Orbitals spatial orientation

Each set of p orbitals has three distinct directions or three different angular momentum m-quantum numbers as discussed in Appendix G. Each set of d orbitals has five distinct directions or m-quantum numbers, etc s orbitals are unidirectional in that they are spherically symmetric, and have only m = 0. Note that the degeneracy of an orbital (21+1), which is the number of distinct spatial orientations or the number of m-values. 

The dependence of the j3-deuterium effect on the spatial orientation of the isotopic bond with respect to the developing -orbital, on the a-carbon atom was elegantly demonstrated by Shiner and Humphrey (1963). This work will not be discussed in detail here suffice it to say the suggestion is made that j8-deuterium effects are better correlated by the postulate of hyperconjugation and its angular dependence than by the simple steric model (Shiner and Humphrey, 1963). 

The relative size of atomic orbitals, which is found to increase as their energy level rises, is defined by the principal quantum number, n, their shape and spatial orientation (with respect to the nucleus and each other) by the subsidiary quantum numbers, Z and m, respectively. Electrons in orbitals also have a further designation in terms of the spin quantum number, which can have the values +j or — j. One limitation that theory imposes on such orbitals is that each may accommodate not more than two electrons, these electrons being distinguished from each other by having opposed (paired) spins, t This follows from the Pauli exclusion principle, which states that no two electrons in any atom may have exactly the same set of quantum numbers. 

FIGURE 17.1 The spatial orientations of the set of five d orbitals for a transition metal. 

As you learned from the previous section, three quantum numbers—n, 1, and mi—describe the energy, size, shape, and spatial orientation of an orbital. A fourth quantum number describes a property of the electron that results from its particle-like nature. Experimental evidence suggests that electrons spin about their axes as they move throughout the volume of their atoms. Like a tiny top, an electron can spin in one of two directions, each direction generating a magnetic field. The spin quantum number (mj specifies the direction in which the electron is spinning. This quantum number has only two possible values or —... 

B) n = 4 corresponds to the 4th energy level 1-2 refers toad orbital, m/ = 0 refers to the magnetic quantum number and defines the spatial orientation of the orbital and is not required to answer the question. 

The spatial orientations of the atomic orbitals of the hydrogen atom are very important in the consideration of the interaction of orbitals of different atoms in the production of chemical bonds. 

The complex [(VO)2(dana)2] (dana = l,5-bis(p-methoxyphenyl)-l,3,5-pentanetrionato) was prepared and temperature dependent Xm measurements show antiferromagnetic behaviour with J = —80 cm 1.902 The / value is much lower than with [M2(dana)2(py)2] (M = Co, Cu) and this probably results from a different spatial orientation of the exchanging electrons if the unpaired electron is considered to be initially in a dxy orbital, a direct metal-metal interaction may be possible as the V—V distance is large (ca. 3.0-3.2 A V atoms are probably 0.5-0.6 A out of the plane and possibly one above and one below the ligand plane902), one would expect a weak exchange for the direct V—V interaction. 

There are five 3d orbitals, each represented by one box in an energy-level diagram These 3d orbitals differ from one another by their spatial orientations and shapes, as shown in Table 5.1. 

Most hybridizations result in equivalent hybrid orbitals, i.e., all the hybrid orbitals are identical in composition (% s and % p character) and in spatial orientation with respect to each other. They have very high symmetries, culminating in tetrahedral and octahedral symmetry. In the case of dsp hybrid orbitals, the resulting... 

The magnetic quantum number (mi) defines the spatial orientation of the orbital with respect to a standard set of coordinate axes. For an orbital whose angular-momentum quantum number is /, the magnetic quantum number mi... 

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