OBJECTIVE: To learn about the shapes of orbitals designated by s, p, and d.
The probability map for the hydrogen electron shown in Figure 11.19 is called an orbital.
The orbital represented in Figure 11.20 is named the 1s orbital, and it describes the hydrogen electron’s lowest energy state (the ground state). In Section 11.4 we saw that the hydrogen atom can absorb energy to transfer the electron to a higher energy state (an excited state). In terms of the obsolete Bohr model, this meant the electron was transferred to an orbit with a larger radius. In the wave mechanical model, these higher energy states correspond to different kinds of orbitals with different shapes. At this point we need to stop and consider how the hydrogen atom is organized. Remember, we showed earlier that the hydrogen atom has dis- crete energy levels. We call these levels principal energy levels and label them with integers (Figure 11.21). Next we find that each of these levels is subdivided into sublevels. The following analogy should help you under- stand this. Picture an inverted triangle (Figure 11.22). We divide the principal levels into various numbers of sublevels. Principal level 1 consists of one sublevel, principal level 2 has two sublevels, principal level 3 has three sub- levels, and principal level 4 has four sublevels. Like our triangle, the principal energy levels in the hydrogen atom contain sublevels. As we will see presently, these sublevels contain spaces for the electron that we call orbitals. Principal energy level 1 consists of just one sub-level, or one type of orbital. The spherical shape of this orbital is shown in Figure 11.20. We label this orbital 1s. The number 1 is for the principal energy level, and s is a shorthand way to label a particular sub level (type of orbital). Principal energy level 2 has two sublevels. (Note the correspondence between the principal energy level number and the number of sublevels.) These sublevels are labeled 2s and 2p. The 2s sublevel consists of one orbital (called the 2s), and the 2p sublevel consists of three orbitals (called 2px, 2py, and 2pz). The orbitals have the shapes shown in Fig- ures 11.24 and 11.25. The 2s orbital is spherical like the 1s orbital but larger in size (see Figure 11.24). The three 2p orbitals are not spherical but have two “lobes.” These orbitals are shown in Figure 11.25 both as electron probabil- ity maps and as surfaces that contain 90% of the total electron probability. Notice that the label x, y, or z on a given 2p orbital tells along which axis the lobes of that orbital are directed.
One important characteristic of orbitals is that as the level number increases, the average distance of the electron in that orbital from the nucleus also increases. That is, when the hydrogen electron is in the 1s orbital (the ground state), it spends most of its time much closer to the nucleus than when it occupies the 2s orbital (an excited state).
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You may be wondering at this point why hydrogen, which has only one electron, has more than one orbital. It is best to think of an orbital as a po- tential space for an electron. The hydrogen electron can occupy only a single orbital at a time, but the other orbitals are still available should the electron be transferred into one of them. For example, when a hydrogen atom is in its ground state (lowest possible energy state), the electron is in the 1s orbital. By adding the correct amount of energy (for example, a specific photon of light), we can excite the electron to the 2s orbital or to one of the 2p orbitals.
So far we have discussed only two of hydrogen’s energy levels. There are many others. For example, level 3 has three sublevels (see Figure 11.22), which we label 3s, 3p, and 3d. The 3s sublevel contains a single 3s orbital, a spherical orbital larger than 1s and 2s (Figure 11.27). Sublevel 3p contains three orbitals: 3px, 3py, and 3pz, which are shaped like the 2p orbitals except that they are larger. The 3d sublevel contains five 3d orbitals with the shapes and labels shown in Figure 11.28. (You do not need to memorize the 3d orbital shapes and labels. They are shown for completeness.) |
Notice as you compare levels 1, 2, and 3 that a new type of orbital (sub- level) is added in each principal energy level. (Recall that the p orbitals are added in level 2 and the d orbitals in level 3.) This makes sense because in going farther out from the nucleus, there is more space available and thus room for more orbitals.
It might help you to understand that the number of orbitals increases with the principal energy level if you think of a theater in the round. Picture a round stage with circular rows of seats surrounding it. The farther from the stage a row of seats is, the more seats it contains because the circle is larger. Orbitals divide up the space around a nucleus somewhat like the seats in this circular theater. The greater the distance from the nucleus, the more space there is and the more orbitals we find.
The pattern of increasing numbers of orbitals continues with level 4. Level 4 has four sublevels labeled 4s, 4p, 4d, and 4f. The 4s sublevel has a single 4s orbital. The 4p sublevel contains three orbitals (4px, 4py, and 4pz). The 4d sublevel has five 4d orbitals. The 4f sublevel has seven 4f orbitals.
The 4s, 4p, and 4d orbitals have the same shapes as the earlier s, p, and d orbitals, respectively, but are larger. We will not be concerned here with the shapes of the f orbitals.
It might help you to understand that the number of orbitals increases with the principal energy level if you think of a theater in the round. Picture a round stage with circular rows of seats surrounding it. The farther from the stage a row of seats is, the more seats it contains because the circle is larger. Orbitals divide up the space around a nucleus somewhat like the seats in this circular theater. The greater the distance from the nucleus, the more space there is and the more orbitals we find.
The pattern of increasing numbers of orbitals continues with level 4. Level 4 has four sublevels labeled 4s, 4p, 4d, and 4f. The 4s sublevel has a single 4s orbital. The 4p sublevel contains three orbitals (4px, 4py, and 4pz). The 4d sublevel has five 4d orbitals. The 4f sublevel has seven 4f orbitals.
The 4s, 4p, and 4d orbitals have the same shapes as the earlier s, p, and d orbitals, respectively, but are larger. We will not be concerned here with the shapes of the f orbitals.