THE ENERGY LEVEL OF ELECTRONS

According to quantum mechanics, electrons in atoms occupy the allowed energy levels of atomic orbitals that are described by four quantum numbers the principal, the azimuthal, the magnetic, and the spin quantum numbers. The orbitals are usually expressed by the principal quantum numbers 1, 2, 3, —increasing from the lowest level, and the azimuthal quantum numbers conventionally eiqiressed by s (sharp), p (principal), d (diffuse), f (fundamental), — in order. For instance, the atom of oxygen with 8 electrons is described by (Is) (2s) (2p), where the superscript indicates the munber of electrons occupying the orbitals, as shown in Fig. 2-1. 

As two atoms X and Y form a molecule XY, the atom-atom interaction splits each atomic frontier orbital into two molecular orbitals a bonding molecular orbital at a low energy level and an antibonding molecular orbital at a high eneigy level as shown in Fig. 2-2. Similarly, a molecule composed of many atoms 

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Figure 1.4 The energy levels of electrons in an atom. The first shell holds a maximum of 2 electrons in one Is orbital the second shell holds a maximum of 8 electrons in one 2s and three 2p orbitals the third shell holds a maximum of 18 electrons in one 3s, three 3p, and five 3dorbitals and so on. The two electrons in each orbital are represented by up and down arrows, 4.

Wigner, E., Trans. Faraday Soc. 34, 678, "Effects of the electron interaction on the energy levels of electrons in metals."... 

The substituents and heteroatoms can be used to tune the spin preference of the acyclic diradicals by changing the energy levels of electron-donating and -accepting orbitals and hence the donor-acceptor interaction. 

In these equations, (24)-(26), orthonormal orbits are denoted by indices Vs. Equation (26) means that the orbiting electron interacting with itself, that is self-interaction, exists. This is unphysical. In order to remove this unphysical term, the SIC is taken into account by the following procedure. The SIC for the LDA in the density functional method has been treated for free atoms and insulators [16], and found an important role in determining the energy levels of electrons. However, no established formula is known to take into account the SIC for semiconductors and metals. As a way of trial, in the present calculation, the atomic SIC potential is introduced for each angular momentum in a way similar to the SIC potential for atoms [17] as follows ... 

In ph ics, the term of work function is frequently used to represent the energy of electrons in metals. In electrochemistry, however, we use the real potenticU, a., instead of the work function, 4>, to represent the energy level of electrons in metals as shown in Eqn. 2-4 ... 

The electrode potential is one of the most important concepts in electrochemistry. It represents the energy level of electrons or ions in electrodes rather than simply the electrostatic potential of electrodes [Trasatti, 1986,1990 Sato, 1993, 1995]. 

The electrode potential can be defined not only by the energy level of electrons (the real potential ofelectrons)butalsoby theener gy/eue/oftons (the real potential of ions) in the electrode. The former maybe called the electronic electrode potenticd and the latter may be called the ionic electrode potential [Sato, 1995]. For instance, the electrode potential of a metal electrode can be defined in terms of the metal ion level (the real potential of metal ions), aM-ai/s/v), in the electrode as... 

Quantum dots are objects with sizes in all three directions equal to few nanometers. Such systems resemble molecules and the energy levels of electrons in them quantize. Energies of the transitions between these levels depend on quantum dots material and size, and those transitions are the base for the quantum dots laser radiation. 

Thermionic work function contact potential. Representing two different metals a and jS, initially separate and each at zero electrostatic potential, by the diagram in Fig. 48 a, in which the ordinates are the energy levels of electrons, we see that the energy level of the electrons in oc is higher than that in / by the difference between the thermionic work functions, On connecting the two metals, as in Fig. 48 6, the... 

On the basis of the simple rules defined above, the shapes of all molecules can in principle be predicted by logical procedures. It will be argued that any quantitative scheme that takes into account, not only the energy levels of electrons in molecules, but also their angular momenta must yield a comparable result that contains a framework for the definition of three-dimensional molecular shape. A few hydrides and other simple molecules will be discussed to demonstrate the principle. 

When a metal is immersed in a solution containing ions of that metal, die electrochemical potential of the ions in the metallic lattice and in die solution will usually be unequal The same will be true for the free electrons (near the Fermi level) in the metal and electrons in the energy levels of electron acceptors m the solution. 

Detailed study of the chart of nuclides makes evident that for certain values of P and N a relatively large number of stable nuchdes exist. These numbers are 2, 8, 20, 28, 50, 82 (126, only for N). The preference of these magic numbers is explained by the shell structure of the atomic nuclei (shell model). It is assumed that in the nuclei the energy levels of protons and of neutrons are arranged into shells, similar to the energy levels of electrons in the atoms. Magic proton numbers correspond to filled proton shells and magic neutron numbers to filled neutron shells. Because in the shell model each nucleon is considered to be an independent particle, this model is often called the independent particle model. 

Similar to for the energy levels in semiconductors, the energy levels of electrons in electrolytes associated with ions are characterized by the redox potential, Eraiox-The redox potential describes the tendency of the species to give up or accept electrons and can be considered as the effective Fermi level of the solution. 

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