Electron quantized energy levels

The model of metal-ammonia solutions that has emerged is based on ionization of the metal atoms to produce metal ions and electrons that are both solvated. The solvated electron is believed to reside in a cavity in ammonia, and thus it may behave as a particle in a three-dimensional box with quantized energy levels. Transitions between the energy levels may give rise to absorption of light and thereby cause the solutions to be colored. The dissolution process can be represented as... 

In fact, electron transfer occurs at the microscopic level where quantum mechanics provides the necessary description of the phenomenon (5-13). In the quantum mechanical solution, associated with the potential curves in Figure 1 are quantized energy levels, Ej = (vj + 1/2) 100., where Vj and 2ttvj are the vibrational... 

Figure 10.9. (a) Schematic structure of a silicon quantum dot crystal and (b) its calculated electronic structure as a function of interparticle distance H. The size of the nanoparticles is L = 6.5 nm. At small H, a splitting of the quantized energy levels of single dots results in the formation of three-dimensional minibands. Reproduced from Ref. 64, Copyright 2001, with permission from the American Institute of Physics. 

The behaviour of electrons in metals shows the translational properties of quantum particles having quantized energy levels. These cannot be approximated to the continuous distribution describing particles in a gas because of the much smaller mass of the electron when compared with atoms. If one gram-atom of a metal is contained in a cube of length L, the valence electrons have quantum wavelengths, X, described by the de Broglie equation... 

In contrast to ESR spectroscopy, which can only be used to study species with unpaired electrons, NMR spectroscopy is applicable to the investigation of all polymer samples. Nuclei with non-zero total nuclear spin (e.g., 1H, l3C, 19F, 14N) will have a magnetic moment which will interact with an external magnetic field resulting in quantized energy levels. Transitions between these energy levels form the basis of NMR spectroscopy. 1H and 13C... 

Abstract Silver clusters, composed of only a few silver atoms, have remarkable optical properties based on electronic transitions between quantized energy levels. They have large absorption coefficients and fluorescence quantum yields, in common with conventional fluorescent markers. But importantly, silver clusters have an attractive set of features, including subnanometer size, nontoxicity and photostability, which makes them competitive as fluorescent markers compared with organic dye molecules and semiconductor quantum dots. In this chapter, we review the synthesis and properties of fluorescent silver clusters, and their application as bio-labels and molecular sensors. Silver clusters may have a bright future as luminescent probes for labeling and sensing applications. 

The colour of a chromophore depends on the way its valence-shell electrons interact with light, i.e. its colour depends on the way it absorbs photons. Photons are absorbed during the promotion of an electron between wave-mechanically allowed (i.e. quantized) energy levels. The magnitude of the energy required to achieve this, E, is given by the Planck equation, as follows ... 

Some older cars vibrate loudly when driving at particular speeds. For example, at 65 mph the car may be most quiet, but at 60 mph the car rattles uncomfortably. How is this analogous to the quantized energy levels of an electron in an atom ... 

To find the energy levels of an electron in a hydrogen atom, we have to solve the appropriate Schrodinger equation. An electron in an atom is like a particle in a box, in the sense that it is confined within the atom by the pull of the nucleus, so we can expect quantized energy levels. However, the Coulomb potential energy of the electron, % varies with distance, r, from the nucleus ... 

These are quantized vibrations of conduction electrons in a metal or semiconductor 4°). The quantized energy levels of the collective longitudinal vibrations of the electron gas are quasi-particles in the sense of the definition given above and are called plasmons. The frequency of this longitudinal vibration, the plasma frequency u>P, is given by 40>... 

The model correctly fits the quantized energy levels of the hydrogen atom as inferred from its emission spectrum. These energy levels correspond to certain allowed circular orbits for the electrons. 

The almost spherical shape of the Ceo molecule favours an approximate approach to the 60 tt electrons, based on an extension of the free particle in the box model to a spherical surface which we have considered in Chapter 2 (page 39). The various quantized energy levels related to an angular momentum quantum number L are given by expression (2.73)... 

Bohr s model explained hydrogen s observed spectral lines remarkably well. Unfortunately, however, the model failed to explain the spectrum of any other element. Moreover, Bohr s model did not fully account for the chemical behavior of atoms. In fact, although Bohr s idea of quantized energy levels laid the groundwork for atomic models to come, later experiments demonstrated that the Bohr model was fundamentally incorrect. The movements of electrons in atoms are not completely understood even now however, substantial evidence indicates that electrons do not move around the nucleus in circular orbits. 

Using Models Niels Bohr proposed that electrons must occupy specific, quantized energy levels in an atom. He derived the following equations for hydrogen s electron orbit energies (fn) and radii (rn). 

In addition to electronic transitions, molecules exhibit two other types ot radiation-induced transitions vibrational transitions and rotational transitions. Vibrational transitions occur because a molecule has a multitude of quantized energy levels (or vibrational states) associated with the bonds that hold the molecule together. 

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