generally understood to be a wave phenomenon. In 1924, the French physicist Prince Louis de Broglie (1892-1987), influenced by Einstein s work on the photoelectric effect, showed that electrons had both wave and particle aspects. Wave mechanics, an alternative approach to quantum physics, was soon developed, based on the wave equation formulated in 1926 by the Austrian-born Erwin Schrodinger (1887-1961). Quantum mechanics and wave mechanics turned out to be complementary and both were fruitful for an understanding of valence. 

It is easy to see that if we regard electrons as particles then no possible explanation of this result of Davisson s can be imagined. Obviously a particle could bounce off the crystal at any angle. 

In addition to the coherent scattering just discussed, X photons can scattered incoherently, that is, with a change in wavelength. This effect can be described with classical mechanics by considering the incident photons and the electrons as particles and by describing their interactions as collisions, as shown in Figure 1.2. 

Since the electronic wave function renders a stationary nuclear geometry po,c, electronic coordinates do not enter in this picture (they are universal or invariant if you prefer). Accordingly, the separability problem discussed by Wooley and Sutcliffe [15] does not arise here, namely, introducing the center of mass including electrons as particles is avoided. 

Louis de Broglie, then a doctoral student at Paris University, knew that whole-number behavior in physics was commonly associated with periodicity in a system. Perhaps a periodic nature had to be a property of electrons in atoms. Since waves are the quintessential example of periodicity, he hypothesized that not only did light have a wave nature, but so must electrons. De Broglie pictured electrons as particles embedded in standing waves around a nucleus. If the two modes of existence were to mesh, he had somehow to relate wavelength to mass or momentum. His famous formula M = h/p (where M is the wavelength, p is the particle momentum, and h is Planck s constant) had the right dimensions, but needed to be confirmed by experimental tests. 

For many purposes it remains expedient to regard electrons as particles, like those of Newtonian dynamics, but to add special rules regsurding the distribution of electrons in space when problems of intensity have to be considered. From this point of view the un-dulatory character is a statistical property and relates to the probability of finding electrons in a given element of volume. But this mode of interpretation may also prove to be of provisional utility only. 

The kinetic energy operator has a very interesting form. Particle 1 rests ri t in the origin of the BFCS (,x = 0, y = 0, z = 0), and therefore its kinetic energy operator is absent in H. There is the kinetic energy of particle 2, but its mass is equal to /r, not to m2. The coordinates x, y, and z (measured from the origin of the BFCS) correspond to particle 2. For example, for the hydrogen-like atom, if someone takes the nucleus as particle 1, and the electron as particle 2, then x, y, and z show the electron from the Cartesian coordinate system BFCS located on... 

Let us first denote the nucleus as particle 1 and the electron as particle 2. Then RcM shows almost the position of the nucleus, and c, v, and z are nearly the coordinates of the electron measured from the nucleus, while is almost equal to the mass of the electron. Thus, we have a situation that resembles Example 1. 

To sum up the argument we find a ubiquitous role played by electrons in chemical theory. Electrons-as-particles phenomena can be obtained from atoms by means of certain procedures such as the cloud chamber. Electrons as wave phenomena can be obtained from atoms by distinctive and independent procedures such as double slit experiments. But it does not follow that the electrons obtained... 

The classical framework assumes electrons as particles forming the current density j under the external applied electric field E between... 

The essential and peculiar feature of the quantum mechanical model of the atom lies in its description of electrons as waves rather than particles. It is far more inmitive to think of electrons as particles, perhaps resembling tiny marbles, than to envision them as waves. But just as we ve seen for light, experimental observations led to the idea that electrons can exhibit wave-like behavior. The first evidence of the wave nature of electrons came through diffraction experiments in 1927. Diffraction was already a well-understood phenomenon of waves, so the observation of electron diffraction strongly suggested the need for a wave-based treatment of the electron. 

Quantimi Mechanics. By the mid-1920 s physicists had developed quantum mechanics, a powerful new theory explaining the behavior of electrons in atoms. Different forms of quantum mechanics emphasized electrons as particles (matrix mechanics) and electrons as waves (wave mechanics), and these theories were eventually shown to be equivalent. Quantum mechanics proved very successful for understanding ionic and covalent crystals, organic chemical molecules, and many other physical and chemical phenomena, but it proved unable to unlock the mysteries of superconductivity. However, in 1933 German physicist Walther Meissner discovered a superconductor s ability to repel magnetism, which provided a clue to understanding superconductivity, since study of the Meissner effect showed how transitions from normal to superconducting states are thermodynamically reversible. Other studies helped explain some of the... 

In the free-electron molecular orbital model, the electrons actually move in three dimensions. For 1,3-butadiene represent the electrons as particles in a three-dimensional box with a length in the x direction equal to 694 pm, width in the y direction equal to 268 pm, and height in the z direction equal to the width. Find the wavelength of the photons absorbed in the longest-wavelength absorption due to changes in the quantum numbers Uy and n. Explain why the representation as a one-dimensional box can successfully be used to understand the near-ultraviolet spectrum. 

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