P orbitals, shapes

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. 

An s orbital is spherically symmetrical and can contain a maximum of two electrons with opposed spins. A p orbital has a solid figure-of-eight shape there are three equivalent p orbitals for each principal quantum number they correspond to the three axes of rectangular coordinates. 

In elements of Periods 2 and 3 the four orbitals are of two kinds the first two electrons go into a spherically symmetrical orbital—an s orbital with a shape like that shown in Figure 2.7—and the next six electrons into three p orbitals each of which has a roughly doublepear shape, like those shown unshaded in each half of Figure 2.10. 

Section 1 1 A review of some fundamental knowledge about atoms and electrons leads to a discussion of wave functions, orbitals, and the electron con figurations of atoms Neutral atoms have as many electrons as the num ber of protons m the nucleus These electrons occupy orbitals m order of increasing energy with no more than two electrons m any one orbital The most frequently encountered atomic orbitals m this text are s orbitals (spherically symmetrical) and p orbitals ( dumbbell shaped)... 

What do orbitals look like There are four different kinds of orbitals, denoted s, p, d, and f] each with a different shape. Of the four, we ll be concerned primarily with s and p orbitals because these are the most common in organic and biological chemistry. The s orbitals are spherical, with the nucleus at their center p orbitals are dumbbell-shaped and four of the five d orbitals are doverleaf-shaped, as shown in Figure 1.3. The fifth d orbital is shaped like an elongated dumbbell with a doughnut around its middle. 

Figure 1.3 Representations of s, p, and d orbitals. The s orbitals are spherical, the p orbitals are dumbbell-shaped, and four of the five d orbitals are cloverleafshaped. Different lobes of p orbitals are often drawn for convenience as teardrops, but their true shape is more like that of a doorknob, as indicated.

The concept of hybridization explains how carbon forms four equivalent tetrahedral bonds but not why it does so. The shape of the hybrid orbital suggests the answer. When an 5 orbital hybridizes rvith three p orbitals, the resultant sp3 hybrid orbitals are unsyimmetrical about the nucleus. One of the two... 

An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons. The electronic structure of an atom can be described by a quantum mechanical wave equation, in which electrons are considered to occupy orbitals around the nucleus. Different orbitals have different energy levels and different shapes. For example, s orbitals are spherical and p orbitals are dumbbell-shaped. The ground-state electron configuration of an... 

Further evidence for the unusual nature of benzene is that all its carbon-carbon bonds have the same length—139 pm—intermediate between typical single (154 pm) and double (134 pm) bonds. In addition, an electrostatic potential map shows that the electron density in all six carbon-carbon bonds is identical. Thus, benzene is a planar molecule with the shape of a regular hexagon. All C-C—C bond angles are 120°, all six carbon atoms are sp2-hybridized. and each carbon has a p orbital perpendicular to the plane of the six-membered ring. 

The shapes and orientations of p orbitals are shown in Figure 6.7. Notice that—... 

Although it is not shown in Figure 6.7, p orbitals, like s orbitals, increase in size as the principal quantum number n increases. Also not shown are the shapes and sizes of d and f orbitals. We will say more about the nature of d orbitals in Chapter 15. 

All p-orbitals have boundary surfaces with similar shapes, including one nodal plane. Note that the orbital has opposite signs (as depicted by the depth of color) on each side of the nodal plane. 

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

STRATEGY Use the VSEPR model to identify the shape of the molecule and then assign the hybridization consistent with that shape. All single bonds are cr-bonds and multiple i bonds are composed of a cr-bond and one or more TT-bonds. Because the C atom is attached to three atoms, we anticipate that its hybridization scheme is sp1 and that one unhybridized p-orbital remains. Finally, we form cr- and Tr-bonds by allowing the 1 orbitals to overlap. 

FIGURE 16.36 I1ie tear-shaped objects are representations of the six ligand atomic orbitals that are used to build the molecular orbitals of an octahedral complex in ligand field theory. They might represent s- or p-orbitals on the ligands or hybrids of the two. 

In this picture of ethylene, the two orbitals that make up the double bond are not equivalent. The ct orbital is ellipsoidal and symmetrical about the C—C axis. The it orbital is in the shape of two ellipsoids, one above the plane and one below. The plane itself represents a node for the it orbital. In order for the p orbitals to maintain... 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

The quantum number / — 1 corresponds to a p orbital. A p electron can have any of three values for Jitt/, so for each value of tt there are three different p orbitals. The p orbitals, which are not spherical, can be shown in various ways. The most convenient representation shows the three orbitals with identical shapes but pointing in three different directions. Figure 7-22 shows electron contour drawings of the 2p orbitals. Each p orbital has high electron density in one particular direction, perpendicular to the other two orbitals, with the nucleus at the center of the system. The three different orbitals can be represented so that each has its electron density concentrated on both sides of the nucleus along a preferred axis. We can write subscripts on the orbitals to distinguish the three distinct orientations Px, Py, and Pz Each p orbital also has a nodal plane that passes through the nucleus. The nodal plane for the p orbital is the J z plane, for the Py orbital the nodal plane is the X Z plane, and for the Pz orbital it is the Jt plane. 

As Increases, the detailed shapes of the p orbitals become more complicated (the number of nodes increases, just as for s orbitals). Nevertheless, the directionality of the orbitals does not change. Each p orbital is perpendicular to the other two in its set, and each p orbital has its lobes along its preferred axis, where electron density is high. To an approaching atom, therefore, an electron in a 3p orbital presents the same characteristics as one in a 2p orbital, except that the 3p orbital is bigger. Consequently, the shapes and relative orientations of the 2p orbitals in Figure 7-22 represent the prominent spatial features of all p orbitals. 

The chemistry of all the common elements can be described completely using s, p, and d orbitals, so we need not extend our catalog of orbital shapes to the f orbitals and beyond. 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

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