Electron wavelike behavior

The underlying principle of RHEED is that particles of matter have a wave character. This idea was postulated by de Broglie in (1924). He argued that since photons behave as particles, then particles should exhibit wavelike behavior as well. He predicted that a particle s wavelength is Planck s constant h divided by its momentum. The postulate was confirmed by Davisson and Germer s experiments in 1928, which demonstrated the diffraction of low-energy electrons from Ni. ... 

For better comprehension of the crystal field theory, we must reconsider to some extent the wavelike behavior of electrons. 

The electron, discovered by J. J. Thomson in 1895, was first considered as a corpuscule, a piece of matter with a mass and a charge. Nowadays things are viewed differently. We rather speak of a wave-particle duality whereby electrons exhibit a wavelike behavior. But, in Levine s own words [45], quanmm mechanics does not say that an electron is distributed over a large region of space as a wave is distributed it is the probability patterns (wavefunctions) used to describe the electron s motion that behave like waves and satisfy a wave equation. 

The description of the wavelike behavior of electrons has been extended and clarified, based on a careful description of an electron diffraction experiment. 

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. 

The electron s wave function (iK atomic orbital) is a mathematical description of the electron s wavelike behavior in an atom. Each wave function is associated with one of the atom s allowed energy states. The probability density of finding the electron at a particular location is represented by An electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus for a particular energy level. Three features of an atomic orbital are described by quantum numbers size (n), shape (/), and orientation (m/). Orbitals with the same n and / values constitute a sublevel sublevels with the same n value constitute an energy level. A sublevel with / = 0 has a spherical (s) orbital a sublevel with / = 1 has three, two-lobed (p) orbitals and a sublevel with / = 2 has five, multi-lobed (d) orbitals. In the special case of the H atom, the energy levels depend on the n value only. 

An equation is constructed to describe the total energy of a hydrogen atom (i.e., one proton plus one electron). This equation, called the wave equation, takes into account the wavelike behavior of an electron that is in the electric field of a proton. 

It is, however, not enough to specify the probability function P, because this fails to take into account another peculiarity of small particles, i.e., the fact that they show wavelike behavior. In particular, electrons appear to undergo diffraction and interference just like light. 

The atomic orbital (ip, wave function) is a mathematical description of the electron s wavelike behavior in an atom. The Schrodinger equation converts each allowed wave function to one of the atom s energy states. 

An electron that crosses the laser beam produces a tiny flash when a single photon is scattered at the point of crossing. If a flash shows up behind a particular sUt, that indicates an electron is passing through that sUt. When the experiment is performed, the flash always originates either from one slit or the other, but never from both at once. Furthermore, the interference pattern, which was present without the laser, is now absent. With the laser on, the electrons hit positions directly behind each slit, as if they were ordinary particles their wavelike behavior is no longer manifested. 

Electronic devices that operate using the spin of the electron and not just its electric charge are on the way to becoming a multibillion-dollar industry—and may lead to quantum microchips (4). As progress in the miniaturization of semiconductor electronic devices leads toward chip features smaller than lOOnm in size, device engineers and physicists are inevitably faced with the fast-approaching presence of quantum mechanics—that counterintuitive, and to some mysterious, realm of physics wherein wavelike properties control the behavior of electrons. 

During this same period de Broglie s brother Maurice was studying experimental physics, and he was particularly interested in x rays. The brothers frequently discussed x rays, and their dual nature (both wavelike and particle-like behavior) suggested to Louis that this same particle-wave duality might also apply to particles such as electrons. 

Planck s revolutionary idea about energy provided the basis for Einstein s explanation of the photoelectric effect in 1906 and for the Danish physicist Niels Bohr s atomic model of the hydrogen atom in 1913. Their success, in turn, lent support to Planck s theories, for which he received the Nobel Prize in physics in 1918. In the mid-1920s the combination of Planck s ideas about the particle-like nature of electromagnetic radiation and Erench physicist Louis de Broglie s hypothesis of the wavelike nature of electrons led to the formulation of quantum mechanics, which is still the accepted theory for the behavior of matter at atomic and subatomic levels. 

A few years after de Broglie pubUshed his theory, the wave properties of the electron were demonstrated experimentally. When X-rays pass through a crystal, an interference pattern results that is characteristic of the wavelike properties of electromagnetic radiation. This phenomenon is called X-ray diffraction. As electrons pass through a crystal, they are similarly diffracted. Thus, a stream of moving electrons exhibits the same kinds of wave behavior as X-rays and all other types of electromagnetic radiation. 

The behavior of electrons, by now known to have wavelike properties, can be described by a mathematical expression called a wavefunction. 

The most serious setback for a modern theory of matter was the deliberate suppression of Erwin Schrodinger s demonstration that the behavior of electrons in an atom cannot be described correctly by a particle model and quantum jumps [5,6]. A beautiful theory, based on a wave model of matter, was buried through professional rivalry to be replaced by incomprehensible concepts such as particles with wavelike properties—even Zitterbewegung, infinite self-energy, probability density, non-Boolean algebra of observables and other weird properties. Remember how Newton described particles as... 

The discovery that waves could have matterlike properties and that matter could have wavelike properties was revolutionary. Although scientists had long believed that energy and matter were distinct entities, the distinction between them, at least at the atomic level, was no longer clear. Bohr s theory was tremendously successful in explaining the line spectram of hydrogen, but it failed to explain the spectra of atoms with more than one electron. The electron appeared to behave as a particle in some circumstances and as a wave in others. Neither description could completely explain the behavior of electrons in atoms. This left scientists frustrated in their quest to understand exactly where the electrons in an atom are. 

The domination of science through the 19th century by the Newtonian model came to an end with the discovery of the subatomic particles in the turn of this century. Physicists soon realized that, in this fine scale, nature portrays a dual behavior sometimes particle-like, other times wavelike, the latter demonstrated in electron and proton diffraction. 

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