Electron Configurations

SECTION 4.3 Electron Configurations Bohr s model of the atom described the possible energy states of the electron in a hydrogen atom. The energy states were deduced from observations of hydrogen s emissionline spectra, but no reason was given for the specific values. The quantum model of the atom improves on Bohr s model in several ways. One improvement is that the energy states can be derived from Schrödinger s equation, and verified by observation. Another improvement is that the quantum model describes the arrangement of electrons in atoms other than hydrogen. Key Terms electron configuration Aufbau principle Pauli exclusion principle Hund s rule noble gases noble-gas configuration The arrangement of electrons in an atom is known as the atom s electron configuration. Atoms of different elements have different numbers of electrons. Therefore, each element has a unique electron configuration. The electrons in an atom tend to be arranged such that their total energy is as small as possible. The arrangement that has the least energy for each element is called the ground-state electron configuration. READING CHECK 1. Name two ways the quantum model of the atom is an improvement over Bohr s model of the atom. Electrons fill in the lowest-energy orbitals first. Energy 6d 5f 7s 6p 5d 4f 6s 5p 4d 5s 4p 3d 4s 3p 3s 2p 2s 7s 6s 5s 4s 3s 2s 6p 5p 4p 3p 2p 6d 5d 4d 3d 5f 4f To determine the ground-state configuration of any atom, first determine the energy levels of the orbitals. The relationship between the energy levels of the orbitals is given in the diagram above. Next, place the electrons in orbitals, one by one, according to three basic rules. 1s 1s The energy of each atomic sublevel is shown on the vertical axis. Each individual box represents one orbital. Arrangement of Electrons in Atoms 107

Aufbau Principle According to the Aufbau principle, an electron occupies the lowest-energy orbital that can receive it. The 1s orbital has the lowest energy. A hydrogen atom in the ground state has an electron in this orbital. The next four sublevels are 2s, 2p, 3s, and 3p. However, the 4s sublevel has a lower energy than the 3d sublevel, so the 4s orbital is filled with electrons before any of the five 3d orbitals are filled. Pauli Exclusion Principle According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers. The principal, angular momentum, and magnetic quantum numbers specify the energy, shape, and orientation of an electron s orbital. The fourth quantum number specifies the spin of the electron. Because there are only two possible values for the spin of an electron, only two electrons can exist in the same orbital. As first stated in Section 2 of this chapter, two electrons in the same orbital must have opposite spin states. Hund s Rule According to Hund s rule, orbitals of equal energy are each occupied by one electron before any are occupied by a second electron. In addition, all electrons in orbitals with just one electron must have the same spin state. Hund s rule reflects the fact that electrons are arranged in the lowest energy state possible. Electrons are not repelled as strongly by other negatively-charged electrons if they are in different orbitals, and therefore different regions, of the atom. In this book, electrons are represented by up and down arrows, such as and. The up arrow represents the +1/2 spin state, and the down arrow represents the 1/2 spin state. TIP 1s orbital The box shows the electron configuration of a helium atom. According to the Pauli exclusion principle, this orbital can only contain two electrons and they must have opposite spin states. (a) (b) (c) The figure shows how (a) two, (b) three, and (c) four electrons fill the p sublevel of any main energy level according to Hund s rule. PRACTICE A. These boxes represent the orbitals of a sulfur atom, with 16 electrons. Draw arrows to fill these orbitals with electrons. 1s 2s 2p 2p 2p 3s 3p 3p 3p 108 CHAPTER 4

There are three ways to indicate electron configuration. Three types of notation are used to describe electron configurations. This page discusses two types of notation, and another part of this section will deal with noble-gas notation. The three notations are summarized as follows: Orbital notation represents an orbital by showing its number and letter below a horizontal line. Arrows above each line represent electrons. Electron-configuration notation eliminates the lines and arrows and represents the electrons by numbers listed to the top right of an orbital s name. Noble-gas notation uses the symbol for a noble gas in place of part of the electron-configuration notation. Electron Configurations of First Period Elements Name Symbol Orbital notation Hydrogen H 1s Helium He 1s Electron-configuration notation 1 s 1 1 s 2 Orbital Notation Orbital notation is a horizontal line with the orbital s name below and the number of electrons above. The space above the line is left blank for an unoccupied orbital. An orbital containing one electron is represented as, and an orbital containing two electrons is represented as. The table above shows the orbital notation for the elements in the first period of the periodic table: hydrogen and helium. Critical Thinking 2. Reasoning Why do you think orbital notation is rarely used for atoms with more than ten electrons? Electron-Configuration Notation Electron-configuration notation eliminates the lines and arrows of orbital notation. Instead, this notation shows the number of electrons in a sublevel by placing a number to the top right of the sublevel s designation. For example, the electron configuration for sulfur is 1 s 2 2 s 2 2 p 6 3 s 2 3 p 4. The s sublevels of the sulfur atom all contain 2 electrons. The 2p sublevel contains 6 electrons, and the 3p sublevel contains 4 electrons. The table above also shows the electron configuration notations for hydrogen and helium. Arrangement of Electrons in Atoms 109

SAMPLE PROBLEM The electron configuration of boron is 1 s 2 2 s 2 2 p 1. How many electrons are present in an atom of boron? What is the atomic number for boron? Write the orbital notation for boron. SOLUTION 1 ANALYZE Determine what information is given and unknown. Given: The electron configuration of boron is 1 s 2 2 s 2 2 p 1. Unknown: number of electrons, atomic number 2 PLAN Determine the information necessary to answer the questions. The number of electrons, which is equal to the atomic number, can be determined by adding the values in the electron configuration. The orbital notation for boron is simply another representation of the given information. 3 SOLVE Answer the questions. The number of electrons in a boron atom is 2 + 2 + 1 = 5. This is also equal to the atomic number of boron. To write the orbital notation, first draw lines to represent the orbitals. 4 CHECK YOUR WORK 1s 2s 2p Next, fill in the electrons one at a time. Complete one sublevel before beginning the next sublevel. 1s 2s } } 2p Determine if the answers make sense. The number of arrows in each orbital match the numbers to the top right of the orbital in the electron configuration. PRACTICE B. The electron configuration of nitrogen is 1 s 2 2 s 2 2 p 3. What is the atomic number of nitrogen? Write the orbital notation for nitrogen. 110 CHAPTER 4

No electron can occupy a higher energy sublevel until the energy sublevel below it is filled. The elements in the second period of the periodic table can have up to five orbitals. The 1s orbital will be filled first, followed by the 2s orbital, and then the 2p orbitals. Thus, the first element of the second period, lithium, has a configuration of 1 s 2 2 s 1. The electron occupying the 2s sublevel of a lithium atom is in the atom s highest-occupied energy level. For the first period elements, the highest-occupied energy level is n = 1. For the second period elements, the highest-occupied energy level is n = 2. In these elements, the elements in the n = 1 level are inner-shell electrons. These electrons are at an energy level below the highest-occupied energy level. The table at the bottom of the page illustrates the patterns that electron configurations follow as you move across the second period of the periodic table. Each element has the same electron configuration as the element just before it, but with the addition of one electron. The last element in the second period is neon. In this element, all of the orbitals in the 2s and 2p sublevels have been filled with two electrons. Any atom that has its s and p sublevels filled in its highest-occupied energy level is said to have an octet of electrons. An octet is a group of eight.! Remember The electrons within the same main energy level of an atom are said to be in the same electron shell. READING CHECK 3. Use the information in the other rows of the table to complete the table. Electron Configurations of Atoms of Second-Period Elements Showing Two Notations Name Symbol 1s 2s Orbital notation 2p Electronconfiguration notation Lithium Li 1 s 2 2 s 1 Beryllium Be 1 s 2 2 s 2 Boron B 1 s 2 2 s 2 2 p 1 Carbon C Nitrogen N 1 s 2 2 s 2 2 p 3 Oxygen O Fluorine F 1 s 2 2 s 2 2 p 5 Neon Ne Arrangement of Electrons in Atoms 111

Elements of the Third Period After the outer octet is filled in neon, the next electron enters the s sublevel in the n = 3 main energy level. Thus, an atom of sodium, the first element in the third period, has the electron configuration 1 s 2 2 s 2 2 p 6 3 s 1. The third period elements have two sets of inner-shell electrons, the electrons in the n = 1 and n = 2 levels, and the additional electrons are placed in the n = 3 energy level. Noble-Gas Notation The Group 18 elements in the periodic table are called the noble gases. Neon is an example of a noble gas. The first ten electrons in a sodium atom have the same configuration as a neon atom. The same is true for all the third period elements. Scientists used this fact to develop a shortened version of electron-configuration notation called noble-gas notation. The symbol for neon is enclosed in brackets and substituted for that portion of the configuration. So, [Ne] = 1 s 2 2 s 2 2 p 6, and the noble-gas notation for sodium is [Ne]3 s 1. The last element in the third period is a noble gas called argon. Argon, like neon, has an octet in its highest-occupied energy level. In fact, all noble gases other than helium have such an octet. A noble-gas configuration refers to an outer main energy level occupied, in most cases, by eight electrons. READING CHECK 4. Use the information in the other rows of the table to complete the table. Electron Configurations of Atoms of Third-Period Elements Name Symbol Atomic number Number of electrons in sublevels 1s 2s 2p 3s 3p Noble-gas notation Sodium Na 11 2 2 6 1 *[Ne]3 s 1 Magnesium Mg 12 2 2 6 2 [Ne]3 s 2 Aluminum Al 13 2 2 6 2 1 [Ne]3 s 2 3 p 1 Silicon Si 14 2 2 6 2 2 [Ne]3 s 2 3 p 2 Phosphorus P 15 [Ne]3 s 2 3 p 3 Sulfur S 16 2 2 6 2 4 Chlorine Cl 17 Argon Ar 18 [Ne]3 s 2 3 p 6 *[Ne] = 1 s 2 2 s 2 2 p 6 112 CHAPTER 4

Elements of the Fourth Period The fourth period of the periodic table contains elements in which the highest-occupied energy level is the n = 4 level. Potassium, K, is the first element in the fourth period. It has an atomic number of 19. Its first 18 electrons are placed in the same way as the 18 electrons of the argon atom. These electrons fill the 1s, 2s, 2p, 3s, and 3p sublevels. However, according to the diagram on the first page of this section, the 4s sublevel has a lower energy than the 3d sublevel. Therefore, the 19th electron fills the 4s sublevel, not the 3d sublevel. Potassium atoms have the electron configuration [Ar]4 s 1. The next element is calcium, Ca, which has the electron configuration [Ar]4 s 2 and an atomic number of 20. The next element after that is scandium, Sc, with an atomic number of 21. Its first 20 electrons are placed in the same way as the calcium atom. The 21st electron is placed at the next lowest energy sublevel, which is the 3d sublevel. 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 3d 4d 5d 6d 4f 5f Follow the diagonal arrows from the top to get the order in which atomic orbitals are filled according to the Aufbau principle. Scandium atoms have the electron configuration [Ar]3 d 1 4 s 2. Note that the 3d sublevel is written first, even though it has a higher energy than the 4s sublevel. Electron-configuration notation and noble-gas notation always show the sublevels in order from lowest to highest main energy level. The next nine elements fill the other remaining positions within the 3d sublevel. The 4p sublevel is then filled starting with gallium, Ga, element number 31. Therefore, the electron configuration of a gallium atom is [Ar]3 d 10 4 s 2 4 p 1. The diagram at the top right provides another way to remember the order in which atomic orbits are filled. Note that according to the diagram, the d sublevel for a given main energy level is never filled until the s sublevel of the next-highest main energy level is filled. READING CHECK 5. Why is the symbol [Ar] used in the electron configuration of potassium, and what does it represent? Arrangement of Electrons in Atoms 113

Electron Configuration of Atoms of Elements in the Fourth Period Number of electrons in sublevels above 2p Name Symbol Atomic number 3s 3p 3d 4s 4p Noble-gas notation Potassium K 19 2 6 1 *[Ar]4 s 1 Calcium Ca 20 2 6 2 [Ar]4 s 2 Scandium Sc 21 2 6 1 2 [Ar]3 d 1 4 s 2 Titanium Ti 22 2 6 2 2 [Ar]3 d 2 4 s 2 Vanadium V 23 2 6 3 2 [Ar]3 d 3 4 s 2 Chromium Cr 24 2 6 5 1 [Ar]3 d 5 4 s 1 Manganese Mn 25 2 6 5 2 [Ar]3 d 5 4 s 2 Iron Fe 26 2 6 6 2 Cobalt Co 27 [Ar]3 d 7 4 s 2 Nickel Ni 28 2 6 8 2 [Ar]3 d 8 4 s 2 Copper Cu 29 2 6 10 1 [Ar]3 d 10 4 s 1 Zinc Zn 30 2 6 10 2 [Ar]3 d 10 4 s 2 Gallium Ga 31 2 6 10 2 1 Germanium Ge 32 [Ar]3 d 10 4 s 2 4 p 2 Arsenic As 33 2 6 10 2 3 Selenium Se 34 [Ar]3 d 10 4 s 2 4 p 4 Bromine Br 35 Krypton Kr 36 2 6 10 2 6 [Ar]3 d 10 4 s 2 4 p 6 *[Ar] = 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 The table above shows all 18 elements in the fourth period of the periodic table. There are two exceptions to the normal rules for placing electrons in orbitals that are reflected in the table. In each case, the configuration listed has the lowest possible energy. The first exception is chromium, in which one of the electrons in the 4s orbital switches to the 3d orbital. The second exception is copper, in which the same switch occurs. There is no simple explanation for this departure from the pattern. READING CHECK 6. Use the information in the other rows of the table to complete the table. 114 CHAPTER 4

Elements of the Fifth Period The patterns seen in the first four periods of the periodic table continue with the fifth period. There are 18 elements in the fifth period. The sublevels are filled in the order 5s, 4d, and finally 5p. All of the elements in the fifth period of the periodic table have a highest-occupied energy level of n = 5. The table at the bottom of the page shows the elements in the fifth period. This table also includes configurations that differ from those predicted by the rules given earlier in this chapter. Critical Thinking 7. Explain Describe why ruthenium, Ru, does not have a noble-gas configuration. Electron Configurations of Atoms of Elements in the Fifth Period Number of electrons in sublevels above 3d Name Symbol Atomic number 4s 4p 4d 5s 5p Noble-gas notation Rubidium Rb 37 2 6 1 *[Kr]5 s 1 Strontium Sr 38 2 6 2 [Kr]5 s 2 Yttrium Y 39 2 6 1 2 [Kr]4 d 1 5 s 2 Zirconium Zr 40 2 6 2 2 [Kr]4 d 2 5 s 2 Niobium Nb 41 2 6 4 1 [Kr]4 d 4 5 s 1 Molybdenum Mo 42 2 6 5 1 [Kr]4 d 5 5 s 1 Technetium Tc 43 2 6 6 1 [Kr]4 d 6 5 s 1 Ruthenium Ru 44 2 6 7 1 [Kr]4 d 7 5 s 1 Rhodium Rh 45 2 6 8 1 [Kr]4 d 8 5 s 1 Palladium Pd 46 2 6 10 [Kr]4 d 10 Silver Ag 47 2 6 10 1 [Kr]4 d 10 5 s 1 Cadmium Cd 48 2 6 10 2 [Kr]4 d 10 5 s 2 Indium In 49 2 6 10 2 1 [Kr]4 d 10 5 s 2 5 p 1 Tin Sn 50 2 6 10 2 2 [Kr]4 d 10 5 s 2 5 p 2 Antimony Sb 51 2 6 10 2 3 [Kr]4 d 10 5 s 2 5 p 3 Tellurium Te 52 2 6 10 2 4 [Kr]4 d 10 5 s 2 5 p 4 Iodine I 53 2 6 10 2 5 [Kr]4 d 10 5 s 2 5 p 5 Xenon Xe 54 2 6 10 2 6 [Kr]4 d 10 5 s 2 5 p 6 *[Kr] = 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 10 4 s 2 4 p 6 Arrangement of Electrons in Atoms 115

SAMPLE PROBLEM Write the complete electron-configuration notation and the noble-gas notation for iron, Fe. How many electron-containing orbitals are in an atom of iron? How many of these orbitals are completely filled? How many unpaired electrons are there in an atom of iron? In what sublevel are the unpaired electrons located? SOLUTION 1 ANALYZE Determine what information is given and unknown. No information is given. The information must be deduced from the periodic table and the rules for electron configurations. 2 PLAN Determine how to answer the questions. All of the questions can be answered by referring to the electron configuration of iron or to the periodic table. 3 SOLVE Write the configurations and answer the questions. Iron is not an exception to the rules, so its configuration can be determined using the normal procedure. Iron s electron configuration can be written as 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 6 4 s 2 or [Ar]3 d 6 4 s 2 All of the s and p sublevels in the configuration are completely filled. The 3d sublevel is not filled. The notation 3 d 6 represents 3d. Each s sublevel has one orbital with electrons, each p sublevel has three orbitals with electrons, and the 3d sublevel has five orbitals with electrons. The total number of orbitals with electrons is given by 1 + 1 + 3 + 1 + 3 + 5 + 1 = 15. All of the p and s orbitals are filled, and one of the 3d orbitals is filled. So, 11 orbitals are filled. The other four 3d orbitals contain unpaired electrons. 4 CHECK YOUR WORK Check to see that the answer makes sense. The atomic number of iron is 26. The complete electron configuration of iron contains 26 electrons because 2 + 2 + 6 + 2 + 6 + 6 + 2 = 26. 116 CHAPTER 4

PRACTICE C. Write both the complete electron-configuration notation and the noble-gas notation for iodine, I. How many inner-shell electrons are in the configuration? How many orbitals contain electrons? How many orbitals are completely filled? How many unpaired electrons are in the configuration? D. Write the noble-gas notation for tin, Sn. How many unpaired electrons are in the configuration? How many d orbitals contain electrons? What fourth-period element has atoms with the same number of electrons in its highest-occupied energy level? E. Write the complete electron configuration for the element with atomic number 18. How many orbitals are completely filled? What is the name of this element? Arrangement of Electrons in Atoms 117

Elements of the Sixth Period The sixth period of the periodic table contains 32 elements. It is much longer than the periods that precede it in the periodic table, because an f sublevel fills with electrons in this period. All of the elements in this period have a highest-occupied energy level of n = 6. The first element of the sixth period is cesium, Cs. It has the same electron configuration as the noble gas xenon, plus one electron in the 6s orbital. The next element, barium, Ba, has a 6s orbital that is completely filled. Lanthanum, La, has one electron in the 5d orbital. In the next 13 elements, listed in the lanthanide series on the periodic table, electrons are added to the 4f orbital. Because the 4f and 5d orbitals are very close in energy, there are many deviations from the rules covered early in this section. The last six elements in the period fill the 6p orbital. Radon, a noble gas, has an octet of electrons in the n = 6 energy level. The seventh period of the periodic table would contain 32 elements, except that not all of the elements have been discovered. Most of the elements in this period do not exist in nature. They are created artificially in a laboratory. These artificial elements break down rapidly into other elements, which is one reason they are not found in nature. READING CHECK 9. Why do the sixth and seventh period of the periodic table have many more elements than the previous periods? The two artificially-created dark blue elements fill gaps in the periodic table. The other highlighted elements are artificially-created and extend the periodic table beyond uranium, element 92. 118 CHAPTER 4

SECTION 4.3 REVIEW VOCABULARY 1. a. What is an atom s electron configuration? b. What three principles guide the electron configuration of an atom? REVIEW 2. What three methods are used to represent the arrangement of electrons in atoms? 3. What is an octet of electrons? Which elements contain an octet of electrons? 4. Identify the elements having the following electron configurations: a. 1 s 2 2 s 2 2 p 6 3 s 2 3 p 3 b. [Ar]4 s 1 c. contains four electrons in its third and outer main energy level Critical Thinking 5. RELATING IDEAS Write the electron configuration for the following third-period elements. a. aluminum, Al b. silicon, Si c. phosphorus, P d. sulfur, S e. chlorine, Cl f. What is the relationship between the group number of each element and the number of electrons in the outermost energy level? Arrangement of Electrons in Atoms 119

Math Tutor Weighted Averages and Atomic Mass The atomic masses listed on the periodic table are not whole numbers. Instead they are decimals that represent average atomic masses. The atomic masses are averages because most elements occur in nature as a specific mixture of isotopes. For example, 75.76% of chlorine atoms have a mass of 34.969 u, and 24.24% have a mass of 36.966 u. If the isotopes were in a 1:1 ratio, you could simply add the masses of the two isotopes together and divide by 2. However, to account for the differing abundance of the isotopes, you must calculate a weighted average. For chlorine, the weighted average is 35.45 u. The following two examples demonstrate how weighted averages are calculated. Problem-Solving TIPS To find an average atomic mass, convert the abundance of each isotope from a percentage to a decimal equivalent. Multiply each decimal equivalent with the atomic mass of each isotope. The result is the contribution of the isotope to the weighted average. Add the contributions of each isotope. The sum is the average atomic mass. SAMPLE Naturally occurring silver consists of two isotopes: 51.839% Ag -107 (106.905 093 u) and 48.161% Ag -109 (108.904 756 u). What is the average atomic mass of silver? Convert the percentages to decimals, multiply by the atomic masses, and add the results. 0.518 39 106.905 093 u 55.419 u 0.481 61 108.904 756 u + 52.450 u 107.869 u Naturally occurring magnesium consists of 78.99% Mg -24 (23.985 042 u), 10.00% Mg-25 (25.985 837 u), and 11.01% Mg -26 (25.982 593 u). What is the average atomic mass of magnesium? Convert the percentages to decimals, multiply by the masses, and add the results. 0.7899 23.985 042 u 18.95 u 0.1000 24.985 837 u 2.499 u 0.1101 25.982 593 u + 2.861 u 24.31 u Practice Problems: Chapter Review practice problem 14 120 CHAPTER 4