Absolutely Small - Michael D. Fayer [62]
The 2py orbital has its lobes pointed along the y axis, and its nodal plane is the xz plane. The 2px orbital has its lobes pointed along the x axis, and its nodal plane is the yz plane. The schematic illustrations of the 2p orbitals in Figure 10.7 are like the representations of the s orbitals in Figure 10.2. Figure 10.7 gives a feel for the regions that have a large amount of electron probability amplitude. However, it is important to recognize that these are probability amplitude waves that die out smoothly away from the nucleus. In the figure, the lobes terminate abruptly, but the wavefunctions decay at long distances in a manner similar to that shown in Figure 10.3 for the 1s orbital. Nonetheless, Figure 10.7 is useful to get a feel for the shapes of the 2p orbitals. These shapes will be very important when we discuss molecular bonding and the shapes of molecules.
THE SHAPES OF THE d ORBITALS
When n = 3, l can equal 0 to give the 3s orbital. l can equal 1 with m = 1, 0, -1 to give the three different 3p orbitals. In addition, l can equal 2 with m = 2, 1, 0, -1, -2 to give five different 3d orbitals. These are shown in the energy level diagram, Figure 10.1. Figure 10.8 shows the five different 3d orbitals. Like the p orbitals, the d orbitals are often given names that reflect their shapes rather than labeling them with the quantum number, m. Four of the orbitals have the same basic shape. Each has four lobes and two angular nodal planes. Two of the lobes are positive and two are negative. When a nodal plane is crossed the wavefunction changes sign. The fifth orbital, the dz2, has a different shape, but it still has two angular nodal surfaces. One is the xy plane, and the other is the conical surface shown in the diagram. Like the p orbitals, the shaded regions in Figure 10.8 indicate where most of the electron probability amplitude is found. These probability amplitude waves go smoothly to zero as the distance from the nucleus increases.
FIGURE 10.7. Schematic of the three hydrogen atom 2p orbitals, 2pz, 2py, and 2px. Each orbital has two lobes, one positive and one negative. Each has an angular nodal plane, that is, a plane where the probability of finding the electron is zero. The 2pzorbital has its lobes along the z axis, and the nodal plane is the xy plane, which is shaded. The 2pyorbital has its lobes along the y axis, and the nodal plane is the xz plane. The 2pxorbital has its lobes along the x axis, and the nodal plane is the yz plane. The lobes in each diagram show where most of the electron probability amplitude is located. These probability amplitude waves delay smoothly to zero away from the nucleus (the proton) and do not stop abruptly as in the diagrams.
When n = 4, in addition to s, p, and d orbitals, l can equal 3, which gives rise to the seven possible m values. These are the seven f orbitals. The f orbitals have three angular nodes and very complicated shapes. As will be discussed in the next chapter on atoms bigger than hydrogen, only very heavy elements have f orbitals containing electrons, and the f electrons do not usually participate in making chemical bonds. Many molecules, particularly those in which the prime element is carbon called organic molecules, involve mainly 2s and 2p orbitals. However, molecules that contain heavier elements, such as metals, may involve d orbitals as well.
In Chapter 11, we will build on our discussion of the hydrogen atom to understand