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11.1 The Mysterious Electron 11.2 Multi-Electron Atoms To see a World in a Grain of Sand And a Heaven in a Wild Flower Hold Infinity in the palm of your hand And Eternity in an hour William Blake (1757-1827) Auguries of Innocence cientists’ attempts to understand the atom have led them into the unfamiliar world of the unimaginably small, where the rules of physics seem to be different from the rules in the world we can see and touch. Scientists explore this world through the use of mathematics. Perhaps this is similar to the way a writer uses poetry to express ideas and feelings beyond the reach of everyday language. Mathematics allows the scientist to explore beyond the boundaries of the world we can experience directly. Just as scholars then try to analyze the poems and share ideas about them in everyday language, scientists try to translate the mathematical description of the atom into words that more of us can understand. Although both kinds of translation are fated to fall short of capturing the fundamental truths of human nature and the physical world, the attempt is worthwhile for the occasional glimpse of those truths that it provides. This chapter offers a brief, qualitative introduction to the mathematical description of electrons and describes the highly utilitarian model of atomic structure that chemists have constructed from it. Because we are reaching beyond the world of our senses, we should not be surprised that the model we create is uncertain and, when described in normal language, a bit vague. In spite of these limitations, however, you will return from your journey into the strange, new world of the extremely small with a useful tool for explaining and predicting the behavior of matter. Chemists try to “see” the structure of matter even more closely than can be seen in any photograph. Review Skills The presentation of information in this chapter assumes that you can already perform the tasks listed below. You can test your readiness to proceed by answering the Review Questions at the end of the chapter. This might also be a good time to read the Chapter Objectives, which precede the Review Questions. Describe the nuclear model of the atom. (Section 2.4) Describe the relationship between stability and potential energy. (Section 7.1)
11.1 The Mysterious Electron Where there is an open mind, there will always be a frontier. Charles F. Kettering (1876-1958) American engineer and inventor Scientists have known for a long time that it is incorrect to think of electrons as tiny particles orbiting the nucleus like planets around the sun. Nevertheless, nonscientists have become used to picturing them in this way. In some circumstances, this “solar system” model of the atom may be useful, but you should know that the electron is much more unusual than that model suggests. The electron is extremely tiny, and modern physics tells us that strange things happen in the realm of the very, very small. The modern description of the electron is based on complex mathematics and on the discoveries of modern physics. The mathematical complexity alone makes an accurate verbal portrayal of the electron challenging, but our difficulty in describing the electron goes beyond complexity. Modern physics tells us that it is impossible to know exactly where an electron is and what it is doing. As your mathematical and scientific knowledge increases, you will be able to understand more sophisticated descriptions of the electron, but the problem of describing exactly where the electron is and what it is doing never goes away. It is a problem fundamental to very tiny objects. Thus complete confidence in our description of the nature of the electron is beyond our reach. There are two ways that scientists deal with the problems associated with the complexity and fundamental uncertainty of the modern description of the electron: Analogies In order to communicate something of the nature of the electron, scientists often use analogies, comparing the electron to objects with which we are more familiar. For example, in this chapter we will be looking at the ways in which electrons are like vibrating guitar strings. Probabilities In order to accommodate the uncertainty of the electron’s position and motion, scientists talk about where the electron probably is within the atom, instead of where it definitely is. Through the use of analogies and a discussion of probabilities, this chapter attempts to give you a glimpse of what scientists are learning about the electron’s character. Standing Waves and Guitar Strings Each electron seems to have a dual nature in which both particle and wave characteristics are apparent. It is difficult to describe these two aspects of an electron at the same time, so sometimes we focus on its particle nature and sometimes on its wave character, depending on which is more suitable in a given context. In the particle view, electrons are tiny, negatively charged particles with a mass of about 9.1096 × 10 -^28 grams. In the wave view, an electron has an effect on the space around it that can be described as a wave of varying negative charge intensity. To gain a better understanding of this electron-wave character, let’s compare it to the wave character of guitar strings. Because a guitar string is easier to visualize than an electron, its vibrations serve as a useful analogy of the wave character of electrons.
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Electrons as Standing Waves The wave character of the guitar string is represented by the movement of the string. We can focus our attention on the blur of the waveform and forget the material the string is made of. The waveform describes the motion of the string over time, not the string itself. In a similar way, the wave character of the electron is represented by the waveform of its negative charge, on which we can focus without concerning ourselves about the electron’s particle nature. This frees us from asking questions about where the electrons are in the atom and how they are moving—questions that we are unable to answer. The waveforms for electrons in an atom describe the variation in intensity of negative charge within the atom, with respect to the location of the nucleus. This can be described without mentioning the positions and motion of the electron particle itself. The following statements represent the core of the modern description of the wave character of the electron: Just as the intensity of the movement of a guitar string can vary, so can the intensity of the negative charge of the electron vary at different positions outside the nucleus. The variation in the intensity of the electron charge can be described in terms of a three-dimensional standing wave like the standing wave of the guitar string. As in the case of the guitar string, only certain waveforms are possible for the electron in an atom. We can focus our attention on the waveform of varying charge intensity without having to think about the actual physical nature of the electron. Thus, the task is not so much to see what no one has yet seen, but to think what nobody has yet thought, about that which everybody sees. Erwin Schrodinger (1887-1961) Austrian physicist and Nobel laureate Waveforms for Hydrogen Atoms Most of the general descriptions of electrons found in the rest of this chapter are based on the wave mathematics for the one electron in a hydrogen atom. The comparable calculations for other elements are too difficult to lead to useful results, so as you will see in the next section, the information calculated for the hydrogen electron is used to describe the other elements as well. Fortunately, this approximation works quite well. The wave equation for the one electron of a hydrogen atom predicts waveforms for the electron that are similar to the allowed waveforms for a vibrating guitar string. For example, the simplest allowed waveform for the guitar string looks something like The simplest allowed waveform for an electron in a hydrogen atom looks like the image in Figure 11.3. The cloud that you see surrounds the nucleus and represents the variation in the intensity of the negative charge at different positions outside the nucleus. The negative charge is most intense at the nucleus and diminishes with increasing distance from the nucleus. The variation in charge intensity for this waveform is the same in all directions, so the waveform is a sphere. The allowed waveforms for objeCtive 4
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the electron are also called orbitals. The orbital shown in Figure 11.3 is called the 1 s orbital. Figure 11. Waveform of the 1 s Electron Theoretically, the charge intensity depicted in Figure 11.3 decreases toward zero as the distance from the nucleus approaches infinity. This suggests the amusing possibility that some of the negative charge created by an electron in a hydrogen atom is felt an infinite distance from the atom’s nucleus. The more practical approach taken by chemists, however, is to specify a volume that contains most of the electron charge and focus their attention on that, forgetting about the small negative charge felt outside the specified volume. For example, we can focus on a sphere containing 90% of the charge of the 1 s electron. If we wanted to include more of the electron charge, we enlarge the sphere so that it encloses 99% (or 99.9%) of the electron charge (Figure 11.4). This leads us to another definition of orbital as the volume that contains a given high percentage of the electron charge. Most of the pictures you will see of orbitals represent the hypothetical surfaces that surround a high percentage of the negative charge of an electron of a given waveform. The 1 s orbital, for example, can either be represented by a fuzzy sphere depicting the varying intensity of the negative charge (Figure 11.3) or by a smooth spherical surface depicting the boundary within which most of the charge is to be found (Figure 11.4). Figure 11. 1 s Orbital Is the sphere in Figure 11.3 the 1 s electron? This is like asking if the guitar string is the blur that you see when the string vibrates. When we describe the standing wave that represents the motion of a guitar string, we generally do not refer to the material composition of the string. The situation is very similar for the electron. We are able to describe the variation in intensity of the negative charge created by the electron without thinking too much about what the electron is and what it is doing. objeCtive 4 objeCtive 4 objeCtive 4
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Other Important Orbitals Just like the guitar string can have different waveforms, the one electron in a hydrogen atom can also have different waveforms, or orbitals. The shapes and sizes for these orbitals are predicted by the mathematics associated with the wave character of the hydrogen electron. Figure 11.6 shows some of them. Figure 11. Some Possible Waveforms, or Orbitals, for an Electron in a Hydrogen Atom Before considering the second possible orbital for the electron of a hydrogen atom, let’s look at another of the possible ways a guitar string can vibrate. The guitar string waveform below has a node in the center where there is no movement of the string. The electron-wave calculations predict that an electron in a hydrogen atom can have a waveform called the 2 s orbital that is analogous to the guitar string waveform above. The 2 s orbital for an electron in a hydrogen atom is spherical like the 1 s orbital, but it is a larger sphere. All spherical electron waveforms are called s orbitals. For an electron in the 2 s orbital, the charge is most intense at the nucleus. With increasing distance from the nucleus, the charge diminishes in intensity until it reaches a minimum at a certain distance from the nucleus; it then increases again to a maximum, and finally it objeCtive 6
diminishes again. The region within the 2 s orbital where the charge intensity decreases to zero is called a node. Figure 11.7 shows cutaway, quarter-section views of the 1 s and 2 s orbitals. Figure 11. Quarter Sections of the 1 s and 2 s Orbitals The average distance between the positive charge of the nucleus and the negative charge of a 2 s electron cloud is greater than the average distance between the nucleus and the charge of a 1 s electron cloud. Because the strength of the attraction between positive and negative charges decreases with increasing distance between the charges, an electron is more strongly attracted to the nucleus and therefore is more stable when it has the smaller 1 s waveform than when it has the larger 2 s waveform. As you discovered in Section 7.1, increased stability is associated with decreased potential energy, so a 1 s electron has lower potential energy than a 2 s electron^1. We describe this energy difference by saying the 1 s electron is in the first principal energy level, and the 2 s electron is in the second principal energy level. All of the orbitals that have the same potential energy for a hydrogen atom are said to be in the same principal energy level. The principal energy levels are often called shells. The 1 in 1 s and the 2 in 2 s show the principal energy levels, or shells, for these orbitals. Chemists sometimes draw orbital diagrams, such as the following, with lines to represent the orbitals in an atom and arrows (which we will be adding later) to represent electrons: The line representing the 2 s orbital is higher on the page to indicate its higher potential energy. Because electrons seek the lowest energy level possible, we expect the electron in a hydrogen atom to have the 1 s waveform, or electron cloud. We say that the electron is in the 1 s orbital. But the electron in a hydrogen atom does not need to stay in the 1 s orbital at all times. Just as an input of energy (a little arm work on our part) can lift a book resting on a table and raise it to a position that has greater potential energy, so can the waveform of an electron in a hydrogen atom be changed from the 1 s shape to the 2 s shape by the addition of energy to the atom. We say that the electron can be excited from the 1 s orbital to the 2 s orbital. Hydrogen atoms with their electron in the (^1) If you are reading this chapter before studying Chapter 7, you might want to read the portions of Section 7.1 that describe energy, kinetic energy, and potential energy. objeCtive 6 objeCtive 7
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In the third principal energy level, there are nine possible waveforms for an electron, in three different sublevels (Figure 11.6). The 3 s sublevel has one orbital that has a spherical shape, like the 1 s and the 2 s , but it has a larger average radius and two nodes. Its greater average distance from the positive charge of the nucleus makes it less stable and higher in energy than the 1 s or 2 s orbitals. The calculations predict that the third principal energy level has a 3 p sublevel, with three 3 p orbitals. They have the same general shape as the 2 p orbitals, but they are larger, which leads to less attraction to the nucleus, less stability, and higher potential energy than for a 2 p orbital. The third principal energy level also has a 3 d sublevel, with five 3 d orbitals. Four of these orbitals have four lobes whose shape is similar to the lobes of a 3 p orbital. We will call these “double dumbbells.” An electron in a 3 d orbital has its negative charge spread out in these four lobes. The fifth 3 d orbital has a different shape, as shown in Figure 11.11. Figure 11. 3 d Orbitals When an electron in a hydrogen atom is excited to the fourth principal energy level, it can be in any one of four sublevels: 4 s , 4 p , 4 d , or 4 f. There is one 4 s orbital, with a spherical shape and a larger volume than the 3 s. There are three 4 p orbitals, similar in shape to the 3 p orbitals but with a larger volume than the 3 p orbitals. There are five 4 d orbitals, similar to but larger than the 3 d orbitals. The 4 f sublevel has seven possible orbitals. Overall Organization of Principal Energy Levels, Sublevels, and Orbitals Table 11.1 shows all the orbitals predicted for the first seven principal energy levels. Notice that the first principal energy level has one sublevel, the second has two sublevels, the third has three sublevels, and the fourth has four. If n is the number associated with the principal energy level, each principal energy level has n sublevels. Thus there are five sublevels on the fifth principal energy level: 5 s , 5 p , 5 d , 5 f , and 5 g. The 5 s , 5 p , 5 d , and 5 f orbitals have shapes similar to the 4 s , 4 p , 4 d , and 4 f orbitals, but they are larger and have higher potential energy. Each s sublevel has one orbital, each p sublevel has three orbitals, each d has five orbitals, and each f sublevel has seven orbitals. Thus there are one 5 s orbital, three 5 p orbitals, five 5 d orbitals, and seven 5 f orbitals. The trend of increasing the number of orbitals by two for each succeeding sublevel continues for 5 g and beyond. There are nine 5 g orbitals with shapes more complex than the shapes of the 4 f orbitals. objeCtive 9 objeCtive 9
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Table 11.1 Possible Sublevels and Orbitals for the First Seven Principal Energy Levels (The sublevels in parentheses are not necessary for describing any of the known elements.) Sublevels (subshells) Number of orbitals 1 s 1 2 s 2 p
3 s 3 p 3 d
4 s 4 p 4 d 4 f
5 s 5 p 5 d 5 f (5 g )
Sublevels (subshells) Number of orbitals 6 s 6 p 6 d (6 f ) (6 g ) (6 h )
7 s 7 p (7 d ) (7 f ) (7 g ) (7 h ) (7 i )
In the next section, where we use the orbitals predicted for hydrogen to describe atoms of other elements, you will see that none of the known elements has electrons in the 5 g sublevel for their most stable state (ground state). Thus we are not very interested in describing the 5 g orbitals. Likewise, although the sixth principal energy level has six sublevels and the seventh has seven, only the 6 s , 6 p , 6 d , 7 s , and 7 p are important for describing the ground states of the known elements. The reason for this will be explained in the next section. None of the known elements in its ground state has any electrons in a principal energy level higher than the seventh, so we are not concerned with the principal energy levels above seven. The orbital diagram in Figure 11.12 shows only the sublevels (or subshells) and orbitals that are necessary for describing the ground states of the known elements. Figure 11. Diagram of the Orbitals for an Electron in a Hydrogen Atom
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if you are asked for an electron configuration for helium, you will write 1 s^2. If you are expected to describe the orbitals with lines and the electrons with arrows, you will be asked to draw an orbital diagram. The Second Period Elements Electrons do not fill the available sublevels in the order we might expect. Thus, to predict the electron configurations of elements larger than helium, we need a way of remembering the actual order of sublevel filling. Probably the least reliable method is to memorize the following list that shows the order of filling of all the orbitals necessary for describing the ground state electron configurations of all of the known elements. 1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p Instead of relying on memorization, you can use the memory aid shown in Figure 11.14 to remind you of the correct order of filling of the sublevels. The following steps explain how to write it and use it yourself. Write the possible sublevels for each energy level in organized rows and columns like in Figure 11.14. To do this, you need to remember that there is one sublevel on the first principal energy level, two on the second, three on the third, etc. Every principal energy level has an s orbital. The second principal energy and all higher energy levels have a p sublevel. The d sublevels start on the third principal energy level, the f sublevels start on the fourth principal energy level, etc. Draw arrows like those you see in Figure 11.14. Starting with the top arrow, follow the arrows one by one in the direction they point, listing the sublevels as you pass through them. The sublevels that are not needed for describing the known elements are enclosed in parentheses in Figure 11.14. Later in this section, you will see how to determine the order of filling of the sublevels using a periodic table. Figure 11. Aid for Remembering the Order of Sublevel Filling objeCtive 11 objeCtive 11
objeCtive 11 An atomic orbital may contain two electrons at most, and the electrons must have different spins. Because each s sublevel has one orbital and each orbital contains a maximum of two electrons, each s sublevel contains a maximum of two electrons. Because each p sublevel has three orbitals and each orbital contains a maximum of two electrons, each p sublevel contains a maximum of six electrons. Using similar reasoning, we can determine that each d sublevel contains a maximum of ten electrons, and each f sublevel contains a maximum of 14 electrons (Table 11.2). Table 11.2 General Information About Sublevels Type of sublevel Number of orbitals Maximum number of electrons s 1 2 p 3 6 d 5 10 f 7 14 We can now predict the electron configurations and orbital diagrams for the ground state of lithium, which has three electrons, and beryllium, which has four electrons: Lithium 1 s^2 2 s^1 Beryllium 1 s^2 2 s^2 A boron atom has five electrons. The first four fill the 1 s and 2 s orbitals, and the fifth electron goes into a 2 p orbital. The electron configuration and orbital diagram for the ground state of boron atoms are below. Even though only one of three possible 2 p orbitals contains an electron, we show all three 2 p orbitals in the orbital diagram. The lines for the 2 p orbitals are drawn higher on the page than the line for the 2 s orbital to show that electrons in the 2 p orbitals have a higher potential energy than electrons in the 2 s orbital of the same atom.^2 Boron 1 s^2 2 s^2 2 p^1 When electrons are filling orbitals of the same energy, they enter orbitals in such a way as to maximize the number of unpaired electrons, all with the same spin. In other words, they enter empty orbitals first, and all electrons in half filled orbitals have the same spin. The orbital diagram for the ground state of carbon atoms is objeCtive 12 (^2) The 2 s and 2 p orbitals available for the one electron of a hydrogen atom have the same potential energy. However, for reasons that are beyond the scope of this discussion, when an atom has more than one electron, the 2 s orbital is lower in potential energy than the 2 p orbitals. objeCtive 11 objeCtive 12 objeCtive 12
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The Periodic Table and the Modern Model of the Atom The periodic table itself can be used as a guide for predicting the electron configurations of most of the elements. Conversely, the electron configurations of the elements can be used to explain the table’s structure and the similarities and differences that were the basis for the table’s creation. The organization of the periodic table reflects the modern model of the atom. For example, the highest-energy electrons for all of the elements in groups 1 (1A) and 2 (2A) Figure 11. 16 The Periodic Table and the Modern Model of the Atom
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in the periodic table are in s orbitals. That is, the highest-energy electrons for lithium, Li, and beryllium, Be, atoms are in the 2 s orbital, and the highest-energy electrons for sodium, Na, and magnesium, Mg, atoms are in the 3 s orbital. This continues down to francium, Fr, and radium, Ra, which have their highest-energy electrons in the 7 s orbital. Therefore, the first two columns on the periodic table are called the s block. Because hydrogen and helium have their electrons in the 1 s orbital, they belong in the s block too (Figure 11.16). All of the elements in the block with boron, B, neon, Ne, thallium, Tl, and radon, Rn, at the corners have their highest energy electrons in p orbitals, so this is called the p block (Figure 11.16). The second principal energy level is the first to contain p orbitals, so atoms of elements in the first row of the p block have their highest-energy electrons in the 2 p sublevel. The highest-energy electrons for elements in the second row of the p block are in the 3 p sublevel. This trend continues, so we can predict that the 81st^ through the 86th^ electrons for the elements thallium, Tl, through radon, Rn, are added to the 6 p sublevel. Moreover, we can predict that the new elements that have been made with atoms larger than element 112 have their highest-energy electrons in the 7 p sublevel. The last electrons to be added to an orbital diagram for the atoms of the transition metal elements go into d orbitals. For example, the last electrons added to atoms of scandium, Sc, through zinc, Zn, are added to 3 d orbitals. The elements yttrium, Y, through cadmium, Cd, have their highest-energy electrons in the 4 d sublevel. The elements directly below them in rows 6 and 7 add electrons to the 5 d and 6 d orbitals. The transition metals can be called the d block. (Figure 11.16). The section of the periodic table that contains the inner transition metals is called the f block. Thus we can predict that the last electrons added to the orbital diagrams of elements with atomic numbers 57 through 70 would go into the 4 f sublevel. Elements 89 through 102 are in the second row of the f block. Because the fourth principal energy level is the first to have an f sublevel, we can predict that the highest energy- electrons for these elements go to the 5 f sublevel. We can also use the block organization of the periodic table, as shown in Figure 11.16, to remind us of the order in which sublevels are filled. To do this, we move through the elements in the order of increasing atomic number, listing new sublevels as we come to them. The type of sublevel ( s , p , d , or f ) is determined from the block in which the atomic number is found. The number for the principal energy level (for example, the 3 in 3 p ) is determined from the row in which the element is found and the knowledge that the s sublevels start on the first principal energy level, the p sublevels start on the second principal energy level, the d sublevels start on the third principal energy level, and the f sublevels start on the fourth principal energy level. We know that the first two electrons added to an atom go to the 1 s sublevel. Atomic numbers 3 and 4 are in the second row of the s block (look for them in the bottom half of Figure 11.16), signifying that the 3rd^ and 4th^ electrons are in the 2 s sublevel.
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Sample Study Sheet 11. Writing Complete Electron Configurations and Orbital Diagrams for Uncharged Atoms objeCtive 11 Tip-off If you are asked to write a complete electron configuration or an orbital diagram, you can use the following guidelines. General STepS To write a complete electron configuration for an uncharged atom: Step 1 Determine the number of electrons in the atom from its atomic number. Step 2 Add electrons to the sublevels in the correct order of filling. Add two electrons to each s sublevel, 6 to each p sublevel, 10 to each d sublevel, and 14 to each f sublevel. Step 3 To check your complete electron configuration, look to see whether the location of the last electron added corresponds to the element’s position on the periodic table. (See Example 11.1.) To draw an orbital diagram for an uncharged atom, Step 1 Write the complete electron configuration for the atom. (This step is not absolutely necessary, but it can help guide you to the correct orbital diagram.) Step 2 Draw a line for each orbital of each sublevel mentioned in the complete electron configuration. Draw one line for each s sublevel, three lines for each p sublevel, five lines for each d sublevel, and seven lines for each f sublevel. As a guide to the order of filling, draw your lines so that the orbitals that fill first are lower on the page than the orbitals that fill later. Label each sublevel. Step 3 For orbitals containing two electrons, draw one arrow up and one arrow down to indicate the electrons’ opposite spin. Step 4 For unfilled sublevels, add electrons to empty orbitals whenever possible, giving them the same spin. The arrows for the first three electrons to enter a p sublevel should each be placed pointing up in different orbitals. The fourth, fifth, and sixth are then placed, pointing down, in the same sequence, so as to fill these orbitals. The first five electrons to enter a d sublevel should be drawn pointing up in different orbitals. The next five electrons are drawn as arrows pointing down and fill these orbitals (again, following the same sequence as the first five d electrons). The first seven electrons to enter an f sublevel should be drawn as arrows pointing up in different orbitals. The next seven electrons are paired with the first seven (in the same order of filling) and are drawn as arrows pointing down. example See Example 11.1. objeCtive 12
exaMple 11.1 - Electron Configurations and Orbital Diagrams Write the complete electron configuration and draw an orbital diagram for iron, Fe. Solution We follow the steps described in Study Sheet 11.1 to write the complete electron configuration: Determine the number of electrons in the atom from its atomic number. The periodic table shows us that iron, Fe, has an atomic number of 26, so an uncharged atom of iron has 26 electrons. Add electrons to the sublevels in the correct order of filling. We can determine the order of filling by either memorizing it, figuring it out from the memory aid shown in Figure 11.14, or using the periodic table and our knowledge of s , p , d , and f blocks. The order of filling is 1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p Next, we fill the orbitals according to this sequence, putting two electrons in each s sublevel, six in each p sublevel, 10 in each d sublevel, and 14 in each f sublevel until we reach the desired number of electrons. For iron, we get the following complete electron configuration: 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 4 s^2 3 d^6 To check your complete electron configuration, look to see whether the location of the last electron added corresponds to the element’s position on the periodic table. Because it is fairly easy to forget a sublevel or miscount the number of electrons added, it is a good idea to quickly check your complete electron configuration by looking to see if the last electrons added correspond to the element’s location on the periodic table. The symbol for iron, Fe, is found in the sixth column of the d block. This shows that there are six electrons in a d sublevel. Because iron is in the first row of the d block, and because the d sublevels begin on the third principal energy level, these six electrons are correctly described as 3 d^6. To draw the orbital diagram, we draw a line for each orbital of each sublevel mentioned in the complete electron configuration above. For orbitals containing two electrons, we draw one arrow up and one arrow down to indicate the electrons’ opposite spin. For unfilled sublevels, we add electrons to empty orbitals first with the same spin. The orbital diagram for iron atoms is displayed below. Note that four of the six electrons in the 3 d sublevel are in different orbitals and have the same spin. objeCtive 11 objeCtive 12
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You can get some practice writing electron configurations on the textbook’s Web site.
