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CHAPTER
5
Electrons in Atoms
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.
p. 136
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116A
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
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Transparency 5 L2 ELL
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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
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Laboratory Manual, pp. 33–36 L2
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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
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Transparency 18 L1
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Teaching
Transparency 16 PL2 ELL
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Study Guide for Content Mastery,
pp. 29–30 LS
L2
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Laboratory Manual,
pp. 37–40 L2
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Section Focus
Transparency 19 L1 ELL
Teaching
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Transparency 17 LS
L2 ELL
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Key to National Science Content Standards: UCP Unifying Concepts
and
Processes, A Science as Inquiry, B Physical Science, C Life Science,
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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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116B
CHAPTER
5
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.
116C
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
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Lesson Plans
Block Scheduling Lesson Plans
Texas Lesson Plans LS
Texas Block Scheduling Lesson Plans
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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.
116D
CHAPTER
CHAPTER
5
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
▲
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.
116
Chapter 5
DISCOVERY
LAB
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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.
116
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?
I
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
ELL
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
5.1 Light and Quantized Energy
117
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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P
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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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Inc.
5.1
Light Wav
es
Use with
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Section
17
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)
117
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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a
c
b
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
{bs`eQa”}
118
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
the nucleus should spiral into the
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in the process. L2 ELL P
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118
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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
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as they are reflected and
refracted by raindrops.
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Figure Caption Questions
c 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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Master L2 ELL
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119
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.
Pages 118–119
3(C), 3(E)
119
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
4
3 10
2
3
3 10
-2
3 10
Radio
-4
3 10
-6
Infrared
3 10
-8
3 10
Ultraviolet
4
6
3 10
-12
3 10
-14
Gamma rays
Microwaves
AM
-10
X rays
TV, FM
10
10
10
Frequency () in hertz
8
10
10
10
12
10
14
16
10
10
18
10
20
22
10
Energy increases
Electromagnetic Spectrum
120
Chapter 5 Electrons in Atoms
Portfolio
Portfolio
Resource Manager
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.
L2
Teaching Transparency 15 and Master
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120
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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)
5.1 Light and Quantized Energy
121
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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121
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
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for Designing an Experiment in
PASC, p. 23. L2
Enrichment
LS
Intrapersonal Have inter-
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
P
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.
LS
122
Chapter 5 Electrons in Atoms
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
LS
122
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
L2 ELL COOP LEARN
P
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
P
LS
P
LS
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VIDEODISC
Cosmic Chemistry:
Disc 1, Side 1
Still: Albert Einstein
{`qê—–}
Disc 3, Side 6 and
Disc 4, Side 8
{`@ÄQ◊}
123
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)
123
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.
124
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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124
P
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.
125
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)
125
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
500
550
600
650
700
750
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.
P
126
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
126
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
P
LS
Inc.
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
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Chemistry:
more en
Matter and
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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
127
M EETING I NDIVIDUAL N EEDS
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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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Pages 126–127
3(A), 3(C), 3(E), 5(A), 6(A)
127
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.
b
P
LS
VIDEODISC
Cosmic Chemistry
Disc 1, Side 1
Still: Niels Bohr
{`Hß¡—}
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Disc 1, Side1
Movie: Atomic Theories 0:41 s
Bohr’s atomic model
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3
Resource
Manager
Study Guide for Content
Mastery, pp. 27–28 L2
Solving Problems: A Chemistry
Handbook, Section 5.2
Section Focus Transparency 18
and Master L1 ELL
n
6
5
4
Energy of hydrogen atom
P
2
1
128
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
M EETING I NDIVIDUAL N EEDS
Gifted
P
P
LS LS
P
128
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
LS
P
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.
LS
L
n 3 wavelengths
n1
VIDEODISC
Cosmic Chemistry
Disc 1, Side 1
Still: Louis-Victor de Broglie
1 half–wavelength
n 5 wavelengths
n2
{`Hß—“}
2 half–wavelengths
Disc 1, Side 1
Still: Bohr-de Broglie Hydrogen
Orbits
n3
b Vibrating guitar string
Only multiples of half wavelengths allowed
{`H©qÿ}
n whole number (not allowed)
3 half–wavelengths
c Orbiting electron
Only whole numbers of wavelengths allowed
5.2 Quantum Theory and the Atom
129
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.
P
Lab Manual, pp. 33–36 L2
Pages 128–129
3(C), 3(E), 6(A)
L2
L1 ELL
LS
Resource
Manager
P
LS
129
LS
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 (25.9 130
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
130
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
P
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
analogy to the photon and
electron. L1 ELL
5.2 Quantum Theory and the Atom
LS
131
P
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
LS
LS
P
LS
Pages 130–131
3(C), 3(E), 5(A), 6(A)
131
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.
Resource
Manager
Challenge Problems, p. 5 L3
Teaching Transparency 16 and
Master L2 ELL
132
Hydrogen’s Atomic Orbitals
Figure 5-13
Enrichment
P
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.
P
P
LS
LS
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.
132
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
5.2 Quantum Theory and the Atom
Portfolio
Portfolio
133
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.
LS
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)
L2 ELL
LS
P
133
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?
P
134
16.
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
LS
Section 5.2
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,
134
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.
ELL
Vocabulary
electron configuration
aufbau principle
Pauli exclusion principle
Hund’s rule
valence electron
electron-dot structure
P
Section
Focus
Transpare
ncy
19
Electron
Configurat
ions
Use wit
h Chapte
r 5, Sectio
n 5.3
LS
P
LS
Inc.
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
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arena are
likely to
Imagine
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Chemistry:
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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.
135
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)
135
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
P
LS
LS
• 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.
Resource
Manager
P
• 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.
LS
LS P P
LSLS
C
1s
136
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
C05 18C 828378 a n
5.3 Electron Configurations
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.
137
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