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.
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CHAPTER
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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
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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?
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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
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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
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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
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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
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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
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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).
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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