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Resource Manager Objectives
Section Section 5.1 Light and Quantized Energy P 11/2 sessions 1/2 block
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of light. 2. Define a quantum of energy and explain
Discovery Lab: What’s Inside?, p. 117 MiniLab: Flame Tests, p. 125 ChemLab: Line Spectra, pp. 142–143
how it is related to an energy change of matter. 3. Contrast continuous electromagnetic spectra and atomic emission spectra.
Section 5.2
4. Compare the Bohr and quantum
Quantum Theory and the Atom P 11/2 sessions 1 block
mechanical models of the atom. 5. Explain the impact of de Broglie’s wave-particle duality and the Heisenberg uncertainty principle on the modern view of electrons in atoms. 6. Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals.
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Problem-Solving Lab: How was Bohr’s atomic model able to explain the line spectrum of hydrogen? p. 130 Physics Connection, p. 131
Section 5.3
7. Apply the Pauli exclusion principle, the
Careers Using Chemistry: Spectroscopist,
Electron Configurations P 3 sessions 11/2 blocks
aufbau principle, and Hund’s rule to write electron configurations using orbital diagrams and electron configuration notation. 8. Define valence electrons and draw electron-dot structures representing an atom’s valence electrons.
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1. Compare the wave and particle models
Activities/Features
How It Works: Lasers, p. 144
CHAPTER 5 RESOURCE MANAGER
National Science Content Standards UCP.1, UCP.2; A.1, A.2; B.1, B.6; G.1, G.2, G.3
State/Local Standards 1(A), 2(B), 2(E), 3(C), 3(E), 5(A)
Reproducible Masters Study Guide for Content Mastery, pp. 25–26 L2 ChemLab and MiniLab Worksheets, pp. 17–20 L2
Transparencies Section Focus Transparency 17 L1 ELL Teaching Transparency 15 L2 ELL Math Skills P Transparency 5 L2 ELL P
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UCP.1, UCP.2; A.2; B.1, B.6; G.2, G.3
3(A), 3(C), 3(E), 5(A), 6(A)
Study Guide for Content Mastery, pp. 27–28 L2 P Laboratory Manual, pp. 33–36 L2 LS Challenge Problems, p. 5 L3
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UCP.1, UCP.2; A.1, A.2; B.1, B.6; E.2; F.6; G.2, G.3
1(A), 2(A), 2(B), 2(C), 2(D), 2(E), 3(D), 3(E), 5(A), 6(A), 8(A)
PLS Section Focus P Transparency 18 L1 P ELL LS Teaching Transparency 16 PL2 ELL
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Section Focus Transparency 19 L1 ELL Teaching LS Transparency 17 LS L2 ELL P P
P P Key to National Science Content Standards: UCP Unifying Concepts and Processes, A Science as Inquiry, B Physical Science, C Life Science, LS D Earth and Space Sciences, E Science and Technology, F Science in Personal and Social Perspectives, G History and Nature of Science
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Refer to pages 4T–5T of the Teacher Guide for an explanation of the National Science Content Standards correlations.
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Electrons in Atoms
Resource Manager Materials List ChemLab (pages 142–143) 40-W tubular light bulb, light socket with power cord, spectrum tubes (hydrogen, neon, and mercury), spectrum tube power supplies (3), Flinn C-Spectra®‚ diffraction grating, colored pencils, food coloring (red, green, blue, and yellow), 275-mL polystyrene culture flasks (4), book, water
Discovery Lab (page 117) wrapped box containing small object
MiniLab (page 125) Bunsen burner, cotton swabs (6), distilled water, lithium chloride, sodium chloride, potassium chloride, calcium chloride, strontium chloride, unknown
Demonstration (pages 136–137) spectrum tubes (hydrogen and neon), spectrum tube power supply, Flinn C-Spectra®‚ diffraction grating, colored pencils or chalk
Preparation of Solutions For a review of solution preparation, see page 46T of the Teacher Guide. There are no solutions to be prepared for the activities in this chapter.
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Assessment Resources
Additional Resources
Chapter Assessment, pp. 25–30 MindJogger Videoquizzes Alternate Assessment in the Science Classroom TestCheck Software Solutions Manual, Chapter 5 Supplemental Problems, Chapter 5 Performance Assessment in the Science Classroom Chemistry Interactive CD-ROM, Chapter 5 quiz
Spanish Resources ELL Guided Reading Audio Program, Chapter 5 ELL Cooperative Learning in the Science Classroom Lab and Safety SkillsP in the Science Classroom P Lesson Plans Block Scheduling Lesson Plans Texas Lesson Plans LS Texas Block Scheduling Lesson Plans LS
CHAPTER 5 RESOURCE MANAGER
Glencoe Technology The following multimedia for this chapter are available from Glencoe. VIDEOTAPE/DVD
CD-ROM
MindJogger Videoquizzes, Chapter 5
Chemistry: Matter and Change Flame Test, Video The Aurora, Video Atomic Emissions, Video Electrons and Energy Levels, Animation Building Atoms, Exploration
VIDEODISC Cosmic Chemistry Greenhouse Effect, Movie Albert Einstein, Still Niels Bohr, Still Atomic Theories, Movie Louis-Victor de Broglie, Still Bohr-de Broglie Hydrogen Orbits, Still
Multiple Learning Styles Look for the following icons for strategies that emphasize different learning modalities. Kinesthetic Linguistic Building a Model, p. 123; Meeting Individual Chemistry Journal, pp. 119, 122, 140; Portfolio, Needs, pp. 127, 139; Quick Demo, p. 131 p. 133 Visual-Spatial Logical-Mathematical Portfolio, p. 118; Chemistry Journal, p. 133; Meeting Individual Needs, p. 128 Reteach, p. 141 Intrapersonal English Language Learners, p. 121; Enrichment, p. 122; Meeting Individual Needs, p. 131; Chemistry Journal, p. 129
Key to Teaching Strategies L1 Level 1 activities should be appropriate for students with learning difficulties. L2 Level 2 activities should be within the ability range of all students. L3 Level 3 activities are designed for above-average students. ELL ELL activities should be within the ability range of English Language Learners. COOP LEARN Cooperative Learning activities are designed P small group work. for P P P These strategies represent student products that can be P placed into a best-work portfolio.
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Assessment Planner Portfolio Assessment Portfolio, TWE, pp. 118, 120, 133, 145 Assessment, p. 139 Performance Assessment Assessment, TWE, pp. 122, 128 MiniLab, SE, p. 125 ChemLab, SE, pp. 142-143 Discovery Lab, SE, p. 117
Knowledge Assessment Assessment, TWE, pp. 126, 134 Section Assessment, SE, pp. 126, 134, 141 Chapter Assessment, SE, pp. 146-149 Skill Assessment Assessment, TWE, p. 141 Problem-Solving Lab, TWE, p. 130 ChemLab, TWE, p. 143 Demonstration, TWE, p. 137
These strategies are useful in a block scheduling format.
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CHAPTER
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Tying to Previous Knowledge
The following themes from the National Science Education Standards are covered in this chapter. Refer to page 4T of the Teacher Guide for an explanation of the correlations. Systems, order, and organization (UCP.1) Evidence, models, and explanation (UCP.2) Form and function (UCP.5)
▲
Chapter Themes
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Point out that the vivid colors of light given off by fireworks are of different origin than colors produced by colored light bulbs or filters. Explain that energy transitions within atoms cause the distinctive colors—something that students will learn more about in the chapter.
What You’ll Learn ▲
Using the Photo
Electrons in Atoms ▲
Have students review the following concepts before studying this chapter. Chapter 4: atomic structure
5
You will compare the wave and particle models of light. You will describe how the frequency of light emitted by an atom is a unique characteristic of that atom. You will compare and contrast the Bohr and quantum mechanical models of the atom. You will express the arrangements of electrons in atoms through orbital notations, electron configurations, and electron dot structures.
Why It’s Important Why are some fireworks red, some white, and others blue? The key to understanding the chemical behavior of fireworks, and all matter, lies in understanding how electrons are arranged in atoms of each element.
Visit the Chemistry Web site at science.glencoe.com to find links about electrons and atomic structure.
The colorful display from fireworks is due to changes in the electron configurations of atoms.
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Chapter 5
DISCOVERY LAB P Purpose
Teaching Strategies
Expected Results
Students will make observations using all the senses except sight.
• Try to use objects in the box that are
Results will vary. Students should try to use senses other than sight to determine the relative size, mass, shape, and number of objects.
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Safety and Disposal Keep boxes for use next year.
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simple, but challenging. • When students are through with the lab, you may want to identity the objects, or, to demonstrate that chemists can’t always see what they are looking for, you may want to leave the object’s identity a mystery!
Analysis Answers will vary. Students will determine that observations typically rely heavily upon sight, although touch and hearing are somewhat useful.
Section 5.1
DISCOVERY LAB What's Inside?
1 Focus
t's your birthday, and there are many wrapped presents for you to open. Much of the fun is trying to figure out what's inside the package before you open it. In trying to determine the structure of the atom, chemists had a similar experience. How good are your skills of observation and deduction?
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Focus Transparency Before presenting the lesson, display Section Focus Transparency 17 on the overhead projector. Have students answer the accompanying questions using Section Focus Transparency Master 17. L1
Procedure 1. Obtain a wrapped box from your instructor. 2. Using as many observation methods as you can, and without
unwrapping or opening the box, try to figure out what the object inside the box is.
Materials a wrapped box from your instructor
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3. Record the observations you make throughout this discovery
process. Analysis
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How were you able to determine things such as size, shape, number, and composition of the object in the box? What senses did you use to make your observations? Why is it hard to figure out what type of object is in the box without actually seeing it?
Section Focus
Transpare ncy
Light and Quantized Energy aw-Hill Comp anies,
• Define a quantum of energy and explain how it is related to an energy change of matter. • Contrast continuous electromagnetic spectra and atomic emission spectra.
Vocabulary electromagnetic radiation wavelength frequency amplitude electromagnetic spectrum quantum Planck’s constant photoelectric effect photon atomic emission spectrum
Although three subatomic particles had been discovered by the early-1900s, the quest to understand the atom and its structure had really just begun. That quest continues in this chapter, as scientists pursued an understanding of how electrons were arranged within atoms. Perform the DISCOVERY LAB on this page to better understand the difficulties scientists faced in researching the unseen atom.
© Glencoe/Mc Graw-Hill, a division of the McGr
• Compare the wave and particle models of light.
Copyright
Objectives
1 2
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Resource Manager Study Guide for Content Mastery, pp. 25–26 L2 Solving Problems: A Chemistry Handbook, Section 5.1 Section Focus Transparency 17 and Master L1 ELL
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What ma kes the colors in a rainbow What ot ? her types of wave s exist?
Chemistry: Matter and Change
Section Focus Tran sparencies
The Nuclear Atom and Unanswered Questions As you learned in Chapter 4, Rutherford proposed that all of an atom’s positive charge and virtually all of its mass are concentrated in a nucleus that is surrounded by fast-moving electrons. Although his nuclear model was a major scientific development, it lacked detail about how electrons occupy the space surrounding the nucleus. In this chapter, you will learn how electrons are arranged in an atom and how that arrangement plays a role in chemical behavior. Many scientists in the early twentieth century found Rutherford’s nuclear atomic model to be fundamentally incomplete. To physicists, the model did not explain how the atom’s electrons are arranged in the space around the nucleus. Nor did it address the question of why the negatively charged electrons are not pulled into the atom’s positively charged nucleus. Chemists found Rutherford’s nuclear model lacking because it did not begin to account for the differences in chemical behavior among the various elements.
Chapter 5, Sectio n 5.1
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2 Teach Concept Development Explain that the concept that matter is made up of atoms is useful in many ways. For example, the fact that water contains two atoms of hydrogen for every atom of oxygen explains why the masses of the two elements are always in the same proportion in the compound. Point out, however, that something well beyond this concept must account for the vastly different chemical behaviors of hydrogen, oxygen, and the other chemical elements.
Pages 116–117 1(A), 3(E)
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Quick Demo Demonstrate that unlike charges attract using the following materials, which can probably be obtained from your school’s physics department: a hard rubber rod; either a piece of cat hide with the fur attached or a piece of wool; a glass rod; a piece of synthetic fabric, such as nylon. Use a Y-shaped piece of string to suspend the rubber rod horizontally from a support. Impart a negative charge to the rod by rubbing it with fur. Then, impart a positive charge to the glass rod by rubbing it with synthetic fabric. When you bring the glass rod close to the suspended rubber rod, the rubber rod will move toward the glass rod. Explain that the rods’ unlike charges cause the attraction. Point out that an atom’s positively charged nucleus exerts the same type of electrostatic P attraction for its negatively charged electrons.
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Figure 5-1 a Chlorine gas, shown here reacting vigorously with steel wool, reacts with many other atoms as well. b Argon gas fills the interior of this incandescent bulb. The nonreactive argon prevents the hot filament from oxidizing, thus extending the life of the bulb. c Solid potassium metal is submerged in oil to prevent it from reacting with air or water.
Go to the Chemistry Interactive CD-ROM to find additional resources for this chapter.
VIDEODISC Cosmic Chemistry Disc 4, Side 8 Movie: Greenhouse Effect 1:00 min Examination of this chemical phenomenon
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For example, consider the elements chlorine, argon, and potassium, which are found in consecutive order on the periodic table but have very different chemical behaviors. Atoms of chlorine, a yellow-green gas at room temperature, react readily with atoms of many other elements. Figure 5-1a shows chlorine atoms reacting with steel wool. The interaction of highly reactive chlorine atoms with the large surface area provided by the steel results in a vigorous reaction. Argon, which is used in the incandescent bulb shown in Figure 5-1b, also is a gas. Argon, however, is so unreactive that it is considered a noble gas. Potassium is a reactive metal at room temperature. In fact, as you can see in Figure 5-1c, because potassium is so reactive, it must be stored under kerosene or oil to prevent its atoms from reacting with the oxygen and water in the air. Rutherford’s nuclear atomic model could not explain why atoms of these elements behave the way they do. In the early 1900s, scientists began to unravel the puzzle of chemical behavior. They had observed that certain elements emitted visible light when heated in a flame. Analysis of the emitted light revealed that an element’s chemical behavior is related to the arrangement of the electrons in its atoms. In order for you to better understand this relationship and the nature of atomic structure, it will be helpful for you to first understand the nature of light.
Wave Nature of Light Electromagnetic radiation is a form of energy that exhibits wavelike behav-
ior as it travels through space. Visible light is a type of electromagnetic radiation. Other examples of electromagnetic radiation include visible light from the sun, microwaves that warm and cook your food, X rays that doctors and dentists use to examine bones and teeth, and waves that carry radio and television programs to your home. All waves can be described by several characteristics, a few of which you may be familiar with from everyday experience. Figure 5-2a shows a standing wave created by rhythmically moving the free end of a spring toy. Figure 5-2b illustrates several primary characteristics of all waves, wavelength, frequency, amplitude, and speed. Wavelength (represented by , the Greek letter lambda) is the shortest distance between equivalent points on a continuous wave. For example, in Figure 5-2b the wavelength is measured from crest to crest or from trough to trough. Wavelength is usually expressed in meters, centimeters, or nanometers (1 nm 1 109 m). Frequency (represented by , the Greek letter nu) is the number of waves that pass a given
Chapter 5 Electrons in Atoms
Portfolio Portfolio Classical Physics and Electrons in Atoms Visual-Spatial Have students research and explain how electrons in atoms should behave according to classical physics. Have them draw diagrams illustrating their findings. Students should include their
explanations and diagrams in their portfolios. Negatively charged electrons orbiting
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Quick Demo Wavelength
Crest Amplitude
Origin
Wavelength
a
Trough
b Figure 5-2
point per second. One hertz (Hz), the SI unit of frequency, equals one wave per second. In calculations, frequency is expressed with units of “waves per second,” 1s or (s1), where the term “waves” is understood. For example, 65 2 652 s1 652 Hz 652 waves/second s The amplitude of a wave is the wave’s height from the origin to a crest, or from the origin to a trough. To learn how lightwaves are able to form powerful laser beams, read the How It Works at the end of this chapter. All electromagnetic waves, including visible light, travel at a speed of 3.00 108 m/s in a vacuum. Because the speed of light is such an important and universal value, it is given its own symbol, c. The speed of light is the product of its wavelength () and its frequency ().
a The standing wave produced with this spring toy displays properties that are characteristic of all waves. b The primary characteristics of waves are wavelength, frequency, amplitude, and speed. What is the wavelength of the wave in centimeters?
Project the beam from a highintensity projector into the side of a large beaker of water. Darken the room and adjust the arrangement so students can see the visible portion of the electromagnetic spectrum on a wall or screen. Explain that reflection and refraction separate the component colors of white light from the projector as they pass through the beaker and water. Point out that rainbows are formed in much the same manner when the colors in sunlight separate P as they are reflected and refracted by raindrops.
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Figure Caption Questions
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Figure 5-2 What is the wavelength of the wave in centimeters?
Although the speed of all electromagnetic waves is the same, waves may have different wavelengths and frequencies. As you can see from the equation above, wavelength and frequency are inversely related; in other words, as one quantity increases, the other decreases. To better understand this relationship, examine the red and violet light waves illustrated in Figure 5-3. Although both waves travel at the speed of light, you can see that red light has a longer wavelength and lower frequency than violet light. Sunlight, which is one example of what is called white light, contains a continuous range of wavelengths and frequencies. Sunlight passing through a prism
4.5 cm
Figure 5-3 Which wave has the larger amplitude? The red wave has a larger amplitude.
Longer wavelength
Lower frequency Shorter wavelength
Higher frequency
Figure 5-3 The inverse relationship between wavelength and frequency of electromagnetic waves can be seen in these red and violet waves. As wavelength increases, frequency decreases. Wavelength and frequency do not affect the amplitude of a wave. Which wave has the larger amplitude?
5.1 Light and Quantized Energy
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CHEMISTRY JOURNAL Frequencies and Daily Living Linguistic In order to reinforce the concept of frequency, have students think of and describe at least five phenomena they encounter that recur or occur at given frequencies in their daily lives. Have them describe these P phenomena in their journals and, when possible, quantify the frequencies.
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Figure 5-4
Quick Demo Borrow a Slinky from the physics department and attach it securely to an object on one side of the room. Demonstrate wave characteristics— wavelength, frequency, and energy—by generating standing waves. Start with a half wave, showing the longest wavelength, lowest frequency, and least energy. Work up to two or two and one-half standing waves. It will be obvious that you must use more energy as the number of standing waves increases. With each increase in the number of waves, ask students what is happening to frequency and wavelength, and how energy is changing. Frequency is
increasing, wavelength is P decreasing, and energy is increasing.
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Figure Caption Question Figure 5-5 Which types of waves or rays have the highest energy?
White light is separated into a continuous spectrum when it passes through a prism.
Figure 5-5 The electromagnetic spectrum includes a wide range of wavelengths (and frequencies). Energy of the radiation increases with increasing frequency. Which types of waves or rays have the highest energy?
is separated into a continuous spectrum of colors. These are the colors of the visible spectrum. The spectrum is called continuous because there is no portion of it that does not correspond to a unique wavelength and frequency of light. You are already familiar with all of the colors of the visible spectrum from your everyday experiences. And if you have ever seen a rainbow, you have seen all of the visible colors at once. A rainbow is formed when tiny drops of water in the air disperse the white light from the sun into its component colors, producing a continuous spectrum that arches across the sky. The visible spectrum of light shown in Figure 5-4, however, comprises only a small portion of the complete electromagnetic spectrum, which is illustrated in Figure 5-5. The electromagnetic spectrum, also called the EM spectrum, encompasses all forms of electromagnetic radiation, with the only differences in the types of radiation being their frequencies and wavelengths. Note in Figure 5-4 that the short wavelengths bend more than long wavelengths as they pass through the prism, resulting in the sequence of colors red, orange, yellow, green, blue, indigo, and violet. This sequence can be remembered using the fictitious name Roy G. Biv as a memory aid. In examining the energy of the radiation shown in Figure 5-5, you should note that energy increases with increasing frequency. Thus, looking back at Figure 5-3, the violet light, with its greater frequency, has more energy than the red light. This relationship between frequency and energy will be explained in the next section.
gamma rays and X rays
Visible light
Wavelengths () in meters 3 10
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Radio
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Microwaves AM
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TV, FM
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Energy increases
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Electromagnetic Waves and Uses Have students research and discuss the many ways humans use electromagnetic waves to transmit information and carry energy from P place to place. Have them write up their findings in their portfolios.
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Because all electromagnetic waves travel at the same speed, you can use the formula c to calculate the wavelength or frequency of any wave. Example Problem 5-1 shows how this is done.
PROBLEMS Have students refer to Appendix D for complete solutions to Practice Problems. 1. 6.12 1014 s1 2. 2.61 1018 s1 3. 3.00 108 m/s 4. 3.17 m
EXAMPLE PROBLEM 5-1 Calculating Wavelength of an EM Wave Microwaves are used to transmit information. What is the wavelength of a microwave having a frequency of 3.44 109 Hz? 1. Analyze the Problem You are given the frequency of a microwave. You also know that because microwaves are part of the electromagnetic spectrum, their speed, frequency, and wavelength are related by the formula c . The value of c is a known constant. First, solve the equation for wavelength, then substitute the known values and solve. Known
Reinforcement When the people in a stadium make a “wave,” the wave travels around the stadium as individual persons move their bodies and arms up and down. Point out, however, that each person transmitting the wave remains in the same place.
Unknown
3.44 Hz c 3.00 108 m/s 109
?m
2. Solve for the Unknown Solve the equation relating the speed, frequency, and wavelength of an electromagnetic wave for wavelength (). c c/
Microwave relay antennas are used to transmit voice and data from one area to another without the use of wires or cables.
Substitute c and the microwave’s frequency, , into the equation. Note that hertz is equivalent to 1/s or s1. 3.00 108 m/s 3.44 109 s1 Divide the values to determine wavelength, , and cancel units as required. 3.00 108 m/s 8.72 102 m 3.44 109 s1 3. Evaluate the Answer The answer is correctly expressed in a unit of wavelength (m). Both of the known values in the problem are expressed with three significant figures, so the answer should have three significant figures, which it does. The value for the wavelength is within the wavelength range for microwaves shown in Figure 5-5.
Math in Chemistry Explain that when two quantities are related mathematically in such a way that the increase in one quantity is proportional to the decrease in the other quantity, the two quantities are said to be inversely proportional. Point out that the relationship c is valid only if the quantities and are inversely related.
PRACTICE PROBLEMS e! Practic
1. What is the frequency of green light, which has a wavelength of 4.90 107 m? 2. An X ray has a wavelength of 1.15 1010 m. What is its frequency? 3. What is the speed of an electromagnetic wave that has a frequency of 7.8 106 Hz?
For more practice with speed, frequency, and wavelength problems, go to Supplemental Practice Problems in Appendix A.
4. A popular radio station broadcasts with a frequency of 94.7 MHz. What is the wavelength of the broadcast? (1 MHz 106 Hz)
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M EETING I NDIVIDUAL N EEDS English Language Learners Intrapersonal Have English language learners look up and then explain the meanings of several key English words used in this section: radiation, spectrum, constant, effect, emission,Pquantum. Then ask them to use the words in a paragraph about waves. L1 ELL
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Particle Nature of Light
Assessment
While considering light as a wave does explain much of its everyday behavior, it fails to adequately describe important aspects of light’s interactions with matter. The wave model of light cannot explain why heated objects emit only certain frequencies of light at a given temperature, or why some metals emit electrons when colored light of a specific frequency shines on them. Obviously, a totally new model or a revision of the current model of light was needed to address these phenomena.
Performance Have
students develop an experiment or demonstration that illustrates the quantum concept. They might use a balance and small objects having nearly equal masses, such as paper clips. Or, they might use a graduated cylinder and small objects having nearly equal volumes, such as marbles or ball bearings. Use the Performance Task Assessment List P for Designing an Experiment in PASC, p. 23. L2
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ested students research and make a class presentation or report on the operationP of an optical pyrometer, a device that measures extremely high temperatures by the wavelengths of light emitted by the objects. L2LS Figure 5-6
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These photos illustrate the phenomenon of heated objects emitting different frequencies of light. Matter, regardless of its form, can gain or lose energy only in small “quantized” amounts.
The quantum concept The glowing light emitted by the hot objects shown in Figure 5-6 are examples of a phenomenon you have certainly seen. Iron provides another example of the phenomenon. A piece of iron appears dark gray at room temperature, glows red when heated sufficiently, and appears bluish in color at even higher temperatures. As you will learn in greater detail later on in this course, the temperature of an object is a measure of the average kinetic energy of its particles. As the iron gets hotter it possesses a greater amount of energy, and emits different colors of light. These different colors correspond to different frequencies and wavelengths. The wave model could not explain the emission of these different wavelengths of light at different temperatures. In 1900, the German physicist Max Planck (1858–1947) began searching for an explanation as he studied the light emitted from heated objects. His study of the phenomenon led him to a startling conclusion: matter can gain or lose energy only in small, specific amounts called quanta. That is, a quantum is the minimum amount of energy that can be gained or lost by an atom. Planck and other physicists of the time thought the concept of quantized energy was revolutionary—and some found it disturbing. Prior experience had led scientists to believe that energy could be absorbed and emitted in continually varying quantities, with no minimum limit to the amount. For example, think about heating a cup of water in a microwave oven. It seems that you can add any amount of thermal energy to the water by regulating the power and duration of the microwaves. Actually, the water’s temperature increases in infinitesimal steps as its molecules absorb quanta of energy. Because these steps are so small, the temperature seems to rise in a continuous, rather than a stepwise, manner. The glowing objects shown in Figure 5-6 are emitting light, which is a form of energy. Planck proposed that this emitted light energy was quantized.
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CHEMISTRY JOURNAL What’s a Quantum? Linguistic Have students research the reactions of Planck’s contemporaries to his quantum concept. Have them listPand explain the reactions of Planck’s contemporaries in their chemistry journals. L2
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Figure 5-7 Electron ejected from surface
In the photoelectric effect, light of a certain minimum frequency (energy) ejects electrons from the surface of a metal. Increasing the intensity of the incident light results in more electrons being ejected. Increasing the frequency (energy) of the incident light causes the ejected electrons to travel faster.
Beam of light Metal surface
Nuclei
Electrons
Explain to students that they might think of the light emitted by an atom as a “window into the atom.” Explain further that the chemical behaviors of the elements are related not to the number of subatomic particles in their atoms, but to the arrangement of electrons within their atoms.
Building a Model
He then went further and demonstrated mathematically that the energy of a quantum is related to the frequency of the emitted radiation by the equation
Kinesthetic Have student
Equantum h
groups build a setup that models the photoelectric effect. For example, the setup might show that impacting small magnets attached to a heavy iron object with lightweight and low-energy objects such as marshmallows will not displace the magnets. Then, the setup could show that heavier objects with greater energy displace the magnets. Have students draw the analogy between the marshmallows and low-energy photons and between the heavier objects and high-energy photons.
where E is energy, h is Planck’s constant, and is frequency. Planck’s constant has a value of 6.626 1034 J s, where J is the symbol for the joule, the SI unit of energy. Looking at the equation, you can see that the energy of radiation increases as the radiation’s frequency, , increases. This equation explains why the violet light in Figure 5-3 has greater energy than the red light. According to Planck’s theory, for a given frequency, , matter can emit or absorb energy only in whole-number multiples of h; that is, 1h, 2h, 3h, and so on. A useful analogy for this concept is that of a child building a wall of wooden blocks. The child can add to or take away height from the wall only in increments of a whole number of blocks. Partial blocks are not possible. Similarly, matter can have only certain amounts of energy—quantities of energy between these values do not exist. The photoelectric effect Scientists knew that the wave model (still very popular in spite of Planck’s proposal) could not explain a phenomenon called the photoelectric effect. In the photoelectric effect, electrons, called photoelectrons, are emitted from a metal’s surface when light of a certain frequency shines on the surface, as shown in Figure 5-7. Perhaps you’ve taken advantage of the photoelectric effect by using a calculator, such as the one shown in Figure 5-8, that is powered by photoelectric cells. Photoelectric cells in these and many other devices convert the energy of incident light into electrical energy. The mystery of the photoelectric effect concerns the frequency, and therefore color, of the incident light. The wave model predicts that given enough time, even low-energy, low-frequency light would accumulate and supply enough energy to eject photoelectrons from a metal. However, a metal will not eject photoelectrons below a specific frequency of incident light. For example, no matter how intense or how long it shines, light with a frequency less than 1.14 1015 Hz does not eject photoelectrons from silver. But even dim light having a frequency equal to or greater than 1.14 1015 Hz causes the ejection of photoelectrons from silver. In explaining the photoelectric effect, Albert Einstein proposed in 1905 that electromagnetic radiation has both wavelike and particlelike natures. That is, while a beam of light has many wavelike characteristics, it also can be thought of as a stream of tiny particles, or bundles of energy, called photons. Thus, a photon is a particle of electromagnetic radiation with no mass that carries a quantum of energy.
Concept Development
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Figure 5-8 The direct conversion of sunlight into electrical energy is a viable power source for lowpower consumption devices such as this calculator. The cost of photoelectric cells makes them impractical for large-scale power production.
5.1 Light and Quantized Energy
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VIDEODISC Cosmic Chemistry: Disc 1, Side 1 Still: Albert Einstein
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Internet Address Book Note Internet addresses that you find useful in the space below for quick reference.
Pages 120–123 3(C), 3(E), 5(A)
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Extending Planck’s idea of quantized energy, Einstein calculated that a photon’s energy depends on its frequency.
PROBLEMS Have students refer to Appendix D for complete solutions to Practice Problems. 5. a. 4.19 1013 J b. 6.29 1020 J c. 6.96 1018 J 6. a. gamma ray or X ray b. infrared c. ultraviolet
Ephoton h Further, Einstein proposed that the energy of a photon of light must have a certain minimum, or threshold, value to cause the ejection of a photoelectron. That is, for the photoelectric effect to occur a photon must possess, at a minimum, the energy required to free an electron from an atom of the metal. According to this theory, even small numbers of photons with energy above the threshold value will cause the photoelectric effect. Although Einstein was able to explain the photoelectric effect by giving electromagnetic radiation particlelike properties, it’s important to note that a dual wave-particle model of light was required.
EXAMPLE PROBLEM 5-2
3 Assess
Calculating the Energy of a Photon Tiny water drops in the air disperse the white light of the sun into a rainbow. What is the energy of a photon from the violet portion of the rainbow if it has a frequency of 7.23 1014 s1?
Check for Understanding Ask students to explain why chemists found Rutherford’s nuclear model of the atom lacking.
1. Analyze the Problem You are given the frequency of a photon of violet light. You also know that the energy of a photon is related to its frequency by the equation Ephoton h. The value of h, Planck’s constant, is known. By substituting the known values, the equation can be solved for the energy of a photon of violet light.
It did not explain or account for the differences in the chemical behavior of the elements.
Known
Unknown
7.23 1014 s1 h 6.626 1034 J s
Ephoton ? J
2. Solve for the Unknown
CD-ROM Chemistry: Matter and Change Video: Flame Test Video: The Aurora Video: Atomic Emissions
Substitute the known values for frequency and Planck’s constant into the equation relating energy of a photon and frequency. Ephoton h Sunlight bathes Earth in white light—light composed of all of the visible colors of the electromagnetic spectrum.
Ephoton (6.626 1034 J s)(7.23 1014 s1) Multiply the known values and cancel units. Ephoton (6.626 1034 J s)(7.23 1014 s1) 4.79 1019 J The energy of one photon of violet light is 4.79 1019 J. 3. Evaluate the Answer The answer is correctly expressed in a unit of energy (J). The known value for frequency has three significant figures, and the answer also is expressed with three significant figures, as it should be. As expected, the energy of a single photon of light is extremely small.
Resource Manager ChemLab and MiniLab Worksheets, p. 17 L2
Extension Begin to extend students’ understanding of wave-particle duality P by explaining that not only do waves have a particle nature, but moving particles have a wave nature, a concept students will LS learn more about in the next section.
PRACTICE PROBLEMS e! Practic
For more practice with photon energy problems, go to Supplemental Practice Problems in Appendix A.
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5. What is the energy of each of the following types of radiation? a. 6.32 1020 s1
c. 1. 05 1016 s1
b. 9.50 1013 Hz
6. Use Figure 5-5 to determine the types of radiation described in problem 5.
Chapter 5 Electrons in Atoms
M EETING I NDIVIDUAL N EEDS Gifted Have capable students research and perhaps explain to the class how astrophysicists determine what elements make up Earth’s Sun and other stars. In general, because a
star is made up of hot, glowing gases, its
emitted light can be gathered by a telescope and analyzed. From the atomic emission and absorption P spectra of the light, the elements present in the star can be determined. L3
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Atomic Emission Spectra
mini LAB P
Have you ever wondered how light is produced in the glowing tubes of neon signs? The process illustrates another phenomenon that cannot be explained by the wave model of light. The light of the neon sign is produced by passing electricity through a tube filled with neon gas. Neon atoms in the tube absorb energy and become excited. These excited and unstable atoms then release energy by emitting light. If the light emitted by the neon is passed through a glass prism, neon’s atomic emission spectrum is produced. The atomic emission spectrum of an element is the set of frequencies of the electromagnetic waves emitted by atoms of the element. Neon’s atomic emission spectrum consists of several individual lines of color, not a continuous range of colors as seen in the visible spectrum. Each element’s atomic emission spectrum is unique and can be used to determine if that element is part of an unknown compound. For example, when a platinum wire is dipped into a strontium nitrate solution and then inserted into a burner flame, the strontium atoms emit a characteristic red color. You can perform a series of flame tests yourself by doing the miniLAB below. Figure 5-9 on the following page shows an illustration of the characteristic purple-pink glow produced by excited hydrogen atoms and the visible portion of hydrogen’s emission spectrum responsible for producing the glow. Note how the line nature of hydrogen’s atomic emission spectrum differs from that of a continuous spectrum. To gain firsthand experience with types of line spectra, you can perform the CHEMLAB at the end of this chapter.
Purpose
Students will observe and record the colors of light emitted when LS certain compounds are burned in a flame. Process Skills
Classifying, comparing and contrasting, observing and inferring, predicting Safety Precautions
Remind students to use caution with the flame. Although the wet swab will not burn very easily, have a beaker of tap water set out for students to drop the hot cotton swabs into—this will decrease the fire hazard. Disposal
Swabs should be thrown in the trash. Remind students not to throw swabs into the sink. Teachers should check local regulations to determine if the chemicals used in the lab are permitted in the school trash. If they are not, waste chemicals must be sent to a landfill site approved for the disposal of chemical and hazardous wastes.
miniLAB Flame Tests Classifying When certain compounds are heated in a flame, they emit a distinctive color. The color of the emitted light can be used to identify the compound.
Materials Bunsen burner; cotton swabs (6); distilled water; crystals of lithium chloride, sodium chloride, potassium chloride, calcium chloride, strontium chloride, unknown
Flame Test Results Compound
Flame color
Lithium chloride Sodium chloride Potassium chloride Calcium chloride Strontium chloride
Teaching Strategies
Unknown
• Darken the room as much as
Procedure 1. Dip a cotton swab into the distilled water. Dip the moistened swab into the lithium chloride so that a few of the crystals stick to the cotton. Put the crystals on the swab into the flame of a Bunsen burner. Observe the color of the flame and record it in your data table. 2. Repeat step 1 for each of the metallic chlorides (sodium chloride, potassium chloride, calcium chloride, and strontium chloride). Be sure to record the color of each flame in your data table. 3. Obtain a sample of unknown crystals from your teacher. Repeat the procedure in step 1 using
1. The colors are due primarily to electron transitions of the metal atoms. The colors are characteristic of lithium, sodium, potassium, calcium, and strontium. 2. The colors are a composite of each element’s visible spectrum. 3. Answers will vary depending on the identity of the unknown sample.
Expected Results
Analysis 1. Each of the known compounds tested contains chlorine, yet each compound produced a flame of a different color. Explain why this occurred. 2. How is the atomic emission spectrum of an element related to these flame tests? 3. What is the identity of the unknown crystals? Explain how you know.
5.1 Light and Quantized Energy
Analysis
possible so that the flame colors can be seen vividly.
the unknown crystals. Record the color of the flame produced by the unknown crystals in your data table. Dispose of used cotton swabs as directed by your teacher.
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Compound
Flame color
lithium chloride
red
sodium chloride
yellow
potassium chloride
violet
calcium chloride
red-orange
strontium chloride
bright red
unknown
depends on compound
Assessment Performance Have students look at the flame color spectra using a Flinn C-Spectra or a spectroscope and relate the spectra to the elements comprising each compound. Use the Performance Task Assessment List for Analyzing the Data in PASC, p. 27. L2
Pages 124–125 1(A), 2(B), 2(E), 3(C), 3(E), 5(A)
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Reteach Reinforce the concept that red light has less energy than blue light. Explaining that you are making a solution of a fluorescent substance, prepare a solution of about 10 g fluorescein in 100 mL water in a 150 mL beaker. Turn out the room lights, and shine a flashlight’s beam through a transparent red cellophane sheet into the fluorescein solution. When you turn out the
Slit
410 434 nm nm
flashlight, the solution will not fluoresce. Then, repeat the process,
Hydrogen gas discharge tube
(nm) 400
but use a blue cellophane sheet rather than a red one. The solution will fluoresce when you turn out the light. Ask students to explain the results. The blue light waves have a higher frequency, shorter wavelength, and greater energy than the red light waves. The P solution may be flushed down the drain with water.
The atomic emission spectrum of hydrogen consists of four distinct colored lines of different frequencies. This type of spectrum is also known as a line spectrum. Which line has the highest energy?
Section
Assessment
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5.1
An atomic emission spectrum is characteristic of the element being examined and can be used to identify that element. The fact that only certain colors appear in an element’s atomic emission spectrum means that only certain specific frequencies of light are emitted. And because those emitted frequencies of light are related to energy by the formula Ephoton h, it can be concluded that only photons having certain specific energies are emitted. This conclusion was not predicted by the laws of classical physics known at that time. Scientists found atomic emission spectra puzzling because they had expected to observe the emission of a continuous series of colors and energies as excited electrons lost energy and spiraled toward the nucleus. In the next section, you will learn about the continuing development of atomic models, and how one of those models was able to account for the frequencies of the light emitted by excited atoms.
Assessment
7.
List the characteristic properties of all waves. At what speed do electromagnetic waves travel in a vacuum?
11.
Thinking Critically Explain how Einstein utilized Planck’s quantum concept in explaining the photoelectric effect.
8.
Compare the wave and particle models of light. What phenomena can only be explained by the particle model?
12.
9.
What is a quantum of energy? Explain how quanta of energy are involved in the amount of energy matter gains and loses.
Interpreting Scientific Illustrations Use Figure 5-5 and your knowledge of light to match the numbered items on the right with the lettered items on the left. The numbered items may be used more than once or not at all.
Figure Caption Question Figure 5-9 Which line has the highest energy? the violet line
450
656 nm
Figure 5-9
ChemLab 5, located at the end of the chapter, can be used at this point in the lesson.
Microwaves have longer wavelengths, lower frequencies, and lower energies than X rays. L2
486 nm
Hydrogen’s atomic emission spectrum
LS CHEMLAB
Knowledge Ask students to compare the wavelengths, frequencies, and energies of microwaves and X rays.
Prism
10.
Explain the difference between the continuous spectrum of white light and the atomic emission spectrum of an element.
longest wavelength 1. gamma rays highest frequency 2. infrared waves c. greatest energy 3. radio waves a.
b.
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Section 5.1
LS Assessment
7. speed, wavelength, frequency, and amplitude; EM waves travel at c. 8. The wave model treats light as an electromagnetic wave. The particle model treats light as being comprised of photons. The wave model could not explain the
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Chapter 5 Electrons in Atoms
photoelectric effect, the color of hot objects, and emission spectra. 9. A quantum is the minimum amount of energy that can be lost or gained by an atom. Matter loses or gains energy in multiples of the quantum. 10. A continuous spectrum contains all the visible colors; an atomic emission spectrum contains only
specific colors.
11. Einstein proposed that electromagnetic radiation has a wave-particle nature, that the energy of a photon depends on the frequency of the radiation, and that the photon’s energy is given by the formula Ephoton h. 12. a: 3, b: 1, c: 1
Quantum Theory and the Atom
Recall that hydrogen’s atomic emission spectrum is discontinuous; that is, it is made up of only certain frequencies of light. Why are elements’ atomic emission spectra discontinuous rather than continuous? Niels Bohr, a young Danish physicist working in Rutherford’s laboratory in 1913, proposed a quantum model for the hydrogen atom that seemed to answer this question. Impressively, Bohr’s model also correctly predicted the frequencies of the lines in hydrogen’s atomic emission spectrum. Energy states of hydrogen Building on Planck’s and Einstein’s concepts of quantized energy (quantized means that only certain values are allowed), Bohr proposed that the hydrogen atom has only certain allowable energy states. The lowest allowable energy state of an atom is called its ground state. When an atom gains energy, it is said to be in an excited state. And although a hydrogen atom contains only a single electron, it is capable of having many different excited states. Bohr went even further with his atomic model by relating the hydrogen atom’s energy states to the motion of the electron within the atom. Bohr suggested that the single electron in a hydrogen atom moves around the nucleus in only certain allowed circular orbits. The smaller the electron’s orbit, the lower the atom’s energy state, or energy level. Conversely, the larger the electron’s orbit, the higher the atom’s energy state, or energy level. Bohr assigned a quantum number, n, to each orbit and even calculated the orbit’s radius. For the first orbit, the one closest to the nucleus, n 1 and the orbit radius is 0.0529 nm; for the second orbit, n 2 and the orbit radius is 0.212 nm; and so on. Additional information about Bohr’s description of hydrogen’s allowable orbits and energy levels is given in Table 5-1.
1 Focus
• Compare the Bohr and quantum mechanical models of the atom.
Focus Transparency
• Explain the impact of de Broglie’s wave-particle duality and the Heisenberg uncertainty principle on the modern view of electrons in atoms.
Before presenting the lesson, display Section Focus Transparency 18 on the overhead projector. Have students answer the accompanying questions using Section Focus Transparency Master 18. L1
• Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals.
ELL
Vocabulary
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ground state de Broglie equation Heisenberg uncertainty principle quantum mechanical model of the atom atomic orbital principal quantum number principal energy level energy sublevel
Section Focus
Transpare ncy
18
Atomic O rbitals Use with
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Chapter 5, Sectio n 5.2
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Bohr Model of the Atom
Objectives
aw-Hill Comp anies,
You now know that the behavior of light can be explained only by a dual wave-particle model. Although this model was successful in accounting for several previously unexplainable phenomena, an understanding of the relationships among atomic structure, electrons, and atomic emission spectra still remained to be established.
Section 5.2
© Glencoe/Mc Graw-Hill, a division of the McGr
5.2
Copyright
Section
1
Does it tak middle ru e more energy fo ng of th r the pa inter to e ladder climb to or to th Suppose e top ru the the paint ng of th er droppe rung of e ladder? the ladde d his pa intbrush r. paintbrus La from the h from th ter, the painter top level did e dropped the paint middle rung of the sam e th brush hit the grou e ladder. From wh nd with ich Chemistry: more en Matter and ergy? Change 2
Section Focus Tran sparencies
Table 5-1 Bohr’s Description of the Hydrogen Atom Bohr atomic orbit
Quantum number
Orbit radius (nm)
Corresponding atomic energy level
First
n1
0.0529
Second
n2
Third Fourth
Relative energy
2 Teach
1
E1
Visual Learning
0.212
2
E2 4E1
n3
0.476
3
E3 9E1
n4
0.846
4
E4 16E1
Fifth
n5
1.32
5
E5 25E1
Sixth
n6
1.90
6
E6 36E1
Seventh
n7
2.59
7
E7 49E1
5.2 Quantum Theory and the Atom
Table 5-1 Ask students to examine the table’s Relative energy column and determine Bohr’s formula relating the hydrogen atom’s relative energy to the electron’s Bohr atomic orbit (n). En n2E1 L2
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Learning Disabled Kinesthetic Demonstrate the electron transitions associated with energy-level changes. Tell students that a book on the floor represents an electron in an atom’s lowest-energy orbit. Raise the book to a higher energy level (their chair). Ask if energy is required. yes Ask what happens when the book returns to the floor. Energy
is released. Explain the analogy between the book’s energy levels and an electron’s transitions between atomic orbits. Point out that the energy needed to raise an electron to a higher-energy orbit is exactly the same P as the energy released when the electron returns to its original orbit. L1 ELL
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An explanation of hydrogen’s line spectrum Bohr suggested that the hydrogen atom is in the ground state, also called the first energy level, when the electron is in the n 1 orbit. In the ground state, the atom does not radiate energy. When energy is added from an outside source, the electron moves to a higher-energy orbit such as the n 2 orbit shown in Figure 5-10a. Such an electron transition raises the atom to an excited state. When the atom is in an excited state, the electron can drop from the higher-energy orbit to a lowerenergy orbit. As a result of this transition, the atom emits a photon corresponding to the difference between the energy levels associated with the two orbits.
Assessment Performance Have students make a large copy of the hydrogen atom’s Bohr orbits (as shown in Figure 5-10b) on a piece of construction paper and tack the paper to a classroom bulletin board. Have them put a large, easily visible thumbtack in the lowest orbit to represent the orbital occupancy related to hydrogen’s lowest energy state. Then, have them move the thumbtack between the appropriate orbits to simulate the following orbit transitions and spectral lines in hydrogen’s atomic emission spectrum: violet (6→2), blue-violet (5→2), blue-green (4→2), and red (3→2). Use the Performance Task Assessment List for Model in PASC, p. 51. L2 ELL
E Ehigher-energy orbit Elower-energy orbit Ephoton = h Figure 5-10 from a higher-energy orbit to a lower-energy orbit, a photon with a specific energy is emitted. Although hydrogen has spectral lines associated with higher energy levels, only the visible, ultraviolet, and infrared series of spectral lines are shown in this diagram. b The relative energies of the electron transitions responsible for hydrogen’s four visible spectral lines are shown. Note how the energy levels become more closely spaced as n increases.
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n 6 5 4
Energy of hydrogen atom
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Visible series (Balmer)
a
a When an electron drops
n 1
n2
n 3
n4 n5 n6
Ultraviolet series (Lyman)
Infrared series (Paschen)
n7
Note that because only certain atomic energies are possible, only certain frequencies of electromagnetic radiation can be emitted. You might compare hydrogen’s seven atomic orbits to seven rungs on a ladder. A person can climb up or down the ladder only from rung to rung. Similarly, the hydrogen atom’s electron can move only from one allowable orbit to another, and therefore, can emit or absorb only certain amounts of energy. The four electron transitions that account for visible lines in hydrogen’s atomic emission spectrum are shown in Figure 5-10b. For example, electrons dropping from the third orbit to the second orbit cause the red line. Note that electron transitions from higher-energy orbits to the second orbit account for all of hydrogen’s visible lines. This series of visible lines is called the Balmer series. Other electron transitions have been measured that are not visible, such as the Lyman series (ultraviolet) in which electrons drop into the n = 1 orbit and the Paschen series (infrared) in which electrons drop into the n = 3 orbit. Figure 5-10b also shows that unlike rungs on a ladder, the hydrogen atom’s energy levels are not evenly spaced. You will be able to see in greater detail how Bohr’s atomic model was able to account for hydrogen’s line spectrum by doing the problem-solving LAB later in this chapter. Bohr’s model explained hydrogen’s observed spectral lines remarkably well. Unfortunately, however, the model failed to explain the spectrum of any other element. Moreover, Bohr’s model did not fully account for the chemical behavior of atoms. In fact, although Bohr’s idea of quantized energy levels laid the groundwork for atomic models to come, later experiments demonstrated that the Bohr model was fundamentally incorrect. The movements of electrons in atoms are not completely understood even now; however, substantial evidence indicates that electrons do not move around the nucleus in circular orbits.
Chapter 5 Electrons in Atoms
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Logical-Mathematical Ask gifted students to work through Bohr’s use of Newton’s second law (F ma), Coulomb’s constant (K), and Bohr’s own concept of quantized angular momenta to derive the
2 2
hn relationship rn 4π2Kmq2 . Then, have them use the equation to calculate the radii of the P hydrogen atom’s first four Bohr orbits. L3
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The Quantum Mechanical Model of the Atom
Quick Demo
Scientists in the mid-1920s, by then convinced that the Bohr atomic model was incorrect, formulated new and innovative explanations of how electrons are arranged in atoms. In 1924, a young French graduate student in physics named Louis de Broglie (1892–1987) proposed an idea that eventually accounted for the fixed energy levels of Bohr’s model. Electrons as waves De Broglie had been thinking that Bohr’s quantized electron orbits had characteristics similar to those of waves. For example, as Figure 5-11b shows, only multiples of half-wavelengths are possible on a plucked guitar string because the string is fixed at both ends. Similarly, de Broglie saw that only whole numbers of wavelengths are allowed in a circular orbit of fixed radius, as shown in Figure 5-11c. He also reflected on the fact that light—at one time thought to be strictly a wave phenomenon—has both wave and particle characteristics. These thoughts led de Broglie to pose a new question. If waves can have particlelike behavior, could the opposite also be true? That is, can particles of matter, including electrons, behave like waves? a
Figure 5-11 a A vibrating guitar string is constrained to vibrate between two fixed end points. b The possible vibrations of the guitar string are limited to multiples of half-wavelengths. Thus, the “quantum” of the guitar string is one-half wavelength. c The possible circular orbits of an electron are limited to whole numbers of complete wavelengths.
Have a fan rotating at high speed when students enter the classroom so that they will not have seen the fan’s blades in a stopped position. As soon as the class period begins, ask them to describe the fan’s blades. They will be able to tell the blades’ approximate length and little else. Explain that scientists experience somewhat the same situation in trying to describe electrons in atoms. The electrons move about the nucleus and appear to fill the entire volume, yet occupy very little volume themselves. Explain that due to the motion of the electrons and certain limitations in our ability to view them (as described by Heisenberg’s uncertainty principle), we are unable to simultaneously describe exactly P where the electrons are and where they are going.
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n 3 wavelengths
n1
VIDEODISC Cosmic Chemistry Disc 1, Side 1 Still: Louis-Victor de Broglie
1 half–wavelength n 5 wavelengths
n2
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Disc 1, Side 1 Still: Bohr-de Broglie Hydrogen Orbits
n3
b Vibrating guitar string Only multiples of half wavelengths allowed
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3 half–wavelengths
c Orbiting electron Only whole numbers of wavelengths allowed
5.2 Quantum Theory and the Atom
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CHEMISTRY JOURNAL
M EETING I NDIVIDUAL N EEDS English Language Learners
Gases for IR and UV
Have English language learners look up and then explain the meanings of several key English words used in this section: state (as in ground state), uncertainty, principal, level P (noun). Ask students to use each word in a sentence or a paragraph.
Intrapersonal Have students research the types of gases used to emit infrared and ultraviolet electromagnetic radiation. Have them summarize P their findings in their chemistry journals.
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problem-solving LAB P Purpose
Students will explore the relationship between electron orbit radii LS and energy states of the hydrogen atom. This relationship will then be used to explain the characteristics of spectroscopic series that result from electron transitions between orbits.
problem-solving LAB How was Bohr’s atomic model able to explain the line spectrum of hydrogen? Using Models Niels Bohr proposed that electrons must occupy specific, quantized energy levels in an atom. He derived the following equations for hydrogen’s electron orbit energies (En) and radii (rn). rn (0.529 1010 m)n2 En (2.18 1018 J)/n2
Process Skills
Constructing models, using numbers, acquiring and analyzing information, drawing conclusions, applying concepts, predicting Teaching Strategies
• Ask students to explain how the force between two magnets depends on the separation distance, and then relate this to the electric force of attraction between an electron and proton.
Where n quantum number (1, 2, 3...).
Analysis Using the orbit radii equation, calculate hydrogen’s first seven electron orbit radii and then construct a scale model of those orbits. Use a compass and a metric ruler to draw your scale model on two sheets of paper that have been taped together. (Use caution when handling sharp objects.) Using the orbit energy equation, calculate the energy of each electron orbit and record the values on your model.
The magnetic force decreases with the cube of the distance. Because of this, magnets are useful in modeling the behavior of electric force, which decreases with the square of the distance.
range of the electromagnetic spectrum and how frequency, , wavelength, , and energy, E, are related. c (c is the speed of
h mv The de Broglie equation predicts that all moving particles have wave characteristics. Why, then, you may be wondering, haven’t you noticed the wavelength of a fast-moving automobile? Using de Broglie’s equation provides an answer. An automobile moving at 25 m/s and having a mass of 910 kg has a wavelength of 2.9 1038 m—a wavelength far too small to be seen or detected, even with the most sensitive scientific instrument. By comparison, an electron moving at the same speed has the easily measured wavelength of 2.9 105 m. Subsequent experiments have proven that electrons and other moving particles do indeed have wave characteristics. Step by step, scientists such as Rutherford, Bohr, and de Broglie had been unraveling the mysteries of the atom. However, a conclusion reached by the German theoretical physicist Werner Heisenberg (1901–1976), a contemporary of de Broglie, proved to have profound implications for atomic models.
light) and E h
Thinking Critically
1. The largest radius is r7 (25.9
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1. What scale did you use to plot the orbits? How is the energy of each orbit related to its radius? 2. Draw a set of arrows for electron jumps that end at each energy level (quantum number). For example, draw a set of arrows for all transitions that end at n 1, a set of arrows for all transitions that end at n 2, and so on, up to n 7. 3. Calculate the energy released for each of the jumps in step 2, and record the values on your model. The energy released is equal to the difference in the energies of each level. 4. Each set of arrows in step 2 represents a spectral emission series. Label five of the series, from greatest energy change to least energy change, as the Lyman, Balmer, Paschen, Brackett, and Pfund series. 5. Use the energy values in step 3 to calculate the frequency of each photon emitted in each series. Record the frequencies on your model. 6. Using the electromagnetic spectrum as a guide, identify in which range (visible, ultraviolet, infrared, etc.) each series falls.
In considering this question, de Broglie knew that if an electron has wavelike motion and is restricted to circular orbits of fixed radius, the electron is allowed only certain possible wavelengths, frequencies, and energies. Developing his idea, de Broglie derived an equation for the wavelength () of a particle of mass (m) moving at velocity (v).
• Ask students to describe the full
1010 m). Thus, a scale of 1 cm 1 1010 m results in a graph about 26 cm in diameter, which will fit on the two sheets of paper. Energy increases with increasing radius. 2. See the Solutions Manual. 3. See the Solutions Manual. 4. greatest energy to least energy: Lyman, Balmer, Paschen, Brackett, and Pfund 5. See the Solutions Manual. 6. Lyman series, ultra-violet; Balmer series, visible; Paschen series, near infrared; Brackett series, middle infrared; Pfund series, far infrared
Thinking Critically
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Chapter 5 Electrons in Atoms
Assessment Skill Have the students extend the ideas presented here to make a prediction concerning the spectrum that would be emitted from hydrogenlike atoms, such as He or Li2. Or, have them predict what would happen to the continuous spectrum of light if it passed through a cell containing hydrogen gas. L2
y
Photon
y
’
Electron x
x
Speed = 0
Before collision
Figure 5-12
Photon's wavelength increases
Electron's speed increases
After collision
A photon that strikes an electron at rest alters the position and velocity of the electron. This collision illustrates the Heisenberg uncertainty principle: It is impossible to simultaneously know both the position and velocity of a particle. Note that after the collision, the photon’s wavelength is longer. How has the photon’s energy changed?
The Heisenberg Uncertainty Principle Heisenberg’s concluded that it is impossible to make any measurement on an object without disturbing the object—at least a little. Imagine trying to locate a hovering, helium-filled balloon in a completely darkened room. When you wave your hand about, you’ll locate the balloon’s position when you touch it. However, when you touch the balloon, even gently, you transfer energy to it and change its position. Of course, you could also detect the balloon’s position by turning on a flashlight. Using this method, photons of light that reflect from the balloon reach your eyes and reveal the balloon’s location. Because the balloon is much more massive than the photons, the rebounding photons have virtually no effect on the balloon’s position. Can photons of light help determine the position of an electron in an atom? As a thought experiment, imagine trying to determine the electron’s location by “bumping” it with a high-energy photon of electromagnetic radiation. Unfortunately, because such a photon has about the same energy as an electron, the interaction between the two particles changes both the wavelength of the photon and the position and velocity of the electron, as shown in Figure 5-12. In other words, the act of observing the electron produces a significant, unavoidable uncertainty in the position and motion of the electron. Heisenberg’s analysis of interactions such as those between photons and electrons led him to his historic conclusion. The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. Although scientists of the time found Heisenberg’s principle difficult to accept, it has been proven to describe the fundamental limitations on what can be observed. How important is the Heisenberg uncertainty principle? The interaction of a photon with an object such as a helium-filled balloon has so little effect on the balloon that the uncertainty in its position is too small to measure. But that’s not the case with an electron moving at 6 106 m/s near an atomic nucleus. The uncertainty in the electron’s position is at least 109 m, about ten times greater than the diameter of the entire atom!
Figure Caption Question Figure 5-12 How has the photon’s energy changed? It has decreased.
Enrichment Make a sign that says “Heisenberg May Have Slept Here.” Show it to students and ask how the uncertainty about whether or not Heisenberg slept in a given location is analogous to an electron’s position in an atom. Heisenberg’s principle states that it is fundamentally impossible to know both a particle’s motion (actually momentum) and position at the same time.
Physics CONNECTION
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eople travel thousands of miles to see the aurora borealis (the northern lights) and the aurora australis (the southern lights). Once incorrectly believed to be reflections from the polar ice fields, the auroras occur 100 to 1000 km above Earth. High-energy electrons and positive ions in the solar wind speed away from the sun at more than one million kilometers per hour. These particles become trapped in Earth’s magnetic field and follow along Earth’s magnetic field lines. The electrons interact with and transfer energy to oxygen and nitrogen atoms in the upper atmosphere. The color of the aurora depends on altitude and which atoms become excited. Oxygen emits green light up to about 250 km and red light above 250 km; nitrogen emits blue light up to about 100 km and purple/violet at higher altitudes.
Quick Demo Kinesthetic Give a heavy ball to a blindfolded student in the middle of an open space (about a 5-foot radius). Quietly, set a 50-mL, plastic graduated cylinder about 5 feet from the student. Surround the blindfolded student with a ring of other students about 10 feet distant, and instruct the student to gently roll the ball in various directions until the cylinder is located. When the ball finally
hits the cylinder, it knocks the cylinder from its original position. Then, ask the students if the information gained from rolling the ball gives the cylinder’s position after impact. The cylinder is
The Schrödinger wave equation In 1926, Austrian physicist Erwin Schrödinger (1887–1961) furthered the wave-particle theory proposed by de Broglie. Schrödinger derived an equation that treated the hydrogen atom’s electron as a wave. Remarkably, Schrödinger’s new model for the hydrogen atom seemed to apply equally well to atoms of other elements—an area in which Bohr’s model failed. The atomic model in which electrons are treated as waves is called the wave mechanical model of the atom or, more commonly, the quantum mechanical model of the atom. Like Bohr’s model,
no longer where it was before being hit with the ball. Then describe the P
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M EETING I NDIVIDUAL N EEDS Gifted Intrapersonal Have capable students investigate and report on whether quantum mechanics invalidates the laws and models of classical physics. In general, classi-
cal physics laws and models are valid approximations of the laws of quantum
mechanics. As such, they accurately describe and predict behavior at the macroscopic level. However, quantum mechanics is needed toPaccurately describe and explain atomic and subatomic behavior. L3
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Applying Chemistry
Nucleus
A photon striking an atom in an excited state stimulates it to make a transition to a lower-energy state and emit a second photon coherent with the first. Coherent means that the photons have the same associated wavelengths and are in phase (crest-tocrest and trough-to-trough). In a laser, photons from many atoms are reflected back and forth until they build to an intense, small beam— typically about 0.5 mm in diameter. Medical lasers can be engineered to produce pulses of varying wavelength, intensity, and duration. For example, ophthalmologists can reshape corneas by removing tissue with 10-ns pulses from a 193-nm wavelength argon laser. Because laser beams can be focused to such small diameters, they can be used for internal surgeries, destroying target tissue without adversely affecting surrounding tissue. And by channeling laser beams through optical fibers, doctors can perform surgeries in previously unreachable parts of the body. For example, bundles of optical fibers threaded through arteries can carry laser beams that destroy blockages.
a
b
a This electron density diagram for a hydrogen atom represents the likelihood of finding an electron at a particular point in the atom. The greater the density of dots, the greater the likelihood of finding hydrogen’s electron. b The boundary of an atom is defined as the volume that encloses a 90% probability of containing its electrons.
Because the boundary of an atomic orbital is fuzzy, the orbital does not have an exactly defined size. To overcome the inherent uncertainty about the electron’s location, chemists arbitrarily draw an orbital’s surface to contain 90% of the electron’s total probability distribution. In other words, the electron spends 90% of the time within the volume defined by the surface, and 10% of the time somewhere outside the surface. The spherical surface shown in Figure 5-13b encloses 90% of the lowest-energy orbital of hydrogen. Recall that the Bohr atomic model assigns quantum numbers to electron orbits. In a similar manner, the quantum mechanical model assigns principal quantum numbers (n) that indicate the relative sizes and energies of atomic
n = 4 (4 sublevels) n = 3 (3 sublevels) n = 2 (2 sublevels)
Students may think the letters s, p, d, and f, which represent sublevels, arbitrary and perhaps mysterious. Explain that the letters originated from descriptions of spectral lines as sharp, principal, diffuse, and fundamental.
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Hydrogen’s Atomic Orbitals
Figure 5-13
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the quantum mechanical model limits an electron’s energy to certain values. However, unlike Bohr’s model, the quantum mechanical model makes no attempt to describe the electron’s path around the nucleus. The Schrödinger wave equation is too complex to be considered here. However, each solution to the equation is known as a wave function. And most importantly, the wave function is related to the probability of finding the electron within a particular volume of space around the nucleus. Recall from your study of math that an event having a high probability is more likely to occur than one having a low probability. What does the wave function predict about the electron’s location in an atom? A three-dimensional region around the nucleus called an atomic orbital describes the electron’s probable location. You can picture an atomic orbital as a fuzzy cloud in which the density of the cloud at a given point is proportional to the probability of finding the electron at that point. Figure 5-13a illustrates the probability map, or orbital, that describes the hydrogen electron in its lowest energy state. It might be helpful to think of the probability map as a time-exposure photograph of the electron moving around the nucleus, in which each dot represents the electron’s location at an instant in time. Because the dots are so numerous near the positive nucleus, they seem to form a dense cloud that is indicative of the electron’s most probable location. However, because the cloud has no definite boundary, it also is possible that the electron might be found at a considerable distance from the nucleus.
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n = 1 (1 sublevels) Figure 5-14 Energy sublevels can be thought of as a section of seats in a theater. The rows that are higher up and farther from the stage contain more seats, just as energy levels that are farther from the nucleus contain more sublevels.
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Chapter 5 Electrons in Atoms
Internet Address Book Note Internet addresses that you find useful in the space below for quick reference.
z
orbitals. That is, as n increases, the z orbital becomes larger, the electron x spends more time farther from the nucleus, and the atom’s energy level x increases. Therefore, n specifies the atom’s major energy levels, called priny y cipal energy levels. An atom’s lowest principal energy level is assigned a prin1s orbital 2s orbital a cipal quantum number of one. When the hydrogen atom’s single electron occupies an orbital with n = 1, the atom is in z z z its ground state. Up to seven energy levels have been detected for the hydrogen atom, giving n values ranging from 1 x x x to 7. Principal energy levels contain y y energy sublevels. Principal energy y level 1 consists of a single sublevel, px py pz principal energy level 2 consists of two b sublevels, principal energy level 3 conp orbitals sists of three sublevels, and so on. To Figure 5-15 better understand the relationship between the atom’s energy levels and sublevels, picture the seats in a wedgeAtomic orbitals represent the electron probability clouds of an shaped section of a theater, as shown in Figure 5-14. As you move away from atom’s electrons. a The spherithe stage, the rows become higher and contain more seats. Similarly, the cal 1s and 2s orbitals are shown number of energy sublevels in a principal energy level increases as n increases. here. All s orbitals are spherical Sublevels are labeled s, p, d, or f according to the shapes of the atom’s in shape and increase in size orbitals. All s orbitals are spherical and all p orbitals are dumbbell shaped; with increasing principal quanhowever, not all d or f orbitals have the same shape. Each orbital may contum number. b The three dumbbell-shaped p orbitals are tain at most two electrons. The single sublevel in principal energy level 1 conoriented along the three persists of a spherical orbital called the 1s orbital. The two sublevels in principal pendicular x, y, and z axes. Each energy level 2 are designated 2s and 2p. The 2s sublevel consists of the 2s of the p orbitals related to an orbital, which is spherical like the 1s orbital but larger in size. See energy sublevel has equal Figure 5-15a. The 2p sublevel consists of three dumbbell-shaped p orbitals energy. of equal energy designated 2px, 2py, and 2pz. The subscripts x, y, and z merely designate the orientations of p orbitals along the x, y, and z coordinate axes, as shown in Figure 5-15b. Figure 5-16 Principal energy level 3 consists of three sublevels designated 3s, 3p, and Four of five equal-energy d 3d. Each d sublevel consists of five orbitals of equal energy. Four d orbitals orbitals have the same shape. have identical shapes but different orientations. However, the fifth, dz2 orbital Notice how the dxy orbital lies in is shaped and oriented differently from the other four. The shapes and orienthe plane formed by the x and y tations of the five d orbitals are illustrated in Figure 5-16. The fourth prinaxes, the dxz orbital lies in the cipal energy level (n 4) contains a fourth sublevel, called the 4f sublevel, plane formed by the x and z which consists of seven f orbitals of equal energy. axes, and so on. The dz 2 orbital has it own unique shape. z z
z
z
z y
y
y
y
x
x
x
dxy
dxz
x y
x
dyz
dx 2y 2
dz2
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Identifying Misconceptions Students may think that the hydrogen atom’s energy levels are evenly spaced. Uncover the Misconception Have students compare hydrogen’s energy levels shown in Figure 5-10b with the rungs on a ladder. Unlike the rungs on a ladder, hydrogen’s energy levels are not evenly spaced.
Demonstrate the Concept
Have students calculate and compare the ratios En/En1 from E2 through E 7. E2 /E1 4, E3/E2 2.25, E4 /E3 1.78, E5 /E4 1.56, E6 /E5 1.44, E7 /E6 1.36 Assess New Knowledge Have students use their calculated energy ratios from Demonstrate the Concept to make their own energy maps for hydrogen’s energy levels. Their energy maps will show clearly that hydrogen’s energy levels P become more closely spaced as n increases.
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3 Assess Check for Understanding Ask students to explain why higher energy levels are made up of sublevels associated with more electrons than lower energy levels. Higher energy levels are associated with larger volumes, which may contain more orbitals than smaller volumes. It is, reasonable, therefore, that more electrons may be contained in the greater number of orbitals associated with higher energy levels.
CHEMISTRY JOURNAL
Models of the Atom
Orbital Shapes
Linguistic Have students explain and trace the experimental evidence accompanying the evolution of models of the atom. Ask them to include Thomson’s plum-pudding model, Rutherford’s nuclear model, the Bohr model, and the quantum mechanical model. Have P students place their explanations in their chemistry portfolios. L2 P
Visual-Spatial Have students sketch the shapes and orientations of hydrogen’s 3s, 3p, and 3d orbitals. Have them label the P orbital sketches and include them in their chemistry journals. Pages 132–133 3(C), 3(E), 6(A)
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Table 5-2
Reteach
Hydrogen’s First Four Principal Energy Levels
Explain that an electron’s position and velocity within an atomic orbital are not known. Reiterate that at a given instant, there is a 10% probability that the electron is outside the orbital’s 90% probability surface.
Principal quantum number (n)
Sublevels (types of orbitals) present
Number of orbitals related to sublevel
1
s
1
1
2
s p
1 3
4
3
s p d
1 3 5
9
4
s p d f
1 3 5 7
16
Extension According to quantum mechanics, each electron in an atom can be described by four quantum numbers. Three of these (n, l, and ml ) are related to the probability of finding the electron at various points in space. The fourth (ms) is related to the direction of electron spin—either clockwise or counterclockwise. The principal quantum number, n, specifies the atom’s energy level associated with the electron. l specifies the energy sublevel and describes the shape of the region of space in which the electron moves. ml specifies the orientation in space of the orbital containing the electron. m s specifies the orientation of the electron’s spin axis.
Total number of orbitals related to principal energy level (n 2)
Hydrogen’s first four principal energy levels, sublevels, and related atomic orbitals are summarized in Table 5-2. Note that the maximum number of orbitals related to each principal energy level equals n2. Because each orbital may contain at most two electrons, the maximum number of electrons related to each principal energy level equals 2n2. Given the fact that a hydrogen atom contains only one electron, you might wonder how the atom can have so many energy levels, sublevels, and related atomic orbitals. At any given time, the atom’s electron can occupy just one orbital. So you can think of the other orbitals as unoccupied spaces—spaces available should the atom’s energy increase or decrease. For example, when the hydrogen atom is in the ground state, the electron occupies the 1s orbital. However, the atom may gain a quantum of energy that excites the electron to the 2s orbital, to one of the three 2p orbitals, or to another vacant orbital. You have learned a lot about electrons and quantized energy in this section: how Bohr’s orbits explained the hydrogen atom’s quantized energy states; how de Broglie’s insight led scientists to think of electrons as both particles and waves; and how Schrödinger’s wave equation predicted the existence of atomic orbitals containing electrons. In the next section, you’ll learn how the electrons are arranged in atomic orbitals of atoms having more than one electron.
Assessment Knowledge Ask students
which hydrogen energy-level transition accounts for the violet line in its emission spectrum. n 6 → n 2 L2
Section
5.2
Assessment
13.
According to the Bohr atomic model, why do atomic emission spectra contain only certain frequencies of light?
14.
Why is the wavelength of a moving soccer ball not detectable to the naked eye?
15.
What sublevels are contained in the hydrogen atom’s first four energy levels? What orbitals are related to each s sublevel and each p sublevel?
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Thinking Critically Use de Broglie’s wave-particle duality and the Heisenberg uncertainty principle to explain why the location of an electron in an atom is uncertain.
17.
Comparing and Contrasting Compare and contrast the Bohr model and quantum mechanical model of the atom.
Chapter 5 Electrons in Atoms
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Assessment
13. Because only certain atomic energies are possible, only certain frequencies of radiation can be emitted from an atom. 14. It is too small to see or detect. 15. First energy level, s; second energy level, s and p; third energy level, s,
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p, and d; fourth energy level, s, p, d, and f. Each s sublevel is related to a spherical s orbital. Each p sublevel is related to three dumbbell-shaped orbitals (px , py , and pz ). 16. An electron has wave-particle characteristics and does not have a single, definite location in space.
The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. 17. Bohr model: the electron is a particle; the hydrogen atom has only certain allowable energy
Electron Configurations
The arrangement of electrons in an atom is called the atom’s electron configuration. Because low-energy systems are more stable than high-energy systems, electrons in an atom tend to assume the arrangement that gives the atom the lowest possible energy. The most stable, lowest-energy arrangement of the electrons in atoms of each element is called the element’s ground-state electron configuration. Three rules, or principles—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—define how electrons can be arranged in an atom’s orbitals. The aufbau principle The aufbau principle states that each electron occupies the lowest energy orbital available. Therefore, your first step in determining an element’s ground-state electron configuration is learning the sequence of atomic orbitals from lowest energy to highest energy. This sequence, known as an aufbau diagram, is shown in Figure 5-17. In the diagram, each box represents an atomic orbital. Several features of the aufbau diagram stand out. • All orbitals related to an energy sublevel are of equal energy. For example, all three 2p orbitals are of equal energy. • In a multi-electron atom, the energy sublevels within a principal energy level have different energies. For example, the three 2p orbitals are of higher energy than the 2s orbital.
1 Focus
• Apply the Pauli exclusion principle, the aufbau principle, and Hund’s rule to write electron configurations using orbital diagrams and electron configuration notation.
Focus Transparency Before presenting the lesson, display Section Focus Transparency 19 on the overhead projector. Have students answer the accompanying questions using Section Focus Transparency Master 19. L1
• Define valence electrons and draw electron-dot structures representing an atom’s valence electrons.
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Vocabulary electron configuration aufbau principle Pauli exclusion principle Hund’s rule valence electron electron-dot structure
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Electron Configurat ions Use wit
h Chapte r 5, Sectio n 5.3
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Ground-State Electron Configurations
Objectives
aw-Hill Comp anies,
When you consider that atoms of the heaviest elements contain in excess of 100 electrons, that there are numerous principal energy levels and sublevels and their corresponding orbitals, and that each orbital may contain a maximum of two electrons, the idea of determining the arrangement of an atom’s electrons seems daunting. Fortunately, the arrangement of electrons in atoms follows a few very specific rules. In this section, you’ll learn these rules and their occasional exceptions.
Section 5.3
© Glencoe/Mc Graw-Hill, a division of the McGr
5.3
Copyright
Section
1
Which sea ts in the arena are likely to Imagine be in mo th re dema Which pa at center court nd? rep rt of the represen arena rep resents an atom’ ts indivi s nucleus res ents energ dual orbit . y levels? als? Which pa Chemistry: rt Matter and 2
7p 7s
Increasing energy
Orbital filling sequence
6s
6p 5p
5s
6d 5d 4d
4p
Figure 5-17
5f 4f
The aufbau diagram shows the energy of each sublevel. Each box on the diagram represents an atomic orbital. Does the 3d or 4s sublevel have greater energy?
3d
4s
Change
Section Focus Tran sparencies
2 Teach Figure Caption Question
3p
Figure 5-17 Does the 3d or 4s sublevel have the greater energy?
3s
The 3d sublevel has the greater energy.
2p 2s
Using Science Terms 1s 5.3 Electron Configurations
states. Quantum mechanical model: the electron is a waveparticle phenomenon; an electron’s energy is limited to certain values. Also, the quantum mechanical model makes no assertions regarding the electron’s path around the nucleus.
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CD-ROM Chemistry: Matter and Change Animation: Electrons and Energy Levels Exploration: Building Atoms
Explain that the name aufbau is derived from the German aufbauen, which means “to build up.”
Pages 134–135 6(A)
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CAREERS
USING
CHEMISTRY
Spectroscopist Are you interested in the composition of the materials around you? Do you wonder what stars are made of? Then consider a career as a spectroscopist.
Career Path A career as
a spectroscopist requires high school courses in chemistry, math, physics, and computer science. Career Issue Have students investigate the various types of spectroscopy and their uses.
Spectroscopy is the analysis of the characteristic spectra emitted by matter. Spectroscopists perform chemical analyses as part of many research laboratory projects, for quality control in industrial settings, and as part of forensics investigations for law enforcement agencies.
For More Information
For more information about careers in spectroscopy, students can contact Society for Applied Spectroscopy 201 B Broadway Street Frederick, MD 21701-6501
Study Guide for Content Mastery, pp. 29–30 L2 Solving Problems: A Chemistry Handbook, Section 5.3 Teaching Transparency 17 and Master L2 ELL Section Focus Transparency 19 and Master L1 ELL Laboratory Manual, P P pp. 37–40 L2
Although the aufbau principle describes the sequence in which orbitals are filled with electrons, it’s important to know that atoms are not actually built up electron by electron. The Pauli exclusion principle Each electron in an atom has an associated spin, similar to the way a top spins on its axis. Like the top, the electron is able to spin in only one of two directions. An arrow pointing up ( ) represents the electron spinning in one direction, an arrow pointing down ( ) represents the electron spinning in the opposite direction. The Pauli exclusion principle states that a maximum of two electrons may occupy a single atomic orbital, but only if the electrons have opposite spins. Austrian physicist Wolfgang Pauli proposed this principle after observing atoms in excited states. An atomic orbital containing paired electrons with opposite spins is written as .
1.
2.
3.
4.
5.
6.
Orbital Diagrams and Electron Configuration Notations
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• Orbitals related to energy sublevels within one principal energy level can overlap orbitals related to energy sublevels within another principal level. For example, the orbital related to the atom’s 4s sublevel has a lower energy than the five orbitals related to the 3d sublevel.
Hund’s rule The fact that negatively charged electrons repel each other has an important impact on the distribution of electrons in equal-energy orbitals. Hund’s rule states that single electrons with the same spin must occupy each equal-energy orbital before additional electrons with opposite spins can occupy the same orbitals. For example, let the boxes below represent the 2p orbitals. One electron enters each of the three 2p orbitals before a second electron enters any of the orbitals. The sequence in which six electrons occupy three p orbitals is shown below.
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• In order of increasing energy, the sequence of energy sublevels within a principal energy level is s, p, d, and f.
You can represent an atom’s electron configuration using two convenient methods. One method is called an orbital diagram. An orbital diagram includes a box for each of the atom’s orbitals. An empty box represents an unoccupied orbital; a box containing a single up arrow represents an orbital with one electron; and a box containing both up and down arrows represents a filled orbital. Each box is labeled with the principal quantum number and sublevel associated with the orbital. For example, the orbital diagram for a ground-state carbon atom, which contains two electrons in the 1s orbital, two electrons in the 2s orbital, and 1 electron in two of three separate 2p orbitals, is shown below.
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Demonstration Emission PSpectra Purpose
To illustrate the relationship between the electron configurations of nonmetals and LS their emission spectra Materials
Spectrum tubes (H and Ne); spectrum tube 136
2s
2p
Chapter 5 Electrons in Atoms
power supply; Flinn C-Spectra diffraction grating; colored pencils or chalk Safety Precautions
Use care around the spectrum tube high voltage power supply. Spectrum tubes will get hot when used. Procedure
An inexpensive alternative to a spectroscope is to tape a small piece of the Flinn C-Spectra diffraction grating to a 3 5
inch card. Have students view the spectrum emitted from the lights in the classroom. Then, darken the room and have them view the excited neon atoms in the powered neon spectrum tubes. Use colored pencils to record the emission spectrum of neon as seen through their diffraction gratings. Remind students that neon contains 10 electrons. Now repeat the process using a hydrogen spectrum tube. Since hydrogen has 1 electron, ask
Table 5-3
Figure Caption Questions
Electron Configurations and Orbital Diagrams for Elements in the First Two Periods Atomic number
Element
Orbital diagram 1s 2s 2px 2py 2pz
Figure 5-18 How many electrons does each of neon’s orbitals hold?
Electron configuration notation
Each orbital contains two electrons. How many electrons in total
Hydrogen
1
1s1
Helium
2
1s2
does neon’s electron cloud contain?
Lithium
3
1s22s1
ten electrons
Beryllium
4
1s22s2
Boron
5
1s22s22p1
Carbon
6
1s22s22p2
Nitrogen
7
1s22s22p3
Oxygen
8
1s22s22p4
Fluorine
9
1s22s22p5
Neon
10
1s22s22p6
Visual Learning Table 5-3 Have students write an electron configuration notation that shows the orbital occupancy related to a phosphorus atom’s 3p sublevel. 3px13py13pz1 A chlorine atom’s 3s and 3p sublevels. 3s23px23py23pz1
Recall that the number of electrons in an atom equals the number of protons, which is designated by the element’s atomic number. Carbon, which has an atomic number of six, has six electrons in its configuration. Another shorthand method for describing the arrangement of electrons in an element’s atoms is called electron configuration notation. This method designates the principal energy level and energy sublevel associated with each of the atom’s orbitals and includes a superscript representing the number of electrons in the orbital. For example, the electron configuration notation of a ground-state carbon atom is written 1s22s22p2. Orbital diagrams and electron configuration notations for the elements in periods one and two of the periodic table are shown in Table 5-3. To help you visualize the relative sizes and orientations of atomic orbitals, the filled 1s, 2s, 2px, 2py, and 2pz orbitals of the neon atom are illustrated in Figure 5-18.
Ask students to think about and explain the analogy between Hund’s rule and the behavior of total strangers as they board an empty bus. By and large, passengers sit in separate rows until people occupy all rows. Only when no more empty rows are available do two passengers occupy a single row. For electrons, the situation is much the same as they occupy orbitals related to a sublevel. Chemistry’s bus principle is known as Hund’s rule.
Figure 5-18
z
z
Concept Development
The 1s, 2s, and 2p orbitals of a neon atom overlap. How many electrons does each of neon’s orbitals hold? How many electrons in total does neon’s electron cloud contain?
x x y y
1s 2s
2s z
z
1s
z 2px
x x y
x y
y
2py 2pz 0
0
0
Neon atom 0
2pz
2py
0
2px
0
0
0
0
0
1s
2s
2p
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students to predict if there will be more or fewer lines in hydrogen’s spectrum. Results
The red-orange spectrum of neon also contains some green lines. Usually only 3 of the 4 lines of hydrogen are visible. Analysis
1. Write the electron configurations of neon and hydrogen. Ne: 1s22s22p6, H: 1s1 2. What is the appearance of neon in the
excited state? In the ground state, neon is a clear, colorless gas. In the excited state it gives off a red-orange light.
3. Of the two spectra viewed, did hydrogen or neon have more lines? Explain why. Neon has more lines than hydrogen because its ten electrons have a greater number of possible energy transitions.
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Assessment Skill Have students view the excited spectral tube of another element such as mercury. Ask them to predict if Hg will have more lines than neon and hydrogen because it has 80 electrons. No, Hg actually has fewer lines in the visible spectrum. However, there are many additional lines in mercury’s IR and UV spectra.
137
Figure Caption Question
Note that electron configuration notation usually does not show the orbital distributions of electrons related to a sublevel. It’s understood that a designation such as nitrogen’s 2p3 represents the orbital occupancy 2px12py12pz1. For sodium, the first ten electrons occupy 1s, 2s, and 2p orbitals. Then, according to the aufbau sequence, the eleventh electron occupies the 3s orbital. The electron configuration notation and orbital diagram for sodium are written
1s
Figure 5-19 Which is filled first, the 5s or 4p orbital? The 4p orbital
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
is filled first.
Reinforcement Point out that some textbooks, reference books, and periodic tables show electron configurations written in energy-level sequence rather than in aufbau sequence. Reinforce that using the energylevel sequence for electron configurations does not render the aufbau sequence invalid.
Figure 5-19 This sublevel diagram shows the order in which the orbitals are usually filled. The proper sequence for the first seven orbitals is 1s, 2s, 2p, 3s, 3p, 4s, and 3d. Which is filled first, the 5s or the 4p orbital?
Na
1s22s22p63s1 1s 2s
2p
3s
Noble-gas notation is a method of representing electron configurations of noble gases using bracketed symbols. For example, [He] represents the electron configuration for helium, 1s2, and [Ne] represents the electron configuration for neon, 1s22s22p6. Compare the electron configuration for neon with sodium’s configuration above. Note that the inner-level configuration for sodium is identical to the electron configuration for neon. Using noble-gas notation, sodium’s electron configuration can be shortened to the form [Ne]3s1. The electron configuration for an element can be represented using the noble-gas notation for the noble gas in the previous period and the electron configuration for the energy level being filled. The complete and abbreviated (using noble-gas notation) electron configurations of the period 3 elements are shown in Table 5-4. When writing electron configurations, you may refer to a convenient memory aid called a sublevel diagram, which is shown in Figure 5-19. Note that following the direction of the arrows in the sublevel diagram produces the sublevel sequence shown in the aufbau diagram of Figure 5-17. Exceptions to predicted configurations You can use the aufbau diagram to write correct ground-state electron configurations for all elements up to and including vanadium, atomic number 23. However, if you were to proceed in this manner, your configurations for chromium, [Ar]4s23d4, and copper, [Ar]4s23d9, would prove to be incorrect. The correct configurations for these two elements are: Cr [Ar]4s13d5 Cu [Ar]4s13d10 The electron configurations for these two elements, as well as those of several elements in other periods, illustrate the increased stability of half-filled and filled sets of s and d orbitals. Table 5-4 Electron Configurations for Elements in Period Three Element
Atomic number
Electron configuration using noble-gas notation
11
1s22s22p63s1
[Ne]3s1
Magnesium
12
1s22s22p63s2
[Ne]3s2
Aluminum
13
1s22s22p63s23p1
[Ne]3s23p1
Silicon
14
1s22s22p63s23p2
[Ne]3s23p2
Phosphorus
15
1s22s22p63s23p3
[Ne]3s23p3
Sulfur
16
1s22s22p63s23p4
[Ne]3s23p4
Chlorine
17
1s22s22p63s23p5
[Ne]3s23p5
Argon
18
1s22s22p63s23p6
[Ne]3s23p6 or [Ar]
Sodium
138
Complete electron configuration
Chapter 5 Electrons in Atoms
The Development of Fireworks Explain that the Chinese likely first used fireworks about the second century B.C. After inventing explosive black powder, which they called “gung pow,” the Chinese developed black-powder “crackers” that produced loud explosions. Most scholars believe that the Chinese used
138
crackers to frighten off evil spirits and to celebrate weddings, births, battle victories, and eclipses of the Moon. Fireworks became much more interesting and colorful in the 1830s, when Italian pyrotechnics experts added potassium chlorate to the mix. The potassium chlorate provided more oxygen for the
chemical reaction, making it burn faster and hotter. This enabled the Italians to include various inorganic compounds that burn at high temperatures and create spectacular colors. Fireworks’ colors are due to energy-level transitions of electrons in the metal atoms of these inorganic compounds.
EXAMPLE PROBLEM 5-3
PROBLEMS
Writing Electron Configurations Germanium (Ge), a semiconducting element, is commonly used in the manufacture of computer chips. What is the ground-state electron configuration for an atom of germanium? 1.
Analyze the Problem You are given the semiconducting element, germanium (Ge). Consult the periodic table to determine germanium’s atomic number, which also is equal to its number of electrons. Also note the atomic number of the noble gas element that precedes germanium in the table. Determine the number of additional electrons a germanium atom has compared to the nearest preceding noble gas, and then write out germanium’s electron configuration.
2. Solve for the Unknown From the periodic table, germanium’s atomic number is determined to be 32. Thus, a germanium atom contains 32 electrons. The noble gas preceding germanium is argon (Ar), which has an atomic number of 18. Represent germanium’s first 18 electrons using the chemical symbol for argon written inside brackets.
Atoms of boron and arsenic are inserted into germanium’s crystal structure in order to produce a semiconducting material that can be used to manufacture computer chips.
Have students refer to Appendix D for complete solutions to Practice Problems. 18. a. [Ar]4s23d104p5 b. [Kr]5s2 c. [Kr]5s24d105p3 d. [Xe]6s24f145d5 e. [Xe]6s24f9 f. [Ar]4s23d2 19. 6 20. 11 21. indium 22. barium
[Ar] The remaining 14 electrons of germanium’s configuration need to be written out. Because argon is a noble gas in the third period of the periodic table, it has completely filled 3s and 3p orbitals. Thus, the remaining 14 electrons fill the 4s, 3d, and 4p orbitals in order. [Ar]4s?3d?4p?
Assessment Portfolio Ask students to
write electron configurations and construct orbital notations and electron dot structures for atoms of all the elements in the third period on the periodic table. Have them include the configurations, notations, and structures in their portfolios. L2 P
Using the maximum number of electrons that can fill each orbital, write out the electron configuration. [Ar]4s23d104p2 3. Evaluate the Answer All 32 electrons in a germanium atom have been accounted for. The correct preceding noble gas (Ar) has been used in the notation, and the order of orbital filling for the fourth period is correct (4s, 3d, 4p).
PRACTICE PROBLEMS e! Practic
For more practice with electron configuration problems, go to Supplemental Practice Problems in Appendix A.
18. Write ground-state electron configurations for the following elements. a. bromine (Br)
d. rhenium (Re)
b. strontium (Sr)
e. terbium (Tb)
c. antimony (Sb)
f. titanium (Ti)
LS P
19. How many electrons are in orbitals related to the third energy level of a sulfur atom? 20. How many electrons occupy p orbitals in a chlorine atom?
LS
21. What element has the following ground-state electron configuration? [Kr]5s24d105p1 22. What element has the following ground-state electron configuration? [Xe]6s2
5.3 Electron Configurations
139
M EETING I NDIVIDUAL N EEDS Visually Impaired Kinesthetic Make or purchase cellular polystyrene (Styrofoam) or papier-mâché models of s, p, and d orbitals. Allow visually impaired students to feel the models and trace their contours P to gain a better appreciation of their shapes and orientations. L1 ELL
LS P
Pages 136–139 6(A)
139
Valence Electrons
Using Science Terms
Only certain electrons, called valence electrons, determine the chemical properties of an element. Valence electrons are defined as electrons in the atom’s outermost orbitals—generally those orbitals associated with the atom’s highest principal energy level. For example, a sulfur atom contains 16 electrons, only six of which occupy the outermost 3s and 3p orbitals, as shown by sulfur’s electron configuration. Sulfur has six valence electrons.
Explain to students that some textbooks and reference books use the word valence in place of oxidation state. For example, such books would say that oxygen has a valence of 2.
S [Ne]3s23p4 Similarly, although a cesium atom contains 55 electrons, it has but one valence electron, the 6s electron shown in cesium’s electron configuration.
Content Background Valence Electrons Explain to
Cs [Xe]6s1
capable students that some innerlevel d electrons are often considered valence electrons for transition elements. For example, although an atom of iron has just two electrons in its outermost (4s) orbitals, an additional electron associated with one of the atom’s 3d orbitals is often involved in bonding. And in an atom of manganese, as many as five 3d-orbital electrons may be involved in bonding.
Francium, which belongs to the same group as cesium, also has a single valence electron. Fr [Rn]7s1 Electron-dot structures Because valence electrons are involved in forming chemical bonds, chemists often represent them visually using a simple shorthand method. An atom’s electron-dot structure consists of the element’s symbol, which represents the atomic nucleus and inner-level electrons, surrounded by dots representing the atom’s valence electrons. The American chemist G. N. Lewis (1875–1946), devised the method while teaching a college chemistry class in 1902. In writing an atom’s electron-dot structure, dots representing valence electrons are placed one at a time on the four sides of the symbol (they may be placed in any sequence) and then paired up until all are used. The groundstate electron configurations and electron-dot structures for the elements in the second period are shown in Table 5-5.
PROBLEMS Have students refer to Appendix D for complete solutions to Practice Problems. 23. a. Mg d. Rb b. S
e. Tl
c. Br
f. Xe
Table 5-5 Electron-Dot Structures for Elements in Period Two Element
Atomic number
Electron configuration
Electron-dot structure
Lithium
3
1s22s1
Li
Beryllium
4
1s22s2
Be
Boron
5
1s22s22p1
B
Check for Understanding
Carbon
6
1s22s22p2
C
Ask students to predict the maximum number of electrons that can exist in orbitals related to an atom’s fourth and fifth energy levels—assuming an element existed that contained enough electrons. You may want to give students the formula 2n2, which can be used to calculate the number of electrons related to each value of n.
Nitrogen
7
1s22s22p3
N
Oxygen
8
1s22s22p4
O
Fluorine
9
1s22s22p5
F
Neon
10
1s22s22p6
Ne
3 Assess
32 and 50 electrons, respectively
140
Chapter 5 Electrons in Atoms
CHEMISTRY JOURNAL Another Solar System—What if?
Pages 140–141 3(E), 6(A), 8(A)
140
Linguistic Ask students to write essays for their journals in which they speculate about flying a spacecraft to a planet in a different solar system. In the new solar system, they discover that each atomic orbital
of the planet’s solid, liquid, and gaseous matter may contain up to three electrons rather than just two. Their speculation P should focus on the characteristics of the elements on this new planet. L2
LS
EXAMPLE PROBLEM 5-4
Reteach
Writing Electron-Dot Structures
Visual-Spatial Have
Some sheet glass is manufactured using a process that makes use of molten tin. What is tin’s electron-dot structure?
students write the electrondot structure of strontium. The
1. Analyze the Problem
structure includes the symbol Sr and two dots. Ask what the two dots represent. They represent the two electrons in a strontium atom’s outermost, 5s, orbital.
You are given the element tin (Sn). Consult the periodic table to determine the total number of electrons an atom of tin has. Write out tin’s electron configuration and determine the number of valence electrons it has. Then use the number of valence electrons and the rules for electron-dot structures to draw the electron-dot structure for tin.
Then, ask what the electron-dot structure does not communicate about the strontium atom’s electrons. It does not specify which
2. Solve for the Unknown From the periodic table, tin is found to have an atomic number of 50. Thus, a tin atom has 50 electrons. Write out the noble-gas form of tin’s electron configuration. [Kr]5s24d105p2 The two 5s and the two 5p electrons (the electrons in the orbitals related to the atom’s highest principal energy level) represent tin’s four valence electrons. Draw tin’s electron-dot structure by representing its four valence electrons with dots, arranged one at a time, around the four sides of tin’s chemical symbol (Sn).
Flat-surfaced window glass may be manufactured by floating molten glass on top of molten tin.
Sn
Assessment Skill Ask students to identify the elements that have the following ground-state electron configurations. [Ar]4s23d5 manganese [Xe]6s24f145d106p3
3. Evaluate the Answer The correct symbol for tin (Sn) has been used, and the rules for drawing electron-dot structures have been correctly applied.
PRACTICE PROBLEMS
bismuth L2 e! Practic
For more practice with electron-dot structure problems, go to Supplemental Practice Problems in Appendix A.
23. Draw electron-dot structures for atoms of the following elements. a. magnesium
orbital contains the two electrons, nor does it give any information about strontium’s inner level electrons.
d. rubidium
b. sulfur
e. thallium
c. bromine
f. xenon
P
Section
5.3
Assessment
24.
State the aufbau principle in your own words.
25.
Apply the Pauli exclusion principle, the aufbau principle, and Hund’s rule to write out the electron configuration and draw the orbital diagram for each of the following elements. silicon b. fluorine a.
26.
26. A valence electron is an elec-
calcium d. krypton c.
What is a valence electron? Draw the electron-dot structures for the elements in problem 25.
27.
28.
Thinking Critically Use Hund’s rule and orbital diagrams to describe the sequence in which ten electrons occupy the five orbitals related to an atom’s d sublevel. Interpreting Scientific Illustrations Which of the following is the correct electron-dot structure for an atom of selenium? Explain. a.
Se
b.
Se
c.
Se
d.
S
5.3 Electron Configurations
Section 5.3
141
Assessment
24. Electrons tend to occupy the lowestenergy orbital available.
25. a. Si 1s22s22p63s23p2 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s 2s 2p b. F 1s22s22p5 ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s 2s 2p
↑↓ 3s
↑↑ 3p
c. Ca 1s22s22p63s23p64s2 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s 2s 2p 3s 3p d. Kr 1s22s22p63s23p64s23d104p6 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s 2s 2p 3s 3p ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 3d 4p
↑↓ 4s ↑↓ 4s
tron in an atom’s outermost orbitals. a. SiLS c. Ca
b. F 27. 1 electron
d. Kr ↑ 2 electrons ↑ ↑ 3 electrons ↑ ↑ ↑ 4 electrons ↑ ↑ ↑ ↑ 5 electrons ↑ ↑ ↑ ↑ ↑ 6 electrons ↑↓ ↑ ↑ ↑ ↑ 7 electrons ↑↓ ↑↓ ↑ ↑ ↑ 8 electrons ↑↓ ↑↓ ↑↓ ↑ ↑ 9 electrons ↑↓ ↑↓ ↑↓ ↑↓ ↑ 10 electrons ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ Single electrons with the same spin occupy each equalenergy orbital before additional electrons with opposite spins occupy the same orbital. 28. c is correct; a shows three two-electron orbitals; b shows one three-electron orbital; d has the wrong symbol 141
CHEMLAB P
5
Preparation Time Allotment
One laboratory period LS Process Skills
Comparing and contrasting, predicting, thinking critically, classifying, observing and inferring, sequencing Safety Precautions
• Do not let students handle the spectrum power supplies or tubes. Warn students not to touch the gas spectrum tubes during use because they are very hot and can cause burns. Exercise caution around the spectrum power supplies, as they present a significant electrical shock hazard.
CHEMLAB
5
Line Spectra
Y
ou know that sunlight is made up of a continuous spectrum of colors that combine to form white light. You also have learned that atoms of gases can emit visible light of characteristic wavelengths when excited by electricity. The color you see is the sum of all of the emitted wavelengths. In this experiment, you will use a diffraction grating to separate these wavelengths into emission line spectra. You also will investigate another type of line spectrum—the absorption spectrum. The color of each solution you observe is due to the reflection or transmission of unabsorbed wavelengths of light. When white light passes through a sample and then a diffraction grating, dark lines show up on the continuous spectrum of white light. These lines correspond to the wavelengths of the photons absorbed by the solution.
Problem
Objectives
Materials
What absorption and emission spectra do various substances produce?
• Observe emission spectra of several gases. • Observe the absorption spectra of various solutions. • Analyze patterns of absorption and emission spectra.
(For each group) ring stand with clamp 40-W tubular light bulb light socket with power cord 275-mL polystyrene culture flask (4) Flinn C-Spectra® or similar diffraction grating
Disposal
You may want to reuse the flasks of food coloring solutions. Preparation of Materials
• Set up light sockets with light bulbs prior to class and have them plugged in. • Set up spectrum power supplies and tubes prior to class.
Pre-Lab 2. When electrons drop from higher-energy orbitals to lower-energy orbitals, the atom emits energy in the form of light. Each orbital transition is associated with a characteristic spectral line. 3. A continuous spectrum contains a continuum of visible colors from red to violet. An absorption spectrum is a continuous spectrum containing black lines at wavelengths associated with the atoms’ energy absorptions. An emission spectrum consists of colored lines associated with the atoms’ energy-level transitions.
Procedure • Have several groups of students start their observations of the gas discharge tubes first so that the area doesn’t become crowded by the end of the class period. 142
food coloring (red, green, blue, and yellow) set of colored pencils book (For entire class) spectrum tubes (hydrogen, neon, and mercury) spectrum tube power supplies (3)
Safety Precautions • Always wear safety goggles and a lab apron. • Use care around the spectrum tube power supplies. • Spectrum tubes will get hot when used.
Pre-Lab Read the entire CHEMLAB. 2. Explain how electrons in an element’s atoms produce an emission spectrum. 3. Distinguish among a continuous spectrum, an emission spectrum, and an absorption spectrum. 4. Prepare your data tables.
Drawings of Absorption Spectra
1.
Drawings of Emission Spectra Hydrogen Neon Mercury
142
Red Green Blue Yellow
Procedure 1.
Use a Flinn C-Spectra® to view an incandescent light bulb. What do you observe? Draw the spectrum using colored pencils.
Chapter 5 Electrons in Atoms
• The Flinn C-Spectra is much easier to use than a spectroscope for viewing spectra. It can be ordered from: Flinn Scientific, Inc. P.O. Box 219 Batavia, IL 60510 www.flinnsci.com. • You may be able to borrow gas spectrum tubes and power supplies from a physics teacher.
Expected Results For each colored solution listed below, all colors are visible except as noted. Red solution: blue and green Green solution: red and orange Blue solution: yellow, orange, and some red Yellow solution: blue
CHAPTER 5 CHEMLAB
2.
Use the Flinn C-Spectra® to view the emission spectra from tubes of gaseous hydrogen, neon, and mercury. Use colored pencils to make drawings in the data table of the spectra observed.
With the room lights darkened, view the light using the Flinn C-Spectra®. The top spectrum viewed will be a continuous spectrum of the white light bulb. The bottom spectrum will be the absorption spectrum of the red solution. The black areas of the absorption spectrum represent the colors absorbed by the red food coloring in the solution. Use colored pencils to make a drawing in the data table of the absorption spectra you observed. 7. Repeat steps 5 and 6 using the green, blue, and yellow colored solutions.
The approximate emission spectra of the gas spectrum tubes are shown below.
Cleanup and Disposal
Blue Green
6.
Turn off the light socket and spectrum tube power supplies. 2. Wait several minutes to allow the incandescent light bulb and the spectrum tubes to cool. 3. Follow your teacher’s instructions on how to dispose of the liquids and how to store the light bulb and spectrum tubes.
Hydrogen Mercury Neon
Yellow Orange
Red
1.
Fill a 275-mL culture flask with about 100-mL water. Add 2 or 3 drops of red food coloring to the water. Shake the solution. 4. Repeat step 3 for the green, blue, and yellow food coloring. CAUTION: Be sure to thoroughly dry your hands before handling electrical equipment. 5. Set up the light 40-W light bulb so that it is near eye level. Place the flask with red food coloring about 8 cm from the light bulb. Use a book or some other object to act as a stage to put the flask on. You should be able to see light from the bulb above the solution and light from the bulb projecting through the solution. 3.
Analyze and Conclude Thinking Critically How can the existence of spectra help to prove that energy levels in atoms exist? 2. Thinking Critically How can the single electron in a hydrogen atom produce all of the lines found in its emission spectrum? 3. Predicting How can you predict the absorption spectrum of a solution by looking at its color? 4. Thinking Critically How can spectra be used to identify the presence of specific elements in a substance? 1.
Real-World Chemistry How can absorption and emission spectra be used by the Hubble space telescope to study the structures of stars or other objects found in deep space? 2. The absorption spectrum of chlorophyll a indicates strong absorption of red and blue wavelengths. Explain why leaves appear green. 1.
CHEMLAB
Resource Manager ChemLab and MiniLab Worksheets, pp. 18–20 L2
143
Analyze and Conclude 1. The spectral lines indicate energy is absorbed or released as the atom transitions from one energy level to another. 2. At any given time, the electron occupies a single orbital. However, it can move into other, vacant orbitals as the atom absorbs or emits energy. 3. The color of a solution is due to the color of light it transmits. The colors not transmitted are absorbed, and these colors comprise the absorption spectrum. 4. The spectrum of each element is unique. Thus, the presence of a unique atomic spectrum indicates the presence of that element.
Real-World Chemistry 1. The light emitted by stars can be analyzed for the presence of unique atomic spectra. Such spectra can identify the types of matter that comprise the star. 2. Leaves appear green because they reflect (do not absorb) green light. The reflected green light is what our eyes see.
Assessment Skill Have students look at the spectrum produced by a fluorescent light and compare this spectrum to the spectrum of an incandescent bulb. L2 Pages 142–143 1(A), 2(A), 2(B), 2(C), 2(D), 2(E), 6(A)
P
143
How It Works P
How It Works
Purpose
Lasers
Students will learn how lasers are an application LSof quantum theory.
A laser is a device that produces a beam of intense light of a specific wavelength (color). Unlike light from a flashlight, laser light is coherent; that is, it does not spread out as it travels through space. The precise nature of lasers led to their use in pointing and aiming devices, CD players, optical fiber data transmission, and surgery.
Background Most sources of light emit incoherent light. Incoherent light waves have different wavelengths, amplitudes, and frequencies, travel in all directions, and are not in phase with each other as they move through space. Laser light is coherent, traveling in the same direction while being in phase. Two conditions must be met for a laser to work. First, the atoms must be excited to a higher state. Second, the atoms must remain in the higher state longer than usual so that they can be stimulated to emit light rather than to emit it spontaneously. How these conditions are achieved depends on the type of laser being used. In a ruby laser, for example, strong flashes of light excite the atoms. The atoms then drop to a lower state that is still excited, which leaves enough time for stimulated emission to occur.
LS
144
E1
2 and 3
Mirror
5 Emitted coherent light
4
Helium and neon filled tube
Before
E1
After
3 The emitted photons hit other excited atoms, causing them to release additional photons. These additional photons are the same wavelength as the photons that struck the excited atoms, and they are coherent (their waves are in sync because they are identical in wavelength and direction).
Excited state
E2
Ground state
E2
Partially transparent mirror Incident photon
4 Photons traveling parallel to the tube are reflected back through the tube by the flat mirrors located at each end. The photons strike additional excited atoms and cause more photons to be released. The intensity of the light in the tube builds.
Two coherent photons emitted
E1
Before
E1
After
5 Some of the laser's coherent light passes through the partially transparent mirror at one end of the tube and exits the laser. These photons make up the light emitted by the laser.
1.
• Ask students to list at least five
Pages 144–145 5(A), P 6(A)
Photon emitted
1
Teaching Strategies
P
Ground state
E2
Sprial flash lamp
Bring a laser pointer to class, and compare its light to that of an ordinary flashlight. CAUTION: Be sure that students do not look directly into the laser light or shine it into anyone’s eyes.
L2 ELL
Excited state
E2
1 The spiral-wound high-intensity lamp flashes, supplying energy to the helium-neon gas mixture inside the tube. The atoms of the gas absorb the light energy and are raised to an excited energy state.
Visual Learning
different types of materials that can be used in a laser to produce light. • Ask students to select an application of laser light to research. Have them create a poster summarizing how the laser is used in this way.
2 The excited atoms begin returning to the ground state, emitting photons in the process. These initial photons travel in all directions.
144
Inferring How does the material used in the laser affect the type of light emitted?
2. Relating
Cause and Effect Why is one mirror partially transparent?
Chapter 5 Electrons in Atoms
Thinking Critically 1. The arrangement of electrons varies from one substance to another. As a result, the characteristics of light emitted by the laser also vary. The material in the laser determines the characteristics of the light produced.
2. If one of the mirrors were not partially transparent, the photons would have no way to escape the laser. If the mirror were totally transparent, the photons would exit the laser after just one pass through the tube. Thus, the photons could not stimulate the emission of additional photons; the laser would soon weaken.
CHAPTER
5
STUDY GUIDE
CHAPTER STUDY GUIDE
5
Using the Vocabulary
Summary • The quantum mechanical model of the atom is
5.1 Light and Quantized Energy • All waves can be described by their wavelength, frequency, amplitude, and speed.
based on the assumption that electrons are waves. • The Heisenberg uncertainty principle states that it is
not possible to know precisely the velocity and the position of a particle at the same time.
• Light is an electromagnetic wave. In a vacuum,
all electromagnetic waves travel at a speed of 3.00 108 m/s.
• Electrons occupy three-dimensional regions of space
• All electromagnetic waves may be described as both
waves and particles. Particles of light are called photons. • Energy is emitted and absorbed by matter in quanta. • In contrast to the continuous spectrum produced by
white light, an element’s atomic emission spectrum consists of a series of fine lines of individual colors.
called atomic orbitals. There are four types of orbitals, denoted by the letters s, p, d, and f. 5.3 Electron Configurations • The arrangement of electrons in an atom is called the atom’s electron configuration. Electron configurations are prescribed by three rules: the aufbau principle, the Pauli exclusion principle, and Hund’s rule. • Electrons related to the atom’s highest principal
5.2 Quantum Theory and the Atom • According to the Bohr model of the atom, hydrogen’s atomic emission spectrum results from electrons dropping from higher-energy atomic orbits to lower-energy atomic orbits.
energy level are referred to as valence electrons. Valence electrons determine the chemical properties of an element. • Electron configurations may be represented using
orbital diagrams, electron configuration notation, and electron-dot structures.
• The de Broglie equation predicts that all moving
particles have wave characteristics and relates each particle’s wavelength to its mass, its frequency, and Planck’s constant.
Key Equations and Relationships • Energy change of an electron: E Ehigher-energy orbit Elower-energy orbit E Ephoton h (p. 128) h • de Broglie’s equation: m (p. 130)
• EM Wave relationship: c (p. 119) • Energy of a quantum: Equantum h (p. 123) • Energy of a photon: Ephoton h (p. 124)
To reinforce chapter vocabulary, have students write a sentence using each term. L2 ELL
Review Strategies • Have students describe P the electromagnetic spectrum and differentiate between visible light and infrared radiation. L2 P • Ask students to write LSthe equation that relates an electromagnetic wave’s frequency and wavelength. L2 LS the equation • Have students write that relates the energy of a P quantum of electromagnetic radiation to the frequency of an associated wave. L2 • Ask students to explain the LS P of Heisenberg’s significance uncertainty principle as it relates to electrons in atoms. L2 • Have students explain the relationshipLS between an atom’s orbitals and itsPenergy levels. L2 • Problems from Appendix A or the Supplemental Problems booklet can be used for review. L2
LS
P
P
Reviewing Chemistry isLS a compo-
Vocabulary • amplitude (p. 119) • atomic emission spectrum (p. 125) • atomic orbital (p. 132) • aufbau principle (p. 135) • de Broglie equation (p. 130) • electromagnetic radiation (p. 118) • electromagnetic spectrum (p. 120)
• • • • • •
electron configuration (p. 135) electron-dot structure (p. 140) energy sublevel (p. 133) frequency (p. 118) ground state (p. 127) Heisenberg uncertainty principle (p. 131) • Hund’s rule (p. 136) • Pauli exclusion principle (p. 136) • photoelectric effect (p. 123)
• • • • • • • •
photon (p. 123) Planck’s constant (p. 123) principal energy level (p. 133) principal quantum number (p. 132) quantum (p. 122) quantum mechanical model of the atom (p. 131) valence electron (p. 140) wavelength (p. 118) Study Guide
145
Portfolio Portfolio Portfolio Options Review the portfolio options that are provided throughout the chapter. Encourage students to select one product that demonstrates their best work for the chapter. Have students explain what they have learned
and why they chose this example for placement into their portfolios. Additional portfolio options may be found in the Challenge Problems booklet of the Teacher Classroom Resources. L2 P
LS
nent of the Teacher Classroom Resources package that was P prepared by The Princeton LS Review. Use the Chapter 5 review materials in this book to review the chapter with LS your students.
VIDEOTAPE/DVD MindJogger Videoquizzes Chapter 5: Electrons in Atoms Have students work in groups as they play the videoquiz game to review key chapter concepts. 145
CHAPTER CHAPTER
CHAPTER ASSESSMENT
ASSESSMENT ASSESSMENT
5 ##
5
40. According to the Bohr model, how do electrons move
in atoms? (5.2)
All Chapter Assessment questions and answers have been validated for accuracy and suitability by The Princeton Review.
41. What does n designate in Bohr’s atomic model? (5.2)
Go to the Chemistry Web site at science.glencoe.com or use the Chemistry CD-ROM for additional Chapter 5 Assessment.
29. Complete the concept map using the following terms:
speed, c , electromagnetic waves, wavelength, characteristic properties, frequency, c, and hertz.
29. 1. electromagnetic waves;
1.
the hydrogen atom’s first three energy levels? (5.2) 48. What atomic orbitals are related to a p sublevel? To a
4.
5.
34.
35.
146
d sublevel? (5.2) 49. Which of the following atomic orbital designations are
incorrect? (5.2)
30. a. Frequency is the number
33.
within an atomic orbital? (5.2) model of the atom? (5.2)
2. 3.
32.
45. What is the probability that an electron will be found
47. How many energy sublevels are contained in each of
Mastering Concepts
31.
44. What is an atomic orbital? (5.2)
46. What does n represent in the quantum mechanical
2. characteristic properties; 3. frequency; 4. wavelength; 5. speed; 6. hertz; 7. c ; 8. c
of waves that pass a given point per second. b. Wavelength is the shortest distance between equivalent points on a continuous wave. c. A quantum is the minimum amount of energy that can be lost or gained by an atom. d. An atom’s ground state is its lowest allowable energy state. Typical answers will say that the model did not explain the following: how the atom’s negatively charged electrons occupy the space around the nucleus; why the electrons are not drawn into the atom’s positively charged nucleus; a rationale for the chemical properties of the elements. light, microwaves, X rays, radio waves Electricity passing through the tube excites neon atoms to higher energy levels. As the excited atoms drop back to lower energy levels, they emit light. a particle of electromagnetic radiation having a rest mass of zero and carrying a quantum of energy a phenomenon in which a metal emits electrons when
objects such as automobiles and tennis balls? (5.2) 43. What is the name of the atomic model in which elec-
trons are treated as waves? Who first wrote the electron wave equations that led to this model? (5.2)
Concept Mapping
Concept Mapping
42. Why are you unaware of the wavelengths of moving
measured in
are related by
of all waves
a. 7f
b. 3f
c. 2d
d. 6p
50. What do the sublevel designations s, p, d, and f spec6.
7.
8.
ify with respect to the atom’s orbitals? (5.2) 51. What do subscripts such as y and xz tell you about
atomic orbitals? (5.2)
Mastering Concepts
may contain? (5.2)
30. Define the following terms. a. frequency (5.1) b. wavelength (5.1)
c. d.
52. What is the maximum number of electrons an orbital
quantum (5.1) ground state (5.2)
31. Why did scientists consider Rutherford’s nuclear
model of the atom incomplete? (5.1) 32. Name one type of electromagnetic radiation. (5.1) 33. Explain how the gaseous neon atoms in a neon sign
emit light. (5.1)
53. Why is it impossible to know precisely the velocity
and position of an electron at the same time? (5.2) 54. What shortcomings caused scientists to finally reject
Bohr’s model of the atom? (5.2) 55. Describe de Broglie’s revolutionary concept involving
the characteristics of moving particles. (5.2) 56. How is an orbital’s principal quantum number related
to the atom’s major energy levels? (5.2)
34. What is a photon? (5.1) 35. What is the photoelectric effect? (5.1) 36. Explain Planck’s quantum concept as it relates to
energy lost or gained by matter. (5.1) 37. How did Einstein explain the previously unexplainable
photoelectric effect? (5.1) 38. Arrange the following types of electromagnetic radia-
57. Explain the meaning of the aufbau principle as it
applies to atoms with many electrons. (5.3) 58. In what sequence do electrons fill the atomic orbitals
related to a sublevel? (5.3) 59. Why must the two arrows within a single block of an
orbital diagram be written in opposite (up and down) directions? (5.3)
tion in order of increasing wavelength. (5.1)
60. How does noble-gas notation shorten the process of
a. ultraviolet light b. microwaves
61. What are valence electrons? How many of a magne-
c. radio waves d. X rays
39. What is the difference between an atom’s ground state
writing an element’s electron configuration? (5.3) sium atom’s 12 electrons are valence electrons? (5.3)
and an excited state? (5.2) 146
Chapter 5 Electrons in Atoms
light of a sufficient frequency shines on it 36. According to Planck, for a given frequency, , matter can emit or absorb energy only in discrete quanta that are whole-number multiples of h. 37. He proposed that photons must have a certain minimum, or threshold, value to cause the ejection of a photoelectron. 38. d. X rays, a. ultraviolet light, b. microwaves, c. radio waves
Resource Manager Chapter Assessment, pp. 25–30 L2 Supplemental Problems, Ch. 5 TestCheck Software MindJogger Videoquizzes Solutions Manual, Ch. 5 Chemistry Interactive CD-ROM, Ch. 5 quiz Reviewing Chemistry: Mastering P the TEKS, Ch. 5
CHAPTER 5 ASSESSMENT CHAPTER 5 ASSESSMENT 62. Light is said to have a dual wave-particle nature. What
does this statement mean? (5.3) photon. (5.3)
75. How long does it take a radio signal from the Voyager
spacecraft to reach Earth if the distance between Voyager and Earth is 2.72 109 km?
64. How many electrons are shown in the electron-dot
structures of the following elements? (5.3)
76. If your favorite FM radio station broadcasts at a fre-
c. calcium d. gallium
quency of 104.5 MHz, what is the wavelength of the station’s signal in meters? What is the energy of a photon of the station’s electromagnetic signal?
Mastering Problems
Electron Configurations (5.3)
65. What is the wavelength of electromagnetic radiation
78. Write orbital notations and complete electron configu-
77. List the aufbau sequence of orbitals from 1s to 7p.
having a frequency of 5.00 1012 Hz? What kind of electromagnetic radiation is this? 66. What is the frequency of electromagnetic radiation
having a wavelength of 3.33 108 m? What type of electromagnetic radiation is this?
67. The laser in a compact disc (CD) player uses light
with a wavelength of 780 nm. What is the frequency of this light? 68. What is the speed of an electromagnetic wave having
a frequency of 1.33 1017 Hz and a wavelength of 2.25 nm? 69. Use Figure 5-5 to determine each of the following
types of radiation. radiation with a frequency of 8.6 1011 s1 radiation with a wavelength 4.2 nm radiation with a frequency of 5.6 MHz radiation that travels at a speed of 3.00 108 m/s
70. What is the energy of a photon of red light having a
frequency of 4.48 1014 Hz? 71. Mercury’s atomic emission spectrum is shown below.
Estimate the wavelength of the orange line. What is its frequency? What is the energy of an orange photon emitted by the mercury atom? Hg
(nm) 400
450
500
550
600
650
700
72. What is the energy of an ultraviolet photon having a
wavelength of 1.18 108 m?
73. A photon has an energy of 2.93 1025 J. What is its
frequency? What type of electromagnetic radiation is the photon?
40. 41. 42.
Wavelength, Frequency, Speed, and Energy (5.1)
a. b. c. d.
39. An atom’s ground state is
the photon’s wavelength? What type of electromagnetic radiation is it?
63. Describe the difference between a quantum and a
a. carbon b. iodine
74. A photon has an energy of 1.10 1013 J. What is
43.
rations for atoms of the following elements. a. b. c. d.
beryllium aluminum nitrogen sodium
44.
79. Use noble-gas notation to describe the electron config-
urations of the elements represented by the following symbols. a. b. c. d. e.
Mn Kr P Zn Zr
f. g. h. i. j.
W Pb Ra Sm Bk
80. What elements are represented by each of the follow-
ing electron configurations? a. b. c. d. e. f.
1s22s22p5 [Ar]4s2 [Xe]6s24f4 [Kr]5s24d105p4 [Rn]7s25f13 1s22s22p63s23p64s23d104p5
47.
48.
81. Draw electron-dot structures for atoms of each of the
following elements. a. b. c. d. e.
45. 46.
carbon arsenic polonium potassium barium
49. 50. 51. 52. 53.
82. An atom of arsenic has how many electron-containing
orbitals? How many of the orbitals are completely filled? How many of the orbitals are associated with the atom’s n 4 principal energy level?
Assessment
54.
147
55. 56. Because the orbital’s principal quantum number indicates the orbital’s relative size and energy, it also specifies the atom’s major energy level. 57. The aufbau principle describes the sequence in which an atom’s orbitals are filled with electrons. 58. Each orbital must contain a single electron before any orbital contains two electrons.
59. Two electrons occupying a single atomic orbital must have opposite spins.
its lowest energy state, while any energy state higher than the ground state is an excited state. Electrons move in circular orbits around the nucleus. The quantum number n specifies the electron’s orbit. Their wavelengths are too small to be seen. the quantum mechanical model of the atom; Erwin Schrödinger a three-dimensional region around the nucleus describing an electron’s probable location The probability is 90%. n represents an orbital’s principal quantum number, which indicates the relative size and energy of the orbital. energy level 1 has one sublevel, energy level 2 has two sublevels, energy level 3 has three sublevels p sublevel: x, y, and z orbitals; d sublevel: xy, xz, yz, x 2y 2, and z 2 orbitals b, c are incorrect their shapes their orientations two electrons The photon required to measure an electron’s velocity or position changes both the position and velocity of the electron. Bohr’s model did not explain the spectra of atoms having more than one electron and did not fully explain the chemical behavior of atoms. de Broglie proposed that all moving particles have wave characteristics.
60. The noble-gas notation uses the bracketed symbol of the preceding noble gas in the periodic table to represent an atom’s inner electrons. 61. Valence electrons are the electrons in an atom’s outermost orbitals; 2 62. Light exhibits wavelike behavior in some situations and particlelike behavior in others.
Pages 146–147 3(E), 5(A), 6(A)
147
CHAPTER CHAPTER 5 ASSESSMENT
63. A quantum is the minimum amount of energy that can be lost or gained by an atom, while a photon is a particle of light that carries a quantum of energy. 64. a. 4 c. 2 b. 7 d. 3
Mastering Problems Complete solutions to Chapter Assessment problems can be found in the Solutions Manual.
Mixed Review
Thinking Critically
Sharpen your problem-solving skills by answering the following. 83. What is the frequency of electromagnetic radiation
having a wavelength of 1.00 m? contained in an atom’s orbitals having the following principal quantum numbers? a. 3
b. 4
c. 6
5.77 1014 Hz? 86. Using the waves shown below, identify the wave or
waves with the following characteristics. 3.
2.
4.
a. longest wavelength c. b. greatest frequency d.
largest amplitude shortest wavelength
87. How many orientations are possible for the orbitals
66. 9.01 1015 s1;
related to each of the following sublevels?
ultraviolet radiation 67. 3.8 1014 s1 68. v 3.00 108 m/s 69. a. infrared b. X ray c. AM radio d. any EM wave
a. s
Level 2 70. Ephoton 2.97 1019 J 71. 615 nm, 4.88 1014 s1, 72. 73. 74. 75. 76.
Ephoton 3.23 1019 J Ephoton 1.68 1017 J 4.42 108 s1; TV or FM wave 1.81 1012 m, an X ray or gamma ray t 9070 s, or 151 min 2.87 m, Ephoton 6.92 1026 J
Electron Configurations (5.3) Level 1 77. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p 78. a. Be 1s22s2 ↑↓ ↑↓ 1s 2s b. Al 1s22s22p63s23p1 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s 2s 2p 3s 3p c. N 1s22s22p3 ↑↓ ↑↓ ↑ ↑ ↑ 1s 2s 2p
148
b. p
c. d
difference between an orbit in Bohr’s model of the atom and an orbital in the quantum mechanical view of the atom. spectra to determine the elements in materials of unknown composition. Explain what makes this method possible. 98. Using Numbers It takes 8.17 1019 J of energy
d. 7
85. What is the wavelength of light with a frequency of
1.
96. Comparing and Contrasting Briefly discuss the
97. Applying Concepts Scientists use atomic emission
84. What is the maximum number of electrons that can be
Wavelength, Frequency, Speed, and Energy (5.1) Level 1 65. 6.00 105 m; infrared radiation
ASSESSMENT
5
to remove one electron from a gold surface. What is the maximum wavelength of light capable of causing this effect? 99. Drawing a Conclusion The elements aluminum,
silicon, gallium, germanium, arsenic, selenium are all used in making various types of semiconductor devices. Write electron configurations and electrondot structures for atoms of each of these elements. What similarities among the elements’ electron configurations do you notice?
Writing in Chemistry 100. In order to make “neon” signs emit a variety of col-
d. f
88. Describe the electrons in an atom of nickel in the
ground state using the electron configuration notation and the noble-gas notation. 89. Which of the following elements have two electrons
in their electron-dot structures: hydrogen, helium, lithium, aluminum, calcium, cobalt, bromine, krypton, and barium? 90. In Bohr’s atomic model, what electron orbit transition
produces the blue-green line in hydrogen’s atomic emission spectrum? 91. A zinc atom contains a total of 18 electrons in its 3s,
3p, and 3d orbitals. Why does its electron-dot structure show only two dots? 92. An X-ray photon has an energy of 3.01 1018 J.
What is its frequency and wavelength? 93. Which element has the following orbital diagram?
ors, manufacturers often fill the signs with gases other than neon. Research the use of gases in neon signs and specify the colors produced by the gases.
Cumulative Review Refresh your understanding of previous chapters by answering the following. 101. Round 20.561 20 g to three significant figures.
(Chapter 2) 102. Identify each of the following as either chemical or
physical properties of the substance. (Chapter 3) a. b. c. d.
mercury is a liquid at room temperature sucrose is a white, crystalline solid iron rusts when exposed to moist air paper burns when ignited
103. Identify each of the following as a pure substance or
a mixture. (Chapter 3) 1s 2s
2p
94. Which element has the ground-state electron configu-
ration represented by the noble-gas notation
[Rn]7s1?
95. How many photons of infrared radiation having a fre-
quency of 4.88 1013 Hz are required to provide an energy of 1.00 J?
148
d. diamond e. milk f. copper metal
104. An atom of gadolinium has an atomic number of 64
and a mass number of 153. How many electrons, protons, and neutrons does it contain? (Chapter 4)
Chapter 5 Electrons in Atoms
d. Na 1s22s22p63s1 79. a. b. c. d. e. f. g. h.
a. distilled water b. orange juice with pulp c. smog
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s 2s 2p 3s Mn [Ar]4s23d5 Kr [Ar]4s23d104p6 P [Ne]3s23p3 Zn [Ar]4s23d10 Zr [Kr]5s24d2 W [Xe]6s24f145d4 Pb [Xe]6s24f145d106p2 Ra [Rn]7s2
i. Sm [Xe]6s24f6 j. Bk [Rn]7s25f9 Level 2 80. a. F b. Ca 81. a. C b. As c. Po 82. 18; 15; 4
c. Nd d. Te d. K e.
Ba
e. Md f. Br
STANDARDIZED TEST PRACTICE CHAPTER 5
0
0
0
0
0
a.
0
0
0
0
0
0
0
0
0
0
0
0
0
3d
0 3d
0
0
0
0
0
0
0
0
4s 0
0
0
3p
0
c.
0
3s
8.90 1022 s1 3.75 1012 s1 8.01 105 s1 1.12 1021 s1
4s 0
0
0
0
3p
0 3d
and 3
0
0
0
0
0
4s
d. shortest wavelength: 3 87. a. 1 c. 5 b. 3 d. 7 88. 1s22s22p63s23p64s23d8
0
2. Wavelengths of light between 5.75 109 m and
3p
0
3s d.
0
a. b. c. d.
3s b.
Mixed Review 83. 3.00 108 s1 84. a. 18 c. 72 b. 32 d. 98 85. 5.20 107 m 86. a. longest wavelength: 4 b. greatest frequency: 3 c. largest amplitude: 1
0
space. What is the frequency of a cosmic ray that has a wavelength of 2.67 1013 m when it reaches Earth? (The speed of light is 3.00 108 m/s.)
for the third and fourth principal energy levels of vanadium? 0
1. Cosmic rays are high-energy radiation from outer
6. Which of the following is the correct orbital diagram
0
Use these questions and the test-taking tip to prepare for your standardized test.
CHAPTER 5 ASSESSMENT
0
0
0
0
0
5.85 109 m appear yellow to the human eye. What is the energy of a photon of yellow light having a frequency of 5.45 1016 s1? (Planck’s constant is 6.626 1034 J s.) a. b. c. d.
3.61 1017 J 1.22 1050 J 8.23 1049 J 3.81 1024 J
chart below to answer questions 3–6. Electron Configurations for Selected Transition Metals Symbol
Atomic number
Electron configuration
Vanadium
V
23
[Ar]4s23d3
Yttrium
Y
39
[Kr]5s24d1
___
___
[Xe]6s24f145d6
_________ Scandium
Sc
21
[Ar]4s23d1
Cadmium
Cd
48
____________
3. Using noble-gas notation, the ground-state electron
configuration of Cd is ________ . a. [Kr]4d104f 2 b. [Ar]4s23d10
3p
4s
3d
7. Which of the following orbitals has the highest
energy? a. b. c. d.
4f 5p 6s 3d
89.
8. What is the electron-dot structure for indium?
Interpreting Charts Use the periodic table and the
Element
3s
c. [Kr]5s24d10 d. [Xe]5s24d10
a.
In
c.
In
b.
In
d.
In
90. 91.
9. The picture below shows all of the orbitals related to
one type of sublevel. The type of sublevel to which these orbitals belong is ________ . z
z
z
x
x
y
x
96. In the Bohr model, an orbit a. s b. p
c. d d. f
10. What is the maximum number of electrons related to
the fifth principal energy level of an atom? a. 10 b. 20
c. 25 d. 50
4. The element that has the ground-state electron config-
uration [Xe]6s24f145d6 is ________ . a. La b. Ti
c. W d. Os
5. The complete electron configuration of a scandium
atom is ________ . a. b. c. d.
1s22s22p63s23p64s23d1 1s22s22p73s23p74s23d1 1s22s22p53s23p54s23d1 1s22s12p73s13p74s23d1
Do Some Reconnaissance
Find out what the conditions will be for taking the test. Is it timed or untimed? Can you eat a snack at the break? Can you use a calculator or other tools? Will those tools be provided? Will mathematical constants be given? Know these things in advance so that you can practice taking tests under the same conditions.
Standardized Test Practice
Cumulative Review 101. 20.6 g 102. a. physical property b. physical property c. chemical property d. chemical property 103. a. pure substance b. mixture c. mixture
93. 94. 95.
Thinking Critically
y
y
92.
[Ar]4s23d8 helium, calcium, cobalt, barium n4→n2 The two dots are the atom’s two 4s valence electrons. 4.54 1015 s1; 6.60 108 m boron francium 3.10 1019 photons
149
d. pure substance e. mixture f. pure substance 104. 64 electrons, 64 protons, 89 neutrons
is a circular path taken by an electron as it moves around the atomic nucleus. In the quantum mechanical model, an orbital is a three-dimensional region around the nucleus that describes the electron’s probable location. 97. Each element emits a characteristic, unique atomic emission spectrum. 98. 2.43 107 m 99. Al [Ne]3s23p1 Si [Ne]3s23p2 Ga [Ar]4s23d104p1 Ge [Ar]4s23d104p2 As [Ar]4s23d104p3 Se [Ar]4s23d104p4 The atoms have filled s orbitals and p orbitals containing 1 to 4 electrons. See the Solutions Manual for electron dot structures.
Standardized Test Practice 1. d 2. a 3. c
4. d 5. a 6. b
7. a 8. c
9. b 10. d
Pages 148–149 5(A), 6(A)
149
