Shapes of s and p orbitals

Since an understanding of orbital theory is critical to understanding organic reaction mechanisms, review of the material presented in primary organic chemistry textbooks is essential. For the purposes of the discussions presented herein, recall that ground-state first-row elements (including C, N, and O) all possess one s orbital and three p orbitals. Figure 5.2 illustrates the shapes of s and p orbitals. 

How well the AOs overlap — looking at the different, shapes of. s and p orbitals, we see that, for bonding orbitals, s orbitals will overlap to a greater extent than p orbitals. Will pz orbitals overlap more or less than px and pv Unfortunately, there are other less obvious factors to be considered and the relative ordering of [Pg.111]

Orbitals are regions of space located aroimd the nucleus of an atom, each having the energy of the sublevel of which it is a part. Orbitals can have different sizes and shapes. There are four types of orbitals that accommodate the electrons for all the atoms of the known elements. Two simple rules apply to these four orbitals. First, an orbital can hold a maximum of two electrons. Second, an orbital has the same name as its sub-level. There is only one s orbital with, at most, 2 electrons. A p sublevel has, at most, 6 electrons, and, thus, there are three p orbitals, each with 2 electrons. Figure 7.7 shows the shapes of s and p orbitals. 

What is an orbital Describe the shapes of s and p orbitals in words and by sketches. 

In an atom, the hybridization of s and p orbitals to form sp orbitals provides electron probability areas where bonds can form to make a molecule more stable than if the bonding had occurred in the individual s and p orbitals. The sp orbitals have one large lobe and one small lobe and are aligned along x, y, and z coordinates so that four sp orbitals, called sp3 orbitals because they are made of one s and three p orbitals, result in a tetrahedral-shaped arrangement. When there are three sp orbitals, made of one s and two p orbitals, called sp orbitals, the molecular has a triangular-planar shape. If there is bonding in two sp orbitals, made of one s and one p orbital, a linear molecule results. 

The general shape of s and p atomic orbitals for carbon. These cartoons are the schematics that chemists typically sketch. Shown also is a more realistic representation for the p orbital produced by quantum mechanical calculations. 

In Chapter 6 we learned that although an electron is a particle with a known mass, it exhibits wavelike properties. The quantum mechanical model of the atom, which gives rise to the fainiliar shapes of s and p atomic orbitals, treats electrons in atoms as waves, rather than particles. Therefore, rather than use arrows to denote the locations and spins of electrons, we will adopt a convention whereby a singly occupied orbital will appear as a light color and a doubly occupied... 

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 1.5 The shapes of some s and p orbitals. Pure, unhybridized p orbitals are almost-touching spheres. The p orbitals in hybridized atoms are lobe-shaped (Section 1.14).

Still another aspect of the Li and F valence orbitals is modified by ionic-bond formation. In an isolated ionic or neutral species, each NAO retains the characteristic angular shape of the pure s and p hydrogenic orbitals shown in Fig. 1.1, reflecting the full rotational symmetry of atoms. However, in the presence of another atom or ion this symmetry is broken, and the optimal valence orbitals acquire sp hybrid form (assumed for simplicity to include only valence s and p orbitals), as represented mathematically by... 

You must know the shapes of the s and p orbitals and be able to draw them. You must also remember that the maximum number of electrons in any orbital is two. 

These five d orbitals are degenerate with each other, but have higher energies than the s and p orbitals in the same shell. Four of the d orbitals are shaped like a double dumbbell. 

Consider one beautifully symmetrical shape predicted by VSEPR theory the tetrahedron. Four equivalent pairs of electrons in the valence shell of an atom should distribute themselves into such a shape, with equal angles and an equal distance between each pair. But what sort of atom has four equivalent electron pairs in its valence shell Aren t valence electrons distributed between different kinds of orbitals, like s and p orbitals (We introduce these orbitals in Chapter 4.)... 

The angular functions for the s and p. orbital are illustrated in Fig. 2.5. For an s orbital, cl> is independent of angle and is of constant value. Hence this graph is circular or, more properly, in three dimensions—spherical. For the p. orbital we obtain two tangent spheres. The px and py orbitals are identical in shape but are oriented along the x and y axes, respectively. We shall defer extensive treatment of the d orbitals (Chapter 11) and / orbitals (Chapter 14) until bond formation in coordination compounds is discussed, simply noting here that the basic angular function for tl orbitals is fout-iobed and that for / orbitals is six-lobed (see Fig. 2.91... 

However, if we examine a carbon with four a-bonds, we find that the four bonds are indistinguishable. Since die bonds are indistinguishable, the orbitals which form them must be equivalent. In order to form four a-bonds, the electrons form four new orbitals. The new orbitals are hybrids of the old s and p orbitals and are equivalent to each other in shape and energy. 

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. 

The shapes of these molecules cannot result from bonding between simple s and p atomic orbitals. Although s and p orbitals have the lowest energies for isolated atoms in space, they are not the best for forming bonds. To explain the shapes of common organic molecules, we assume that the s and p orbitals combine to form hybrid atomic orbitals that separate the electron pairs more widely in space and place more electron density in the bonding region between the nuclei. 

The s subshell contains one orbital or region where an electron can be found. The p sublevel has three orbitals, while the d and f levels have five and seven orbitals, respectively. The shapes of the s and p orbitals are shown in Figure 3.5. 

What shapes do orbitals hav e Them are (our different kinds of orbitals, denoted p, [Pg.24]

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