Electrons probability cloud

Atomic orbitals represent the electron probability clouds of an atom s electrons. Q The spherical 1s and 2s orbitals are shown here. All s orbitals are spherical in shape and increase in size with increasing principal quantum number. The three dumbbell-shaped p orbitals are oriented along the three perpendicular X, y, and z axes. Each of the p orbitals related to an energy sublevel has equal energy. 

The d orbitals are more complex in shape and arrangement in space. In 1925 Touis de Broglie suggested that electrons behaved like waves. This led to the idea of electron probability clouds. The electron probability cloud for one type of d orbital is very strange -it is like a modified p orbital with a ring around the middle (Figure 3.8). You will not need to know the d-orbital shapes at AS level, but you will for A level when studying the transition elements (see Chapter 24). 

A molecule is composed of positively charged nuclei surrounded by electrons. The stability of a molecule is due to a balance among the mutual repulsions of nuclear pairs, attractions of nuclear-electron pairs, and repulsions of electron pairs as modified by the interactions of their spins. Both the nuclei and the electrons are in constant motion relative to the center of mass of the molecule. However, the nuclear masses are much greater than the electronic mass and, as a result, the nuclei move much more slowly than the electrons. Thus, the basic molecular structure is a stable framework of nuclei undergoing rotational and vibrational motions surrounded by a cloud of electrons described by the electronic probability density. 

The wavefunction of an electron associated with an atomic nucleus. The orbital is typically depicted as a three-dimensional electron density cloud. If an electron s azimuthal quantum number (/) is zero, then the atomic orbital is called an s orbital and the electron density graph is spherically symmetric. If I is one, there are three spatially distinct orbitals, all referred to as p orbitals, having a dumb-bell shape with a node in the center where the probability of finding the electron is extremely small. (Note For relativistic considerations, the probability of an electron residing at the node cannot be zero.) Electrons having a quantum number I equal to two are associated with d orbitals. 

PROBABILITY CLOUDS AND ATOMIC ORBITALS HELP US VISUALIZE ELECTRON WAVES... 

Electron waves are three-dimensional, which makes them difficult to visualize, but scientists have come up with two ways of visualizing them as probability clouds and as atomic orbitals. 

A probability cloud is therefore a close approximation of the actual shape of an electrons three-dimensional wave. 

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. 

Probability cloud The pattern of electron positions plotted over time to show the likelihood of an electrons being at a given position at a given time. 

If the two atoms in a covalent bond are identical, their nuclei have the same positive charge, and therefore the electrons are shared evenly. We can represent these electrons as being centrally located by using an electron-dot structure in which the electrons are situated exactly halfway between the two atomic symbols. Alternatively, we can draw a probability cloud (see Section 5-5) in which the positions of the two bonding electrons over time are shown as a series of dots. Where the dots are most concentrated is where the electrons have the greatest probability of being located ... 

FIGURE 1.2. Molecular structure of widely used it-conjugated and other polymers (a) poly(para-phenylene vinylene) (PPV) (b) a (solid line along backbone) and it ( clouds above and below the a line) electron probability densities in PPV (c) poly(2-methoxy-5-(2 -ethyl)-hexoxy-l,4-phenylene vinylene) (MEH-PPV) (d) polyaniline (PANI) (d.l) leucoemeraldine base (LEB), (d.2) emeraldine base (EB), (d.3) pernigraniline base (PNB) (e) poly(3,4-ethylene dioxy-2,4-thiophene)-polystyrene sulfonate (PEDOT-PSS) (f) poly(IV-vinyl carbazole) (PVK) (g) poly(methyl methacrylate) (PMMA) (h) methyl-bridged ladder-type poly(jf-phenylene) (m-LPPP) (i) poly(3-alkyl thiophenes) (P3ATs) (j) polyfluorenes (PFOs) (k) diphenyl-substituted frares -polyacetylenes (f-(CH)x) or poly (diphenyl acetylene) (PDPA). 

Atomic orbitals show the forms of the electron-probability-density clouds for the outermost electrons of the atoms. Where clouds on adjacent atoms overlap, bonds can be formed by electrons with paired spins. 

Thus the effective force acting on a nucleus in a molecule can be calculated by simple electrostatics as the sum of the Coulombic forces exerted by the other nuclei and by a hypothetical electron cloud whose charge density ep(x, y, z) is found by solving the electronic Schrodinger equation. This is the Hellmann-Feynman electrostatic theorem. The electron probability density depends on the parameters defining the nuclear configuration p = p x, y, z x , y , Zc x, ...). 

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