Absolutely Small: How Quantum Theory Explains Our Everyday World - Michael D. Fayer (2010)

Chapter 11. Many Electron Atoms and the Periodic Table of Elements

THE PROPERTIES OF ATOMIC and molecular matter are determined by the quantum mechanical details of the atoms that make up a substance. Common table salt is sodium chloride, NaCl. Na is the symbol for the sodium atom. Sodium’s atomic number is 11. The atomic number is the number of protons in the nucleus, that is, it is the positive charge on the nucleus. Na has 11 protons in its nucleus and 11 negatively charged electrons. Chlorine (symbol Cl) has an atomic number of 17. Cl has 17 protons in its nucleus and 17 electrons. When table salt, which is composed of little white crystals of NaCl, is put in water, it dissolves. In water, the Na becomes the positively charged sodium ion, Na+ (sodium has lost an electron), and the Cl becomes the negatively charged chloride ion, Cl- (chlorine has gained an electron). Sodium gives up an electron to chlorine to form the sodium cation (positively charged ion) and the chloride anion (negatively charged ion). The charges on the sodium cation and the chloride anion make these ions very soluble in water.

Methane is natural gas that we burn in our gas stoves, gas clothes dryers, and power plants. Its chemical formula is CH4. This means it is composed of one carbon atom (symbol C, atomic number 6) bonded to (attached to) four hydrogen atoms (symbol H, atomic number 1). Methane does not become ions when put in water. In fact, it does not dissolve in water. Unless it is raised to very high temperature as in a flame, it does not come apart at all. Why does NaCl become separated ions, Na+ and Cl-, when dissolved in water, while carbon always makes four chemical bonds and methane does not come apart in water to form ions? The answers to these questions and many of the properties of all of the atoms can be understood by looking at the nature of many electron atoms and the collection of systemic information about atoms contained in the Periodic Table of the Elements.


The hydrogen atom is different from all other atoms, and the difference is highly significant. The hydrogen atom consists of a positively charged nucleus (a proton) and one negatively charged electron. The sole electrostatic interaction is the attraction of the electron to the proton because oppositely charged particles attract. The next simplest atom is helium. Helium consists of a positively charged nucleus, with a positive charge of +2 (symbol He, atomic number 2) and two electrons, each with a negative charge of -1. Each electron is attracted to the nucleus. In addition, the two electrons repel each other because like changes repel. The repulsion is referred to as electron-electron repulsion. Because a hydrogen atom has only a single electron, there is no electron-electron repulsion.

In the energy level diagram for the hydrogen atom (Figure 10.1), all of the orbitals with the same principal quantum number n have the same energy. So the 2s and the 2p orbitals have the same energy. The 3s, 3p, and 3d orbitals all have the same energy, and so on. The fact that energy only depends on the principal quantum number is a result of hydrogen having a single electron. In Figures 10.2, 10.7, and 10.8, the s, p, and d orbitals have very different shapes. However, in hydrogen, the electron, on average, is the same distance from the nucleus independent of the shape of the orbitals. So an electron has the same energy whether it is in a 3s, 3p, or 3d orbital. Why? Because the electron has the same attraction to the nucleus when averaged over the spatial distribution given by its 3s, 3p, or 3d wavefunctions.


With more than one electron, the shapes of the orbitals matter. In helium, if its two electrons are placed in the 2s orbital the energy is lower than if they are placed in a 2p orbital. On average, two electrons in the 2s orbital are farther apart than two electrons in a 2p orbital. Electron-electron repulsion increases the energy. Because the two electrons are farther apart in the 2s orbital, the electron-electron repulsion (increase in energy) is not as severe as having the two electrons in a 2p orbital. Therefore, the 2s orbital in many electron atoms (all atoms but hydrogen) is lower in energy than the 2p orbital. For n = 3, two electrons on average are farther apart in a 3s orbital than in a 3p orbital, and two electrons in a 3p orbital are farther apart than if they are in a 3d orbital. So, the 3s orbital is lower in energy than the 3p orbitals, which are lower in energy than the 3d orbitals. However, the 3s orbital is higher in energy than the 2s orbital. On average electrons in a 3s orbital are farther from the nucleus because the 3s orbital is larger than the 2s orbital (see Figures 10.2, 10.5, and 10.6), and therefore have a weaker attractive interaction with the nucleus. Less attractive interaction results in a higher energy. The attraction to the nucleus binds the electron to the nucleus. The sign convention is that the stronger the binding, the lower the energy. The electron falls into the attractive well of the positively charged nucleus. The stronger the attraction, the deeper the electron is in the well. It will take more energy to remove the electron from the well, that is, pull it away from the nucleus.


For a given principal quantum number n, the order of the energy is ns < np < nd < nf. For the same type of orbital, the larger the n the higher the energy. The important feature of many electron atoms is that the energy depends on two quantum numbers, n and ll is the angular momentum quantum number that determines the shape of the orbital. Figure 11.1 is the energy level diagram for many electron atoms. For n = 1, there is only one type of orbital, l = 0, an s orbital. So the 1s orbital has the lowest energy level. For n = 2, l can be 0 or 1. The l values give rise to the 2s orbital and the three different 2p orbitals. With l = 1, there are three possible values of m, m = 1, 0, -1. This is the same as in hydrogen. The big difference is that for many electron atoms, the 2s orbital is lower in energy than the 2p orbitals, as shown in Figure 11.1. For n = 3, there is the 3s orbital, the 3p orbitals, and the 3d orbitals. As can be seen in Figure 11.1, the 3s orbital is below (lower in energy) the 3p orbitals, which are below the 3d orbitals.

A very important aspect of the ordering of the energy levels is that energy levels with different n quantum numbers are interspersed. Although the 3d orbitals are above the 3p orbitals, the 4s orbital energy is actually below that of the 3d orbitals (see Figure 11.1). The ordering of the orbitals is also shown in Figure 11.1. We see that the energy levels go 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, and so on. As discussed below, switching the order between the 4s and the 3d gives rise to what is called the first transition series, and switching the 5s and the 4d gives rise to the second transition series. The ordering is very important in determining the properties of various atoms. The switches in the order and the meaning of the transition series will become clear as we discuss the Periodic Table of the Elements. However, first we need to discuss how to “put” the electrons into the energy levels shown in Figure 11.1.


FIGURE 11.1. Energy level diagram for atoms with many electrons. The spacings between the levels are not to scale. The energy depends on the principal quantum number, n, and the angular momentum quantum number, l, in contrast to the hydrogen atom (Figure 10.1), where the energy only depends on n. For n = 4, there is a single s orbital (l = 0), three different p orbitals (l = 1), five different d orbitals (l = 2), and seven different f orbitals (l = 3).


The hydrogen atom has a nucleus with charge +1 and a single negative electron. The helium atom has a nucleus with charge +2 and two negative electrons. Next comes the lithium atom (symbol Li) with a +3 charge on the nucleus (atomic number 3) and three negative electrons, which is followed by beryllium (Be) with a +4 nucleus and four negative electrons, and so on. The question is if we have an atom with a certain number of electrons, like beryllium with four, which energy levels do these four electrons go into? For hydrogen, the lowest energy state is the one in which the single electron is in the 1s orbital. If we excited the hydrogen 1s electron to say a 2p state (adding energy by absorbing light or with an electrical arc), it will fall back to the lowest energy state and conserve energy by emitting a photon. Such photon emission from the various energy levels of the hydrogen atom gives rise to its line spectrum discussed in Chapters 9 and 10. But it is not clear what to do when there is more than one electron. Should the four electrons of beryllium all go in the 1s orbital? It turns out that this is impossible.

Quantum theory, confirmed by countless experiments, has given us three rules that tell us how to place the electrons into the energy levels (Figure 11.1) to obtain the configuration of electrons for the various atoms. We use what is called the Aufbau procedure, that is, the build-up procedure. The three rules tell us how to place the electrons in the energy levels in the correct order to represent atoms. We will build up the atoms and construct the periodic table by “putting” more and more electrons for bigger and bigger atoms into the proper energy levels. Many properties of atoms, their tendency to gain or lose electrons to form ions, and the number of chemical bounds they form will be understandable from this Aufbau procedure, which gives rise to the form of the Periodic Table.

Rule 1—the Pauli Exclusion Principle

Rule 1 is the Pauli Exclusion Principle. It states that no two electrons in an atom (or molecule) can have all four quantum numbers identical. There are four quantum numbers, n, l, m, and s. For hydrogen we only used the first three, but now s is important. s can only have two values, s = +1/2 or -1/2. Therefore, a given orbital defined by the quantum numbers n, l, m can have at most two electrons in it. One of the electrons will have s = +1/2 and one will have s = -1/2. For example, the 1s orbital has n = l, l = 0, m = 0, and s = +1/2 or -1/2. Therefore, two electrons can go into the 1s orbital, one with “spin” +1/2 and one with spin -1/2. For the 2p orbitals, n = 2, l = 1, m = 1, 0, -1 and s = +1/2 or -1/2. The orbitals are px, py, and pz (see Figure 10.7). Each of these can have two electrons in it, one with s = +1/2 and the other must have s = - 1/2. Therefore, there can be a total of six 2p electrons, two in each of the three orbitals. 3d orbitals have quantum numbers n = 3, l = 2, m = 2, 1, 0, -1, -2, and s = +1/2 or -1/2. There are five 3d orbitals, and two electrons can go in each (s = +1/2 or -1/ 2) for a total of 10 d electrons, two in each of five orbitals. Finally, there are seven 4f orbitals with quantum numbers, n = 4, l = 3, m = 3, 2, 1, 0, -1, -2, -3, and s = +1/2 or -1/2. The result is a total of 14 f electrons, two in each of seven orbitals.

When two electrons are in a single orbital, the spins are said to be paired. An electron in an orbital (energy level) is represented by an arrow (see Figure 11.2). The spin quantum number s = +1/2 is represented by an arrow pointing up. The spin quantum number s = -1/2 is represented by an arrow pointing down. In any single orbital there can be at most one up arrow and one down arrow.

Rule 2—Lowest Energy First but Don’t Violate the Pauli Principle

Rule 2 is the orbitals are filled with electrons in order of increasing energy. Electrons are placed in the lowest possible energy level first, but the Pauli Principle cannot be violated. So for the helium atom (He), both electrons can go in the 1s energy level, one with spin up (s = +1/2) and one with spin down (s = -1/2). Three of the quantum numbers are the same, but s is different, so the Pauli Principle is not violated. Li is the next largest atom with three electrons. The third electron cannot go in the 1s level because it would have all four quantum numbers, n, l, m, and s, the same as one of the other two electrons. So, the third electron must go into a higher energy level, the 2s orbital. The 2s is the lowest possible level for the third electron. Therefore, rule 2 dictates it will go there.


FIGURE 11.2. Left-hand side: an electron represented by an arrow in an orbital. Right-hand side: two electrons in the same orbital. The s quantum numbers must be +1/2 and -1/2, represented by an up arrow and a down arrow, to obey the Pauli Exclusion principle. The spins are said to be paired.

Rule 3—Hund’s Rule: Don’t Pair Spins If Possible Without Violating Rules 1 and 2

Rule 3 is called Hund’s Rule. Hund’s Rule states that electrons remain unpaired if possible when filling orbitals of identical energy. Figure 11.3 illustrates Hund’s Rule using the 2p orbitals as an example. The first electron, labeled 1 in the figure, is placed in the 2px orbital. This choice is arbitrary since all three 2p orbitals have the same energy. According to Hund’s Rule, the second electron will go into one of the other two 2p orbitals, which have the same energy, so that the spins are not paired. Here it is placed in the 2py orbital. The third electron must go in the 2pz orbital, which is the only choice that obeys Hund’s Rule as well as Rules 1 and 2. Finally, the fourth electron pairs with one of the other electrons. As shown, it is in the 2px. It must be spin down to obey the Pauli Principle, Rule 1.


FIGURE 11.3. Illustration of Hund’s Rule. When filling the 2p orbitals, electron 1 is placed in 2px, electron 2 in 2py, and electron 3 in 2pz. These are all spin up. Electron 4 will have to have its spin down, that is, pair, to avoid violating the Pauli Principle.

Hund’s Rule comes about because it gives electron configurations with the lowest possible energy. Putting two electrons in two different 2p orbitals keeps them further apart on average than putting them in the same orbital. The energy is lowered because keeping the electrons further apart reduces electron-electron repulsion. So what Hund’s Rule says in effect is to put electrons in different orbitals if possible. While the energy reduction associated with keeping the electrons unpaired is significant, the amount the energy is lowered is not large. Therefore, it is better to pair electron 4 in the 2px than to put it unpaired in the next higher energy orbital, the 3s.


We have laid down the rules for putting electrons in the energy levels shown in Figure 11.1. Now we will use these rules to understand many properties of atoms and the Periodic Table of Elements. In addition, these same rules will be very important in our discussion of molecules presented in subsequent chapters. But first we need to introduce the Periodic Table shown on the next page.

The Periodic Table has one box for each element. The box has the symbol for the element, as well as its atomic number. The atomic number is the number of positively charged protons in the nucleus. For a neutral atom (not a positively or negatively charged ion), the atomic number is also the number of negatively charged electrons. The form of the Periodic Table will be explained in detail below. In the upper left corner is hydrogen, with symbol H and atomic number 1. In the upper right corner is helium, with symbol He and atomic number 2. Below hydrogen is lithium, with symbol Li and atomic number 3. Many of the symbols are just abbreviations for the names. But this is not always true. For example, lead is element 82 and has the symbol, Pb. Pb derives from the Latin word for lead, plumbum. Because it is not always obvious from the symbol what the name of the element is, Table 11.1 gives the element names, their symbols, and their atomic numbers. The table is alphabetical by the element name. If you have the symbol but don’t know the name, move down the symbol column until you find the one you want.

The Periodic Table (Figure 11.4) is coded for metals (white), semimetals (semiconductors, dark gray), and nonmetals (light gray). The semimetals are a band between the metals (most of the elements) and the nonmetals, which are in the upper right portion of the table. At the bottom of the table are two strips of elements called the Lanthanide series and the Actinide series. The Lanthanide series, usually referred to as the Lanthanides, begins with the element La, lanthanum, and the Actinides begins with the element Ac, actinium. These two strips go in the gap indicated in the table. These two series of atoms, which involve the f orbitals, are placed below the rest so that the table will not be too wide.


FIGURE 11.4. The Periodic Table of Elements.

Before reviewing the properties of the elements, we will quickly go through the first two rows of the Periodic Table to get a feel for the layout and to understand what a “closed shell” electron configuration is. Then we will come back and use the table to understand properties of the elements.

The Periodic Table Layout

Referring to the energy level diagram (Figure 11.1) and the three rules for placing electrons in the energy levels, hydrogen (symbol H, atomic number 1) has one electron in the 1s orbital from the rule, lowest energy first without violating the Pauli Principle. H is in the upper left corner of the Periodic Table. It is the first element in row 1. The next element is helium (He, 2). It has two electrons in the 1s orbital with opposite spins (arrow up and arrow down, as shown in Figure 11.2). This configuration obeys the Pauli Principle and the lowest energy first rule, which overrides Hund’s Rule because it would take too much energy to put the second helium electron in the 2s energy level (see Figure 11.1). He is in the upper right corner of the Periodic Table; it completes the first row. The first row has the two elements, H and He, with electrons in the n = 1 level. The rows are also referred to as shells. Helium completes the first shell. We say that He has a closed shell configuration because it is the largest element with n = 1.


TABLE 11.1. List of the Elements—Alphabetical by Element

The next element is lithium (Li, 3). It has three electrons. The first two electrons go into the 1s energy level obeying the lowest energy first rule. The third electron cannot go into the 1s orbital because that would violate the Pauli Principle. So the third electron goes in the 2s orbital. Li is below H in the Periodic Table. H is the first element with an electron in the n = 1 shell. Li is the first element in the second row, the n = 2 shell. The next element is beryllium (Be, 4). The fourth electron also goes into the 2s orbital. This is the lowest energy state, and it does not violate the Pauli Principle. The next element is boron (B, 5) with five electrons. The fifth electron cannot go in the 2s orbital because that would violate the Pauli Principle, which states that no more than two electrons can go into a single orbital and those two must have opposite spins (spin quantum number, s = +1/2 and s = -1/2). So, the fifth electron goes into a 2p orbital. It doesn’t matter which 2p orbital. Following Figure 11.3, we will put it in the 2px orbital. There is a gap in the table between Be and B. The reason for this will be clear when we discuss the fourth row below. The next element is carbon (C, 6) with six electrons. Now Hund’s Rule comes into play, and we put the sixth electron into the 2py orbital following the layout of Figure 11.3. Nitrogen is next (N, 7). Following Hund’s Rule, the seventh electron of N goes into the 2pz orbital so none of the electrons in the p orbitals are paired. Oxygen (O, 8) has eight electrons. The eighth electron must pair because the first seven electrons put two electrons in the 1s, two electrons in the 2s, and one electron in each of the 2p orbitals. To avoid spin pairing requires putting the eighth electron in the 3s orbital, which is much higher energy. So as in Figure 11.3, the eighth electron goes in the 2px orbital. Fluorine (F, 9), has its ninth electron go into the 2py orbital. Finally, Neon (Ne, 10) completes the n = 2 row or shell with 10 electrons. The 10th electron goes in the 2pz orbital.

Closed Shell Configurations

The electron configuration for neon is shown in Figure 11.5. No additional electrons can go in the second shell (n = 2 orbitals) without violating the Pauli Principle. As will be discussed, the elements, He, Ne, Ar, Kr, etc., that run down the last column on the right-hand side of the Periodic Table are special. These elements are called the noble gases. They all have closed shells, that is, the next element with one more electron goes into an orbital with the n quantum number one unit larger, which is substantially higher in energy.


FIGURE 11.5. The electron configuration for neon (Ne, 10). The second shell is complete.

Atoms Want to Form Closed Shell Configurations

We are now ready to use the energy level diagram, Figure 11.1, and the three rules for placing electrons in the energy levels to understand the structure of the Periodic Table and the properties of the atomic elements. The following chapters investigate in considerable detail what holds atoms together to make molecules. However, a great deal can be learned from an amazingly simple rule: Atoms will gain or lose electrons to obtain the nearest closed shell configuration. The closed shell electron configurations are the configurations of the noble gases that comprise the right-hand column of the Periodic Table. A closed shell configuration is particularly stable. The noble gases, also called the inert gases, have the closed shell configuration and are essentially chemically inert. The noble gases with small atomic numbers, helium, neon, and argon, do not form chemical compounds at all. The higher atomic number noble gases can be forced to form a small number of compounds under specialized conditions. Atoms other than the noble gases change in ways so that they achieve a stable closed shell electron configuration.

There are two ways that an atom can change the number of electrons it has to achieve a closed shell configuration. The first is to become a positive ion (cation) or negative ion (anion). The atom gives up one or more electrons and becomes positively charged (cation), or the atom takes on extra electrons, and becomes negatively charged (anion). The other is for an atom to share electrons with one or more other atoms. When two or more atoms share electrons, it is as if each atom has the electrons it needs. So an atom with fewer electrons than the number needed for the next closed shell configuration obtains the correct number, but so do the other atoms that are involved in the sharing. When atoms share electrons to get to the next closed shell number of electrons, the sharing holds the atoms together. The sharing makes the energy of the combined atoms lower than the energies of the individual open shell atoms. The lowering of the energy bonds the atoms together. This type of chemical bond is called a covalent bond. Covalent bonds are responsible for most of chemistry. The detailed nature of the covalent bond is presented for the simplest molecule, the hydrogen molecule in Chapter 12, and more complex molecules are discussed in subsequent chapters.

The Properties of Atoms

To begin our discussion of the properties of atoms based on the Periodic Table, we start with hydrogen. As usual, hydrogen is special because it only has one electron and is the first element in the Periodic Table. For the first row of the periodic table, helium has a closed shell with two electrons in the 1s orbital. Hydrogen can obtain the helium closed shell configuration by sharing with another atom to pick up an electron. For example, one H atom can share electrons with a second H atom, to form the hydrogen molecule. The symbol for the hydrogen molecule is H2. The subscript tells how many of a given type of atom are in a molecule. Because of the sharing, each H atom feels as if it has two electrons, the helium closed shell configuration. As we will see, hydrogen can form other molecules, but because it only needs one electron to get to the helium closed shell configuration, it only makes one chemical bond. Helium has the closed shell. It does not make any chemical bonds. There are no molecules with a helium atom in them. Exactly why this is true is described in detail in Chapter 12. Helium completes the first shell.

The next atom is lithium, Li, which is directly below H on the periodic table. Li can obtain the helium closed shell configuration by giving up an electron. Therefore, Li forms +1 ions, Li+1. A solid piece of Li is a metal. Metals can conduct electricity, which means electrons can move easily from one atom to another. The nature of metals and electrical conductivity will be discussed in Chapter 19. Metals have the property that as single atoms they can easily give up one or more electrons. The electron Li loses has to go somewhere. It will go to another atom that wants an electron to form a negative ion. So to form Li+1, Li needs a partner (see the discussion below when we get to the other side of the Periodic Table). The next element is beryllium. Beryllium will give up two electrons to go back to the He closed shell configuration. Therefore, Be will form +2 ions, Be+2. Because Be can readily give up electrons, solid beryllium is a metal. The next element is boron. Boron can lose three electrons to go back to the He closed shell configuration. Therefore, it forms +3 ions, and it is a metal.

Now things change. The next element is carbon. Carbon would have to give up four electrons to go back to the He configuration, but it can also gain four electrons to go to the next closed shell configuration, that of neon. As shown in Figure 11.5, Ne has a closed shell configuration, with the second shell filled. It has two electrons in the 1s orbital and then has the n = 2 shell filled with two electrons in the 2s and six electrons in the three 2p orbitals. Rather than losing so many electrons to go back to the He configuration, C goes forward to the Ne configuration, picking up four electrons by making four covalent bonds. For example, methane (natural gas) is the molecule CH4. Each H is bonded to the central C. The carbon shares four electrons, one from each of the hydrogens, so C obtains the Ne closed shell configuration by sharing four electrons with the four H atoms. Each H shares one electron with the C, so each H picks up one electron to have the He closed shell configuration. This is very important. Through covalent bonds (electrons sharing), each atom obtains a closed shell configuration. Another exceedingly important fact is that C always makes four bonds because it needs to share four electrons to get to the Ne configuration. This fact is fundamental to organic chemistry and to the chemistry of life. The bonding and chemistry of carbon will be discussed extensively in subsequent chapters

The next element is nitrogen. N needs three electrons to get to the Ne configuration, so it makes three covalent bonds. For example, it will combine with H to make NH3, which is ammonium. Oxygen needs two electrons to get to the Ne closed shell configuration, so it forms two bonds and, for example, makes H2O, water. So from these simple considerations we can understand the sequence of compounds, CH4, NH3, and H2O. Bonding involving C, N, and O will be discussed in later chapters to understand molecules involving these atoms, but they will always make 4, 3, and 2 bonds, respectively.

The next atom is fluorine. Fluorine is only one electron away from the Ne closed shell. It only needs one electron to obtain the Ne configuration. It has such a strong affinity for an electron that it tends to form the negative ion F-1by picking up an electron. The electron has to come from somewhere, and F forms what are generically called salts. For example, LiF is a white crystalline solid. In the crystal, an Li that wants to give up an electron to obtain the He configuration gives its electron to an F. The result is that an LiF crystal is composed of Li+1 ions and F-1 ions. The Li+1 ions have the He closed shell configuration, and the F-1 ions have the Ne closed shell configuration. LiF crystals, like all salts, dissolve readily in water. The crystal is held together by electrostatic interactions. The positive and negative ions attract each other. They are arranged in the crystal in such a way that the attractive interactions among cations and anions overcome the repulsive interactions of the cations with other cations and the anions with other anions. Water can surround both positive and negative ions in a way that makes the energy of the total system, water surrounding cations and anions, lower than that of an LiF crystal sitting in water. This is called solvation. Water can solvate ions, so ionic crystals like LiF dissolve in water. Solvation is discussed in Chapter 15.

F will form salts with atoms on the left side of the Periodic Table, which want to give up electrons to obtain a closed shell configuration. In LiF, F gains an electron and Li loses an electron. F can also obtain the closed shell Ne configuration by making covalent bonds under some circumstances. As discussed below, it can combine with sulfur (S) to form the compound, SF2.

After F comes Ne in the periodic table. It has a closed shell (see Figure 11.5). Ne does not want to gain or lose electrons. It does not form chemical compounds. Ne completes the second row of the Periodic Table. After Ne is sodium. Sodium is one electron (3s) past the Ne configuration. Like Li directly above it, Na will readily give up an electron to form the cation, Na+1. It does this to obtain the Ne configuration. Solid sodium is a metal that can conduct electricity (electrons) because its 3s electron is not tightly bound. Like LiF, NaF is a salt that will readily dissolve in water. Next comes magnesium. Mg will give up two electrons to obtain the Ne closed shell configuration, forming Mg+2 ions. It is a metal that conducts electricity because it can readily give up its two 2s electrons. It will make salts of the form, for example, MgF2. This means the crystal has two fluorine anions for every magnesium +2 cation. MgF2 will readily dissolve in water. After Mg comes aluminum. Solid Al is a metal. Al will form Al+3 cations.

As with carbon in the second row, things change with silicon. Si will make four covalent bonds to share (effectively gain) four electrons to obtain the argon closed shell configuration (see the Periodic Table). For example, it will form SiH4. Phosphorous will make three covalent bonds to obtain the Ar configuration, for example, PH3, and S will make two covalent bonds to get to the Ar closed shell configuration. It will form the compound H2S, which is hydrogen sulfide, the very smelly and poisonous gas that gives rotten eggs their smell. As mentioned above, S can also make covalent bonds with F, to form SF2. After S comes chlorine. Like F, which only needs one electron to obtain the Ne closed shell configuration, Cl only needs one electron to obtain the Ar closed shell configuration, so it tends to form Cl-1 by gaining an electron. All of the elements in the column next to the noble gases, the second column from the right in the Periodic Table, form -1 anions. These elements (F, Cl, Br, I, At) are called the halogens. This brings us to common table salt, sodium chloride, NaCl, which is a crystalline solid composed of Na+1 and Cl-1. Like LiF, NaCl can dissolve in water because the cations and anions can be solvated by the H2O molecules. This is in contrast to methane, CH4, which does not dissolve in water. The carbon and the hydrogens close their shells by sharing electrons with each other to form covalent bonds. If methane separates into pieces, the atoms will no longer have closed shells. This is different than an NaCl crystal, which can come apart into Na+1 and Cl-1. Both the cation and anion have closed shells. Molecules that are only composed of carbon and hydrogen, like oil, gasoline, and methane, are called hydrocarbons. They do not dissolve in water. Hydrocarbons are discussed in Chapters 14, 15, and 16. After Cl is Ar. Argon has a closed shell, as shown in Figure 11.6. It has 18 electrons, two in the 1s, two in the 2s, six in the three 2p orbitals, two in the 3s, and six in the three 3p orbitals. Ar is an inert gas. It does not form chemical compounds.

Going Down a Column, Atoms Get Bigger

Going down a column in the Periodic Table, the atoms get bigger. So, Li is bigger than H, Na is bigger than Li, and so forth. Two considerations explain this. First, the additional electrons go into orbitals with a larger principal quantum number, n. H has a 1s electron, Li has a 2s electron, and Na has a 3s electron. Looking at Figures 10.2 through 10.6, which are for hydrogen, you can see that the 3s wavefunction is much bigger than the 2s, which is much bigger than the 1s. However, as we go down a column, the positive nuclear charge also increases. The nuclear charge is the same as the atomic number, which is given for each atom in the Periodic Table as well as in the List of Elements. The increased nuclear positive charge pulls the negatively charged electrons in closer. This increased attraction is not sufficient to offset the fact that going down a column puts electrons in orbitals with larger principal quantum numbers (n). The increase in size with n wins out over the increased nuclear attraction for the electrons, resulting in larger atoms as you move down a column.


FIGURE 11.6. The electron configuration for argon (Ar, 18). The third row is complete.

Going Left to Right Across a Row, Atoms Get Smaller

As you go along a row from left to right, the atoms get smaller. So Be is smaller than Li, B is smaller than Be, C is smaller than Be, etc. The reduction in size occurs because all of the atoms have the same principal quantum number n, but the nuclear charge increases. Again two phenomena are playing off against each other. The positive nuclear charge increases as you move to the right along a row. The increased positive charge will pull the electrons in closer to the nucleus. However, there are also more electrons. The negative electrons repel each other (electron-electron repulsion). To reduce the electron-electron repulsion, the electron cloud (probability amplitude wave) gets larger. The positive charge is at the center, pulling all of the electrons in. But the negative electron cloud is spread out around the nucleus. Speaking very classically, at a given instant, the electrons on one side of the atom don’t feel (aren’t repelled by) the electrons all the way on the other side of the atom as much as they are attracted to the nucleus at the center. So the attraction wins, and the atoms get smaller as you move along a row from left to right.

The First Transition Series

Now we are at the fourth row. After Ar, the first element in the fourth row is potassium, K. K has one 4s electron past the Ar configuration. By now it should be clear that potassium will form K+1 ions so that it can obtain the Ar closed shell configuration. Solid K is a metal that conducts electricity. The salt KCl is a small component of sea salt, which is mainly NaCl. KCl dissolves in water to give the ions K+1 and Cl-1. Next to K is calcium, Ca. Ca has two 4s electrons past the Ar configuration. It is a metal that forms Ca+2 ions, giving up its two 4s electrons to obtain the Ar closed shell configuration. It will form salts like CaCl2, which readily dissolve in water to give a calcium +2 cation and two chloride anions.

Now things change again in a big way. The energy level diagram for many electron atoms (Figure 11.1) shows that the 3d orbitals are above the 4s orbitals in energy, but they are below the 4p orbitals. As mentioned earlier in this chapter, the interposition of the 3d orbitals between the 4s and the 4p orbitals gives rise to the first transition series in the Periodic Table. There are five 3d orbitals. The Pauli Principle states that there can be at most two electrons in an orbital. Then there can be 10 electrons in the five 3d orbitals, resulting in the 10 transition metals, scandium through zinc (see the Periodic Table). So after Ca come 10 elements that arise from filling the 3d orbitals. All of these are metals. Many of them are very common metals that we are familiar with in everyday life, such as iron (Fe), copper (Cu), nickel (Ni), zinc (Zn), and chromium (Cr). They can readily form ions. The first two elements in a row, such as K and Ca or Na and Mg, always form cations with a particular charge, +1 for the first column (Na+1 and K+1) and +2 for the second column (Mg+2 and Ca+2). However, the transition metals can form a variety of cations. They are said to have various oxidation states. When a metal loses an electron it is said to be oxidized. The oxidation state is the number of electrons it loses.

Consider iron. It can form the oxidation states +2 and +3, that is, it forms the cations Fe+2 and Fe+3. Fe+2 is readily understandable. Fe can lose the two 4s electrons just like Ca to make the +2 oxidation state. In addition, Fe has six 3d electrons. Hund’s Rule says that electrons will stay unpaired if possible. Five electrons can go into one of each of the five 3d orbitals. This half-filled configuration is particularly stable. Iron is one 3d electron past the half-filled 3d orbitals, so it will readily lose a 3d electron in addition to the two 4s electrons to give an oxidation state of +3. So Fe can form salts like FeCl2 and FeCl3.

In addition to giving rise to the first transition series (first group of transition metals), the 3d electrons are involved in another important molecular phenomenon. We discussed that oxygen will form two covalent bonds (share two electrons with other atoms) to obtain the Ne configuration. An example is water, H2O. Sulfur, which is directly below oxygen, forms H2S, analogous to H2O. However, it can also form SF6 through involvement of the 3d orbitals, which are close in energy to the 3p orbitals. There is no equivalent for oxygen because the first set of d orbitals, the 3d’s, are much higher in energy than the 2s and 2p orbitals that are involved in bonding in the second row of the Periodic Table.

After the first series of transition metals are completed by filling the 3d orbitals, the next element is gallium (Ga). Ga is a metal, and like aluminum, it will form +3 ions. The configuration in which the 3d orbitals are completely filled is very stable, so Ga only forms +3 cations. The stability of the filled 3d orbitals can also be seen in zinc. Zn only forms +2 ions by losing the two 4s electrons. Following Ga are germanium (Ge), arsenic (As), and selenium (Se), which tend to form four, three, and two covalent bonds, respectively, to obtain the krypton (Kr) closed shell configuration. Like the elements immediately above Ge, As, and Se, additional bonds can be formed by involving the 4d electrons, which are very close in energy to the 4p orbitals. The next element is bromine, which is a halogen, and forms a -1 anion to obtain the Kr closed shell configuration. Finally, the row ends with krypton, which has a closed shell.

Larger Atoms and the Lanthanides and Actinides

The elements in the fifth row of the Periodic Table follow the same trends as those in the fourth row. The fifth row has the second series of transition metals. The elements in the sixth and seventh rows behave like those in the fourth and fifth rows except that they also have the lanthanides (first inner transition series) and actinides (second inner transition series). These come about by filling the 4f and 5f orbitals (see the many electron atom energy level diagram, Figure 11.1). The 4f (lanthanides) and 5f (actinides) orbitals (n = 4 and 5) are spatially much smaller than the 6s and 6p and 7s and 7p orbitals (n = 6 and 7) that are filled in the sixth and seventh rows because the principal quantum numbers, n, are smaller. The outermost electrons (largest principle quantum number) determine the chemical properties of atoms, that is, how many covalent bonds they make or what types of ions they form. Therefore, the 4f and 5f orbitals do not influence the chemical properties significantly. The lanthanides begin with lanthanum (La). The 4f energy levels are very close in energy to the 5d levels (see Figure 11.1). La comes after barium (Ba), which has two electrons in the 6s orbital. La has one more electron, which is actually in a 5d orbital. After La the 4f orbitals are filled. Lutetium (Lu, element 71) begins the third transition metal series. It has two electrons in the 6s orbital, 14 electrons in the 4f orbitals, and one electron in a 5d orbital. All of the lanthanides have chemical properties that are quite similar to La and Lu. In the same manner, the actinides begin with actinium (Ac). After filling the 5f orbitals with 14 electrons, lawrencium (Lr, the manmade element 103) begins the fifth transition metal series. All of the actinides have chemical properties that are very similar to Ac and Lr.

Most Elements Are Metals

The Periodic Table is color coded (shaded in Figure 11.4), with the elements divided into metals, semimetals (semiconductors), and nonmetals (insulators). (A detailed quantum theory explanation of why materials are metals, semiconductors, or insulators is presented in Chapter 19.) The Periodic Table shows that the vast majority of elements are metals. It is easy to see why this is. The left two columns are metals because they are comprised of elements that are either one or two s electrons past the previous noble gas closed shell configuration. They can readily give up these electrons to fall back to the closed shell configuration. Therefore, in solid form, it is easy to move electrons, and the solids are electrical conductors. Adding d electrons in the transitions series doesn’t eliminate the ability of an element to give up its outermost (highest n) s electrons. The d electrons only add more electrons that can be lost under the right circumstances. Adding f electrons doesn’t change things. Therefore, in addition to the two left-hand columns of elements, all of the transition series of elements are metals, usually called the transition metals. The inner transition series (addition of f electrons) are also metal. The elements that can lose three electrons to fall back to the previous closed shell configuration, like aluminum, are also metals. All of these together comprise most of the elements. The nonmetals are the group of elements in the upper right triangle-like block of elements in the Periodic Table. Some of these are the elements that tend to form covalent bonds by sharing electrons. They do not want to give up electrons. The halogens want to gain electrons or form covalent bonds. And the noble gases, by and large, do not want to gain or lose electrons or form covalent bonds. Therefore, all of these are nonmetals. If they are solids, the atoms do not want to give up electrons, a property necessary to conduct electricity. They are insulators. The small group of elements that form a diagonal block near the right side of the Periodic Table are semimetals or semiconductors. They are between the true metals and the nonmetals. Under some circumstances, they will conduct electricity. Silicon is the most well known and most technologically important of these semiconductors. Silicon is used in all of the microelectronics in our computers and other digital devices. In Chapter 19, we will discuss the differences among metals, insulators, and semiconductors, using the ideas of molecular orbital theory, which will be introduced in Chapter 12 and expanded on in the following chapters.

In this chapter, we used the many electron energy level diagram (Figure 11.1), and the rules for filling the atomic orbitals (the Pauli Principle, lowest energy first if possible, Hund’s Rule) to discuss the Periodic Table. It was shown that very simple considerations can go a long way toward understanding the properties of the atomic elements and some aspects of chemical bond formation to make molecules. However, we did not use our ideas of quantum theory to discuss why chemical bonds should form and properties of molecules, such as their shapes, that arise from quantum considerations. We will begin the explication of the quantum theory of molecules with the simplest molecule, the hydrogen molecule H2, in Chapter 12.