ELECTRONS EXHIBIT WAVE PROPERTIES

Bohr s planetary atomic model proved to be a tremendous success. By utilizing Planck s quantum hypothesis, Bohr s model solved the mystery of atomic spectra. Despite its successes, though, Bohr s model was limited because it did not explain why energy levels in an atom are quantized. Bohr himself was quick to point out that his model was to be interpreted only as a crude beginning, and the picture of electrons whirling about the nucleus like planets about the sun was not to be taken literally (a warning to which popularizers of science paid no heed). 

In an atom, an electron moves at very high speeds—on the order of 2 million meters per second—and therefore exhibits many of the properties of a wave. An electron s wave nature can be used to explain why electrons in an atom are 

For the fixed circumference of a wire loop, only some wavelengths are self-reinforcing, (a) The loop affixed to the post of a mechanical vibrator at rest. Waves are sent through the wire when the post vibrates, (b) Waves created by vibration at particular rates are self-reinforcing, (c) Waves created by vibration at other rates are not self-reinforcing. 

What must an electron be doing in order to have wave properties  

Was this your answer Moving According tode Broglie, particles of matte1 behave like waves by virtue of their motion.The wave nature of electrons in atoms is pronounced because electrons move at speeds of about 2 million meters per second. 

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An electron, in a beam of electrons, exhibits wave properties (p. 42), the wave length being dependent on the exciting voltage. These wave properties are employed to measure bond lengths and bond angles in gas... 

The discovery that moving electrons exhibit wave properties led to a new kind of diffraction analysis... 

Separately, the photoelectric effect and the Compton effect experiments unambiguously demonstrated that Ught photons behave like particles do. And around the same time the Davisson-Germer experiments showed how electrons exhibit wave properties. 

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. 

Davisson and Genner, and Thomson demonstrated in separate ingenious experiments that electrons indeed exhibit wave properties (using crystals as diffraction gratings). 

In words, an electron beam should exhibit wave properties for example, like light, it should produce a diffraction pattern. This prediction has been verified by numerous experiments. Fig. 6.12. Thus, like electromagnetic radiations, particles of matter exhibit wave properties and particle properties. The electron microscope, now a common laboratory tool (Fig. 26.6, page 562), is an application of the de Broglie concept. 

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. 

The electrochemical properties of [14] and [15] were studied using CV. Each compound exhibited a reversible one-electron oxidation wave. Anodic redox potential perturbations of the CV oxidation waves were observed (due to a through space interaction as the methylene linkage is insulating) on addition of excess amounts of Na+, K+, Mg2+ and Ba2+ cations. 

Recently, Romero and Andrews [1], and Lipinski [2] have shown that the calculated sum over states of a one-electron nonlinear optical property of a molecular system must vanish provided that the wave function employed satisfies the Hellmann-Feynman theorem. This statement applies, in particular, to the electric dipole polarizahility and, as a consequence, there must exist systems which exhibit, most prohahly in excited states, a negative polarizability. Several examples of atomic and molecular systems with negative polarizability can be found in Refs. [3-8]. In search for such systems we study the state of... 

Before giving a brief discussion of wave-function-based methods, we must first describe the common ways in which the wave function is described. We mentioned earlier that the wave function of an /V-particle system is an tV-dimension al function. But what, exactly, is a wave function Because we want our wave functions to provide a quantum mechanical description of a system of N electrons, these wave functions must satisfy several mathematical properties exhibited by real electrons. For example, the Pauli exclusion principle prohibits two electrons with the same spin from existing at the same physical location simultaneously. We would, of course, like these properties to also exist in any approximate form of the wave function that we construct. 

The tetramethyltetraaza[14]annulene (165) reacts with vanadyl acetate to yield (166) similar to complexes of (163) and (164).660 It was the starting material for several reactions shown in Scheme 22, and exhibits a reversible one-electron oxidation wave at +0.245 V (vs. SCE) but reacts irreversibly with mild oxidants (02, Ag+, Ce4+ or I2) to yield (167). With Et3N, (167) yielded a complex with properties similar to (166) but which mass spectral data indicate is a dimer. Structure (170) was proposed. 

Unlike molecular mechanics, the quantum mechanical approach to molecular modelling does not require the use of parameters similar to those used in molecular mechanics. It is based on the realization that electrons and all material particles exhibit wavelike properties. This allows the well defined, parameter free, mathematics of wave motions to be applied to electrons, atomic and molecular structure. The basis of these calculations is the Schrodinger wave equation, which in its simplest form may be stated as ... 

By exhibiting clearly the basic fact that electrons are wave-like fermions (de Broglie particles that obey the Pauli Exclusion Principle), the LMO-electride ion model of electronic structure enables one to utilize systematically many features of classical physics in developing an understanding , or "explanation , of the properties of quantum mechanical systems. 

The observation that the wavelength of light is linked to the particle-like momentum of a photon prompted de Broglie to postulate the likelihood of an inverse situation whereby particulate objects may exhibit wave-like properties. Hence, an electron with linear momentum p could under appropriate conditions exhibit a wavelength A = h/p. The demonstration that an electron beam was diffracted by periodic crystals in exactly the same way as X-radiation confirmed de Broglie s postulate and provided an alternative description of the electronic stationary states on an atom. Instead of an accelerated particle the orbiting electron could be described as a standing wave. To avoid self-destruction by wave interference it is necessary to assume an... 

Wave/particle duality is the postulate that all objects of physical reality possess both localized (particle) and distributed (wave) properties. Due to their low rest mass, electrons exhibit both particle and wave behavior on the scale of length of atoms (nanometers). Thus, every electron has a wavelength associated with it. This wavelength is called the de Broglie wavelength Adb,... 

Before we delve further into the properties of the nucleus, let us momentarily shift our attention back to one of the electrons zooming around the nucleus. Just like photons, electrons exhibit both wave and particle properties. Each electron wave in an atom is characterized by four quantum numbers. The first three of these numbers can be taken as the electron s address and describe the energy, shape, and orientation of the volume the electron occupies in the atom. This volume is called an orbital. The fourth quantum number is the electron spin quantum number s, which can assume only two values, or - f. (Why J was selected rather than, say, 1 will be described a little later.) The Pauli exclusion principle tells us that no two electrons in an atom can have exactly the same set of four quantum numbers. Therefore, if two electrons occupy the same orbital (and thus possess the same first three quantum numbers), they must have different spin quantum numbers. Therefore, no orbital can possess more than two electrons, and then only if their spins are paired (opposite). 

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