Equatorial orbitals

To make a calculation for three double bonds we need three more orbitals. These may be the three equatorial bonds of the trigonal prism with three caps that is, with 6 = 90° and = 60°, 180°, and 300° (the three other orbitals have 9 = 43.47° and 0 = 0°, 120°, and 240°). The axis for each of the three double bonds is placed midway between an equatorial orbital and one of the other orbitals. The double-bond axes lie at 6 = 63.73°, which corresponds to 101.85° for the bond angle for doubly bonded carbonyls in the M(CO)3 group (bond number n = 2). 

Most sets of hybrid orbitals are equivalent and symmetric, that is, four sp orbitals directed to the comers of a regular tetrahedron, six tPsp orbitals to the corners of an octahedron, etc. (n the case of hybrids the resulting orbitals are not equivalent. In the trigonal bipyramidal arrangement three orbitals directed trigonally form one set of equivalent orbitals (these may be considered sp hybrids) and two orbitals directed linearly (and perpendicular to the plane of the first three) form a second set of two (these may be considered dp hybrids). The former set is known as the equatorial orbitals and the latter as the axial orbitals. Because of the nature of the different orbitals involved, bonds formed from the two are intrinsically different and will have different properties even when bonded to irJenlica] atoms. For example, in molecules like PFj bond lengths differ for axial and equatorial bonds (see Chapter 6). 

FIGURE 8.30 (a) Hybrid orbitals formed from linear combinations of Pm P>r and orbitals. The pair of orbitals that point along the positive and negative z-axes are the same except for their orientation in space they are called axial orbitals. The set of three orbitals in the x-y plane are equivalent to one another and are called equatorial orbitals, (b) This set of hybrid orbitals can be used to describe the bonding in PF5, for example. 

The expanded octet model includes one or more d orbitals in the valence shell, allowing an electron count greater than eight. The energy cost of promoting electrons from an p orbital io d orbital (with the same principle quantum number) is presumed to be made up by the additional covalent bonding. The electron hybridization of a ten-electron system, for example, is sp d, which can be broken down into a pd pair of axial orbitals and a sp trio of equatorial orbitals. Expansion of the octet is not feasible for the second-row elements, such as C, N, O, and F, because there are no 2d orbitals. 

The mixing of 5, p, Py, p and d i atomic orbitals gives a set of five sp d hybrid orbitals, the mutual orientations of which correspond to a trigonal bipyramidal arrangement (Figure 4.7a). The five sp d hybrid orbitals are not equivalent and divide into sets of two axial and three equatorial orbitals the axial orbital lobes lie along the z axis. The model of sp d hybridization can be used to... 

Equatorial orbit The plane of a satellite orbit which coincides with that of the equator of the primary body. 

The p and d orbitals with m = 0, i.e., the z and z orbitals, respectively, which lie along the z axis, can conveniently be called the polar or axial orbitals. Analogously, the p and d orbitals with m = /, i.e., the x, y, xy, and x -y orbitals, which lie in the equatorial plane (z = 0) can conveniently be called the equatorial orbitals. The remaining d orbitals with m = 1, i.e., the xz and yz orbitals, can conveniently be called the temperate orbitals, since their lobes are oriented towards the temperate zones of an earth where the z axis passes through the north and south poles. 

Satelhte orbits are classified as high and low orbits, polar orbits (when the orbital plane contains the spin axis of the earth), equatorial orbits (orbital plane coincides with the eqnatorial plane of the earth), and pro-grade and retro-grade or bits (the direction of sateUite motion is either eastward or westward). The lower the orbit is, the faster the satelhte circles the earth. At an altitnde of about 36,000 km, the orbital velocity matches that of the earth s... 

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