CHAPTER 5 Chapter 5 Assessment pages 166–169 Section 5.1 Mastering Concepts 34. Define the following terms. a. frequency Frequency is the number of waves that pass a given point per second. b. wavelength Wavelength is the shortest distance between equivalent points on a continuous wave. c. quantum A quantum is the minimum amount of energy that can be lost or gained by an atom. d. ground state An atom’s ground state is its lowest allowable energy state. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 35. Arrange the following types of electromagnetic radiation in order of increasing wavelength. a. ultraviolet light b. microwaves c. radio waves d. X rays d. X rays, a. ultraviolet light, b. microwaves, c. radio waves 36. A gamma ray has a frequency of 2.88 3 1021 Hz. What does that mean? 1021 2.88 3 gamma-ray electromagnetic waves of this frequency pass a given point per second. 37. What is the photoelectric effect? SOLUTIONS MANUAL 39. Explain Planck’s quantum concept as it relates to energy lost or gained by matter. According to Planck, for a given frequency, n, matter can emit or absorb energy only in discrete quanta that are whole-number multiples of hn, where h is Planck’s constant. 40. How did Einstein explain the photoelectric effect? He proposed that photons must have a certain minimum energy level, or threshold, value to cause the ejection of a photoelectron. 41. Rainbow What are two differences between the red and green electromagnetic waves in a rainbow? The red waves have a longer wavelength and a lower frequency. 42. Temperature What happens to the light emitted by a heated, glowing object as its temperature increases? The color of the light changes as the object acquries more and more energy. 43. What are three deficiencies of the wave model of light related to light’s interaction with matter? The wave model does not explain the photoelectric effect, atomic emission spectra, and why matter emits different frequencies of light at different temperatures. 44. How are radio waves and ultraviolet waves similar? How are they different? Both types of waves travel at the same speed in a vacuum, 3.00 3 108 m/s. Radio waves have a longer wavelength and lower frequency than ultraviolet waves. a phenomenon in which a metal emits electrons when light of a sufficient frequency shines on it 38. Neon Sign How does light emitted from a neon sign differ from sunlight? The light from a neon sign contains only certain visible colors, while sunlight contains the full spectrum of colors. Solutions Manual Chemistry: Matter and Change • Chapter 5 73 5 CHAPTER SOLUTIONS MANUAL Mastering Problems 45. Use Figure 5.20 to determine each of the following types of radiation. Radio Infrared Microwaves 49. What is the energy of a photon of red light having a frequency of 4.48 3 1014 Hz? Ephoton 5 hn 5 (6.626 3 10234 J ? s)(4.48 3 1014 s 21) 5 2.97 3 10219 J Ultraviolet Gamma rays X rays 50. Mercury’s atomic emission spectrum is shown 10 4 6 10 8 10 10 10 12 10 14 10 10 16 10 18 20 10 22 10 Frequency (ν) in hertz Electromagnetic Spectrum a. radiation with a frequency of 8.6 3 1011 s21 in Figure 5.21. 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 infrared λ (nm) 400 b. radiation with a wavelength 4.2 nm c. radiation with a frequency of 5.6 MHz 550 600 650 700 n 5 c/l 5 (3.00 3 108 m/s)/(6.15 3 1027 m) 5 4.88 3 1014 s21 Ephoton 5 hn 5 (6.626 3 10234 J ? s) (4.88 3 1014 s21) AM radio 5 3.23 3 10219 J d. radiation that travels at a speed of 3.00 3 108 m/s 51. What is the energy of an ultraviolet photon that has a wavelength of 1.18 3 1028 m? 46. What is the wavelength of electromagnetic radi- n 5 c/l 5 1012 ation having a frequency of 5.00 3 Hz? What kind of electromagnetic radiation is this? 3.00 3 10 m/s __ 5 6.00 3 10 8 25 5.00 3 1012 s21 m infrared radiation 47. What is the frequency of electromagnetic radiation having a wavelength of 3.33 3 1028 m? What type of electromagnetic radiation is this? __ 3.00 3 108 m/s 5 9.01 3 1015 s21 3.33 3 10-8 m UV radiation 3.00 3 10 m/s __ 5 2.54 3 10 8 Ephoton 5 hn 5 (6.626 3 10234 J ? s) (2.54 3 1016 s21) 5 1.68 3 10217 J 52. A photon has an energy of 2.93 3 10225 J. What is its frequency? What type of electromagnetic radiation is the photon? n 5 4.42 3 108 s21; TV or FM wave 53. A photon has an energy of 1.10 3 10213 J. What is the photon’s wavelength? What type of electromagnetic radiation is it? having a frequency of 1.33 3 1017 Hz and a wavelength of 2.25 nm? n 5 c/l c 5 ln 5 (2.25 3 10–9 m) (1.33 3 1017 s−1) (1.10 3 10 J) __ 213 n 5 Ephoton/h 5 48. What is the speed of an electromagnetic wave 16 s21 1.18 3 1029 m (6.626 3 10234 J ? s) 5 1.66 3 1020 s21 l 5 c/n 5 (3.00 3 108 m/s)/(1.66 3 1020 s21) 5 1.81 3 10212 m an X ray or gamma radiation c 5 3.00 3 108 m/s 74 Chemistry: Matter and Change • Chapter 5 Solutions Manual Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. any EM wave l 5 c/n 5 500 l ≈ 615 nm 5 6.15 3 1027 m X ray l 5 c/n 5 450 5 CHAPTER SOLUTIONS MANUAL 54. Spacecraft 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 3 109 km? velocity 5 distance d _ 5_ _ __ 1000 m d 5 2.72 3 109 km 3 5 2.72 3 1012 m 1 km (2.72 3 1012 m) 5 9070 s or 151 min t 5 d/v 5 (3.00 3 108 m/s) 55. Radio Waves If your favorite FM radio station broadcasts at a frequency 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? n 5 104.5 MHz 3 l 5 c/n 5 10 Hz _ 5 1.045 3 10 6 8 MHz Hz 3.00 3 10 m/s __ 5 2.871 m 8 1.045 3 108 s21 Ephoton 5 hn 5 (6.626 3 10234 J ? s)(1.045 3 108 s21) 5 6.924 2 10226 J Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. is needed to eject a photoelectron from atoms of platinum, which require at least 9.08 × 10219 J/photon? (9.08 3 10 J) __ 219 (6.626 3 5 1.37 3 1015 Hz 450 500 656 nm 550 600 650 700 750 The line is blue-green. Its frequency is 6.17 3 1014 s21 (3.00 3 108 m/s) 5 6.17 3 1014 s21 n 5 c/l 5 (4.86 3 1027 m) __ Section 5.2 Mastering Concepts 59. According to the Bohr model, how do electrons move in atoms? Electrons move in circular orbits around the nucleus. 60. What does n designate in Bohr’s atomic model? The quantum number n specifies the electron’s orbit. 61. What is the difference between an atom’s 56. Platinum What minimum frequency of light n 5 Ephoton/h 5 λ (nm) 400 486 nm Hydrogen’s Atomic Emission Spectrum t time 410 434 nm nm 10234 J ? s) 57. Eye Surgery The argon fluoride (ArF) laser used in some refractive eye surgeries emits electromagnetic radiation of 193.3 nm wavelength. What is the frequency of the ArF laser’s radiation? What is the energy of a single quantum of the radiation? n 5 1.55 3 1015 s21; E 5 1.03 3 10218 J (3.00 3 108 m/s) n 5 c/l 5 (1.933 3 1027 m) 5 1.55 3 1015 s21 __ Ephoton 5 hn 5 (6.626 3 10234J ? s)(1.55 3 1015 Hz) 5 1.03 3 10218 J ground state and an excited state? An atom’s ground state is its lowest energy state, while any energy state higher than the ground state is an excited state. 62. What is the name of the atomic model in which electrons are treated as waves? Who first wrote the electron wave equations that led to this model? The quantum mechanical model of the atom; Erwin Schrödinger 63. What is an atomic orbital? A three-dimensional region around the nucleus describing an electron’s probable location 64. What does n represent in the quantum mechan- ical model of the atom? n represents an orbital’s principal quantum number, which indicates the relative size and energy of the orbital. 58. One line in hydrogen’s emission spectrum has a wavelength of 486 nm. Examine Figure 5.22 to determine the line’s color. What is the line’s frequency? Solutions Manual Chemistry: Matter and Change • Chapter 5 75 5 CHAPTER SOLUTIONS MANUAL 65. Electron Transition According to the Bohr model shown in Figure 5.23, what type of electron-orbit transitions produce the ultraviolet lines in hydrogen’s Lyman series? Visible series (Balmer) atom describe the paths of an atom’s electrons? The quantum mechanical makes no description of the electrons’ paths. 74. Macroscopic Objects Why are you unaware of the wavelengths of moving objects such as automobiles and tennis balls? n=1+ n=2 n=3 Their wavelengths are too small to be seen. n=4 n=5 n=6 n=7 Ultraviolet series (Lyman) 73. How does the quantum mechanical model of the 75. Why is it impossible to know precisely the Infrared series (Paschen) The Lyman series is caused by electron transitions from Bohr’s higher energy orbits to the n 5 1 orbit velocity and position of an electron at the same time? The photon required to measure an electron’s velocity or position changes both the position and velocity of the electron. 66. How many energy sublevels are contained in each of the hydrogen atom’s first three energy levels? Section 5.3 Energy level 1 has one sublevel; energy level 2 has two sublevels; energy level 3 has three sublevels Mastering Concepts 76. In what sequence do electrons fill the atomic orbitals related to a sublevel? Px, Py, and Pz orbitals 68. What do the sublevel designations s, p, d, and f specify with respect to the atom’s orbitals? Their shapes Each orbital must contain a single electron before any orbital contains two electrons. 77. Rubidium Using Figure 5.24, explain why one electron in a rubidium atom occupies a 5s orbital rather than a 4d or 4f orbital? 7p 69. How are the five orbitals related to an atom’s d 7s 2 y2, z2 70. What is the maximum number of electrons an orbital may contain? two electrons 71. Describe the relative orientations of the orbitals Increasing energy xy, xz, yz, x2 Orbital filling sequence sublevel designated? 6s 5s 6p 5p 4p 4s 6d 5f 5d 4f 4d 3d 3p 3s 2p 2s related to an atom’s 2p sublevel. Lying along the x, y, and z coordinate axes, the three p orbitals are mutually perpendicular. 72. How many electrons can be contained in all the 1s The orbital related to the 5s sublevel has a lower energy than orbitals related to the 4d and 4f sublevels. orbitals related to an argon atom’s third energy level? Eight electrons 76 Chemistry: Matter and Change • Chapter 5 Solutions Manual Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 67. What atomic orbitals are related to a P sublevel? CHAPTER 5 78. What are valence electrons? How many of a magnesium atom’s 12 electrons are valence electrons? Valence electrons are the electrons in an atom’s outermost orbitals; 2 79. Light is said to have a dual wave-particle nature. What does this statement mean? Light exhibits wave-like behavior in some situations and particle-like behavior in others. 80. Describe the difference between a quantum and a photon. A quantum is the minimum amount of energy that can be lost or gained by an atom. A photon is a particle of light that carries a quantum of energy. 81. How many electrons are shown in the electron- dot structures of the following elements? a. carbon 4 b. iodine Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7 SOLUTIONS MANUAL Mastering Problems 84. List the aufbau sequence of orbitals from 1s to 7p. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p 85. Write orbital notations and complete electron configurations for atoms of the following elements. a. beryllium Be: 1s22s2 )( )( 1s b. aluminum Al: 1s22s22p63s23p1 )( )( )( )( )( )( 1s d. gallium )( )( 1s 83. Write the electron configuration and draw the orbital notation for atoms of oxygen and sulfur. oxygen: 1s22s22p4; The orbital diagram has five boxes with two arrows in the first three and single arrows in the last two. sulfur: [Ne]3s23p4; The orbital diagram has nine boxes with two arrows in the first seven and single arrows in the last two. 3s 3p ) 2s ) ) 2p d. sodium Na: 1s22s22p63s1 )( )( )( )( )( 1s 82. When writing the electron configuration nota- Pauli exclusion principle, aufbau principle, and Hund’s rule 2p N: 1s22s22p3 3 tion for an atom, what three principles or rules do you follow? 2s ) c. nitrogen c. calcium 2 2s 2s 2p ) 3s 86. Use noble-gas notation to describe the electron configurations of the elements represented by the following symbols. a. Kr Kr [Ar]4s23d104p6 b. P P [`Ne]3s23p3 c. Zr Zr [Kr]5s24d2 d. Pb Pb [Xe]6s24f145d106p2 Solutions Manual Chemistry: Matter and Change • Chapter 5 77 5 CHAPTER SOLUTIONS MANUAL 87. What elements are represented by each of the following electron configurations? a. 1s22s22p5 90. Draw electron-dot structures for atoms of each of the following elements. a. carbon • •C• • F b. [Ar]4s2 b. arsenic •• • A s• • Ca c. [Xe]6s24f4 c. polonium • • • •Po • • Nd d. potassium d. [Kr]5s24d105p4 •K Te e. barium e. [Rn]7s25f13 •Ba• Md 91. Arsenic An atom of arsenic has how many Br 88. Which of the following electron configuration notations describes an atom in an excited state? a. [Ar]4s23d104p2 b. [Ne]3s23p5 c. [Kr]5s24d1 d. [Ar]4s23d84p1 d 89. Which orbital diagram in Figure 5.25 is correct 18; 15; 4 92. Which element could have the ground-state electron-dot notation shown in Figure 5.26? a. manganese b. antimony → c. calcium d. samarium → → → → → → a. → for an atom in its ground state? electron-containing orbitals? How many of the orbitals are completely filled? How many of the orbitals are associated with the atom’s n 5 4 principal energy level? → → → → → 3d X → → → → 4s → → 3p → b. → 3s → → → → → 3d b 93. For an atom of tin in the ground state, write the → → → → 4s → → 3p → c. → 3s → → → → → 3d → → → 4s → → 3p → d. → 3s → → → → → → → 3s 3p 4s electron configuration using noble-gas notation and draw the electron-dot structure. 3d Sn b [Kr]5s24d105p2 78 Chemistry: Matter and Change • Chapter 5 Solutions Manual Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. f. 1s22s22p63s23p64s23d104p5 5 CHAPTER SOLUTIONS MANUAL Mixed Review 94. What is the maximum number of electrons that can be contained in an atom’s orbitals having the following principal quantum numbers? a. 3 18 5 d. f 7 98. Which elements have only two electrons in their electron-dot structures: hydrogen, helium, lithium, aluminum, calcium, cobalt, bromine, krypton, and barium? b. 4 32 helium, calcium, cobalt, barium c. 6 18 99. In Bohr’s atomic model, what electron orbit transition produces the blue-green line in hydrogen’s atomic emission spectrum? d. 7 8 n54→n52 95. What is the wavelength of light with a frequency of 5.77 31014 Hz? ________ (3.00 3 108 m/s) (5.77 3 1014 s21) 5 5.20 3 1027 m l 5 c/n 5 c. d 100. Zinc A zinc atom contains a total of 18 elec- trons in its 3s, 3p, and 3d orbitals. Why does its electron-dot structure show only two dots? The two dots are the atom’s two 4s valence electrons. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 96. Using the waves shown in Figure 5.27, identify the wave or waves with the following characteristics. 1. 3. 2. 4. a. longest wavelength longest wavelength: 4 b. greatest frequency greatest frequency: 3 c. largest amplitude largest amplitude: 1 and 3 d. shortest wavelength shortest wavelength: 3 97. How many orientations are possible for the orbitals related to each of the following sublevels? a. s 101. X Ray An X-ray photon has an energy of 3.01 3 10218 J. What is its frequency and wavelength? Ephoton 5 hn n 5 Ephoton/h 5 (3.01 2 10 J) __ 218 (6.626 3 5 4.54 3 1015 s21 10234 J ? s) c = ln (3.00 3 10 m/s) _vc 5 __ 5 6.60 3 10 8 l5 (4.54 3 28 1015 s21) m 102. Which element has the ground-state electron configuration represented by the noble-gas notation [Rn]7s1? francium 103. How did Bohr explain atomic emission spectra? Bohr proposed that atoms emit light of certain wavelengths, and energies, when electrons move from higher-energy orbits to lower-energy orbits. 1 b. p 3 Solutions Manual Chemistry: Matter and Change • Chapter 5 79 5 CHAPTER SOLUTIONS MANUAL 104. Infrared Radiation How many photons of infrared radiation with a frequency of 4.88 3 1013 Hz are required to provide an energy of 1.00 J? Ephoton 5 hv 5 3.23 3 ? s) (4.88 3 1013 s21) J per photon E 5_ n E (1.00 J) 5 ___ photon (6.626 3 10234 J ? s) 5 1.23 3 1015 s21 _ __ (3.00 3 108 m/s) c 5 2.43 3 1027 m l5 n 5 (1.23 3 1015 s21) 109. Describe Describe the shapes of the atomic 5 (6.626 3 10234 J 10220 (8.17 3 10 J) __ 219 5 orbitals shown in Figure 5.28. Specify their orientations and relate each orbital to a particular type of energy sublevel. z photon z (3.23 3 10220 J/photon) 5 3.10 3 1019 photons x x 105. Light travels slower in water than it does in air; however, its frequency remains the same. How does the wavelength of light change as it goes from air to water? 106. According to the quantum mechanical model py p orbital 1s orbital z y of the atom, what happens when an atom absorbs a quantum of energy? The energy of the atom increases as one or more electrons move into orbitals farther from the nucleus. x dxz Think Critically 107. Compare and Contrast Briefly discuss the difference between an orbit in Bohr’s model of the atom and an orbital in the quantum mechanical view of the atom. In the Bohr model, an orbit 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. 108. Calculate It takes 8.17 3 10219 J of energy to remove one electron from a gold surface. What is the maximum wavelength of light capable of causing this effect? n5 80 _ Ephoton h Chemistry: Matter and Change • Chapter 5 d orbital The first orbital is spherical and related to an s sublevel. The second orbital is dumbbellshaped, oriented along the y-axis, and related to a p sublevel. The third orbital consists of two, perpendicular dumbbell-shaped parts, lies in the xz plane, and is related to a d sublevel. 110. Infer Suppose that you live in a universe in which the Pauli exclusion principle states that a maximum of three, rather than two, electrons can occupy a single atomic orbital. Assuming that were the case, evaluate the new chemical properties of the elements lithium and phosphorus. Explain your evaluations. Both lithium and phosphorus would be noble gases. Lithium, with an electron configuration notation of 1s3, would be analogous to helium (1s2). Phosphorus, with an electron configuration notation of 1s32s32p9, would be analogous to neon (1s2, 2s2, 2p6). Solutions Manual Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Its wavelength decreases. y y 5 CHAPTER SOLUTIONS MANUAL Challenge Problem essay about the use of gases in neon signs and the colors produced by the gases. 111. Hydrogen atom The hydrogen atom’s energy is 26.05 3 10220 J when the electron is in the n 5 6 orbit and 22.18 3 10218 J when the electron is in the n 5 1. Calculate the wavelength of the photon emitted when the electron drops from the n 5 6 orbit to the n 5 1 orbit. Use the following values: h 5 6.626 3 10234 J?s and c 5 3.00 3 108 ms21 Student answers might include the following elements and colors: helium (yellow); neon (orange-red); sodium (yellow); argon (lavender); krypton (white); xenon (blue). 116. Rutherford’s Model Imagine that you are a scientist in the early twentieth century, and you have just learned the details of a new, nuclear model of the atom proposed by the prominent English physicist Ernest Rutherford. After analyzing the model, you discern what you believe to be important limitations. Write a letter to Rutherford in which you express your concerns regarding his model. Use diagrams and examples of specific elements to help make your point. hc _ (E 2E ) J ? s 3 3.00 3 10 m/s) 5 (6.626 3 10 ____ l5 1 6 234 8 (22.18 3 10218 J 2 (26.05 3 10220 J)) l 5 9.38 3 1028 m Cumulative Review 112. Round 20.56120 g to three significant figures. (Chapter 2) Answers will vary. 20.6 g 113. Identify each of the following as either chem- Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. ical or physical properties of the substance. (Chapter 3) a. mercury is a liquid at room temperature physical property b. sucrose is a white, crystalline solid physical property Additional Assessment Document-Based Questions Sodium Vapor When sodium metal is vaporized in a gas-discharge lamp, two closely spaced, bright yellow-orange lines are produced. Because sodium vapor lamps are electrically efficient, they are used widely for outdoor lighting, such as streetlights and security lighting. c. iron rusts when exposed to moist air chemical property d. paper burns when ignited chemical property Figure 5.29 shows the emission spectrum of sodium metal. The entire visible spectrum is shown for comparison. Data obtained from: Volland, W. March 2005. Spectroscopy, Element Identification and Emission Spectra. 114. 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) 64 electrons, 64 protons, 89 neutrons Writing in Chemistry 115. Neon Signs To make neon signs emit different colors, manufacturers often fill the signs with gases other than neon. Write an Solutions Manual Na Chemistry: Matter and Change • Chapter 5 81