Electron probable location

A functional is a function of a function. Electron probability density p is a function p(r) of a point in space located by radius vector r measured from an origin (possibly an atomic mi dens), and the energy E of an electron distribution is a function of its probability density. E /(p). Therefore E is a functional of r denoted E [pfr). ... 

The wave function T is a function of the electron and nuclear positions. As the name implies, this is the description of an electron as a wave. This is a probabilistic description of electron behavior. As such, it can describe the probability of electrons being in certain locations, but it cannot predict exactly where electrons are located. The wave function is also called a probability amplitude because it is the square of the wave function that yields probabilities. This is the only rigorously correct meaning of a wave function. In order to obtain a physically relevant solution of the Schrodinger equation, the wave function must be continuous, single-valued, normalizable, and antisymmetric with respect to the interchange of electrons. 

This formulation is not just a mathematical trick to form an antisymmetric vravefunction. Quantum mechanics specifies that an electron s location is not deterministic but rather consists of a probability density in this sense, it can he anywhere. This determinant mixes all of the possible orbitals of all of the electrons in the molecular system to form the wavefunction. 

We now know that electrons in atoms can hold only particular energies and that their probable whereabouts are described by Schrodiiiger s wave function. The energies and probable locations depend on integer numbers, or quantum numbers. Quantum numbers describe the energy and geometry of the possible electronic states of an atom. These states, in turn, deteriiiilie the chemical behavior of the elements—that is, how chemical bonds can form. 

Figure 8. Pauli principle for a diatomic molecule (e.g., HF). In any diatomic molecule, the two tetrahedra (Figs. 7a and 7b) of opposite spin electrons in the valence shell of an atom are brought into coincidence at only one apex, leaving the most probable locations of the remaining six electrons equally distributed in a ring.

Our goal for this chapter is to help you to learn about electrons and the current models for where those electrons are located within the atom. You may want to briefly review Chapter 2 concerning electrons, proton, and neutrons. Your text will probably have some nice pictures of orbitals, so when you get to the section on quantum numbers and orbitals, you might want to have your text handy. And don t forget to Practice, Practice, Practice. 

Fig. 9.3. Electron-microscopic reconstructions of the 26S proteasome. Three images of a doubly-capped 26S proteasome are presented to illustrate the positions of the lid and base subcomplexes of the 19S RC and to identify the most probable location of the RC ATPases.

As one shell fills up with electrons, the Pauli principle rules that any further electrons have to move to shells more removed from the nucleus. (The electrons in an incomplete outermost shell are known as valence electrons, and those in filled inner shells are known as core electrons.) The location of the various electrons can be described by talking of an electron cloud the density of this cloud at any point is a measure of the probability of finding the electron at that point. 

An atomic orbital, like a probability cloud, specifies a volume of space where the electron is most likely to be found. By convention, atomic orbitals are drawn to delineate the volume inside which the electron is located 90 percent of the time. This gives the atomic orbital an apparent border, as shown in Figure 5.17b. This border is arbitrary, however, because the electron may exist on either side of it. Most of the time, though, the electron remains within the border. 

Who developed the equation that relates the intensity of an electron s wave to the electron s most probable location ... 

These complexes are usually named as follows I, NADH-ubiquinone oxidoreductase II, succinate-ubiquinone oxidoreductase III, ubiquinol-cytochrome c oxidoreductase IV, cytochrome c oxidase. The designation complex V is sometimes applied to ATP synthase (Fig. 18-14). Chemical analysis of the electron transport complexes verified the probable location of some components in the intact chain. For example, a high iron content was found in both complexes I and II and copper in complex IV. 

Figure 3.3 The quantum mechanical model states that individual electrons do not orbit around the nucleus in exact paths but instead are located in an "electron cloud." The electron cloud indicates the probable location of an electron at a given moment. The darker the area, the more likely an electron will be found there.

We learned in Chapter 1 that electrons are outside the atomic nucleus. Though we do not know the exact location of these electrons, we can use equations to determine their most probable location. This location or region in atomic space is called an orbital. Electrons fill into orbitals around the atomic nucleus. As the electrons fill into orbitals, they move farther from the nucleus. Their distance from the nucleus is described as their energy level, or shell. The first shell is closest to the nucleus. The periodic table organizes the elements according to their electron configurations. 

The quantum mechanics model is more modern and more mathematical. It describes a volume of space surrounding the nucleus of an atom where electrons reside, referred to earlier as the electron cloud. Similar to the Bohr model, the quantum mechanics model shows that electrons can be found in energy levels. Electrons do not, however, follow fixed paths around the nucleus. According to the quantum mechanics model, the exact location of an electron cannot be known, but there are areas in the electron cloud where there is a high probability that electrons can be found. These areas are the energy levels each energy level contains sublevels. The areas in which electrons are located in sublevels are called atomic orbitals. The exact location of the electrons in the clouds cannot be precisely predicted, but the unique speed, direction, spin, orientation, and distance from the nucleus of each electron in an atom can be considered. The quantum mechanics model is much more complicated, and accurate, than the Bohr model. 

The second quantum number describes the shape of the orbital as s, p, d, f or g. These shapes do not describe the electron s path but rather are mathematical models showing the probability of the electron s location. The s and p orbital shapes are shown in Figure 8.9, but descriptions of the d and f orbitals are reserved for more advanced texts. 

Orbitals An orbital is the space where one or two paired electrons can be located or the probability of an electron s location. These are mathematical functions (i.e., figures) with specific shapes (s orbitals spherical p orbitals dumbbell, etc. see Figure 10.1) and restricted zones (called nodes see Figure 10.2). The nodes represent areas where the probability of an electron is zero. 

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