Chapter 5 Organizer: Electrons in Atoms
")' )DEA
The atoms of each element have a unique arrangement of electrons.
Section Objectives
National
Standards
State/
Local
Standards
Resources to Assess Mastery
Section 5.1
1. Compare the wave and particle natures of
light.
2. Define a quantum of energy, and explain
how it is related to an energy change of
matter.
3. Contrast continuous electromagnetic
spectra and atomic emission spectra.
UCP.1, UCP.2;
A.1, A.2; B.1,
B.6; G.1, G.2,
G.3
Entry-Level Assessment
Focus Transparency 17
Progress Monitoring
Formative Assessment, p. 145
Reading Check, pp. 139, 141, 142, 144
Section Assessment, p. 145
Section 5.2
1. Compare the Bohr and quantum
mechanical models of the atom.
2. Explain the impact of de Broglie’s waveparticle duality and the Heisenberg
uncertainty principle on the current view
of electrons in atoms.
3. Identify the relationship among a
hydrogen atom’s energy levels, sublevels,
and atomic orbitals.
UCP.1, UCP.2;
A.2; B.1, B.6;
G.2, G.3
Entry-Level Assessment
Focus Transparency 18
Progress Monitoring
Formative Assessment, pp. 147, 150, 155
Reading Check, pp. 148, 150, 151, 152, 153, 154
Section Assessment, p. 155
Section 5.3
1. Apply the Pauli exclusion principle, the
aufbau principle, and Hund’s rule to write
electron configurations using orbital
diagrams and electron configuration
notation.
2. Define valence electrons, and draw
electron-dot structures representing an
atom’s valence electrons.
UCP.1, UCP.2;
A.1, A.2; B.1,
B.6; E.2; F.6;
G.2, G.3
Entry-Level Assessment
Focus Transparency 19
Progress Monitoring
Formative Assessment, pp. 157, 159, 162
Reading Check, pp. 157, 159
Section Assessment, p. 162
Summative Assessment
Chapter Assessment, p. 166
ExamView® Assessment Suite CD-ROM
134A
Suggested Pacing
Period
Section 5.1
Section 5.2
Section 5.3
Assessment
Single
2
2
1
1
Block
1
1
0.5
0.5
Leveled Resources
Science Notebook 5.1 OL
FAST FILE Chapter Resources:
MiniLab Worksheet, p. 12 OL
ChemLab Worksheet, p. 4 OL
Study Guide, p. 14 OL
Transparencies:
Section Focus Transparency 17 BL EL
Teaching Transparency 15 OL EL
Math Skills Transparency 5 OL EL
Customize any lab with
the LabManager™
CD-ROM.
Lab Materials
Launch Lab, p. 135: wrapped box
10 min
MiniLab, p. 144: cotton swabs, lithium chloride,
Bunsen burner, sodium chloride, potassium chloride,
calcium chloride, strontium chloride, unknown
solution
30 min
ChemLab, p. 164: ring stand with clamp, 40-W
tubular lightbulb, light socket with power cord,
275-mL polystyrene culture flask, Flinn C-Spectra®
or similar diffraction grating, red food coloring,
green food coloring, blue food coloring, yellow food
coloring, set of colored pencils, spectrum tubes,
spectrum-tube power supply
45 min
Science Notebook 5.2 OL
FAST FILE Chapter Resources:
Study Guide, p. 16 OL
Transparencies:
Section Focus Transparency 18 BL EL
Teaching Transparency 16 OL EL
Additional Print and
Technology Resources
Technology:
ExamView® Assessment Suite CD-ROM
StudentWorks™ Plus DVD-ROM
TeacherWorks™ Plus DVD-ROM
Virtual Labs CD-ROM
Video Labs DVD
What’s CHEMISTRY Got To Do With It? DVD
Interactive Classroom DVD-ROM
LabManager™ CD-ROM
Assessment:
Performance Assessment in the Science
Classroom
Challenge Problems AL
Supplemental Problems BL OL
Chapter Test (Scaffolded)
FAST FILE Resources:
Section Focus Transparency Masters
Math Skills Transparency Masters
and Worksheets
Teaching Transparency Masters
and Worksheets
Additional Resources:
Solving Problems: A Chemistry Handbook
Cooperative Learning in the Science
Classroom
Lab and Safety Skills in the Science
Classroom
glencoe.com
Lab Resources:
Laboratory Manual OL
CBL Laboratory Manual OL
Small-Scale Laboratory Manual OL
Forensics Laboratory Manual OL
Science Notebook 5.3 OL
FAST FILE Chapter Resources:
Study Guide, p. 18 OL
Transparencies:
Section Focus Transparency 19 BL EL
Teaching Transparency 17 OL EL
BL Below Level
OL On Level
AL Advanced Learners
EL English Learners
COOP LEARN Cooperative Learning
134B
Electrons in Atoms
BIG Idea
Electron Arrangements and
Properties To introduce this chap-
ter Big Idea, have students give the
symbols and names of the elements
with atomic numbers 17, 18, and 19.
17, Cl, chlorine; 18, Ar, argon; 19, K, potassium
Compare and contrast the radically
different properties of the three
elements and point out that each
successive element has one more
proton and one more electron than
the previous element. Chlorine is a
yellow-green gas at room temperature and
is very reactive. Argon, a gas used in incandescent bulbs, is very unreactive. Potassium,
a metal at room temperature, is so reactive
that it must be stored in kerosene or oil to
prevent reaction with the oxygen and water
in the air. Explain that the different
properties of the three elements can
be attributed to the arrangements
of electrons in their atoms.
Tie to Previous
Knowledge
Have students review the following
concepts before studying this
chapter.
Chapter 4: atomic structure
Use the Photo
BIG Idea The atoms of
each element have a unique
arrangement of electrons.
5.1 Light and Quantized
Energy
Absorption spectrum
of Betelgeuse
MAIN Idea Light, a form of
electromagnetic radiation, has
characteristics of both a wave
and a particle.
5.2 Quantum Theory and
the Atom
MAIN Idea Wavelike properties of
electrons help relate atomic emission
spectra, energy states of atoms, and
atomic orbitals.
5.3 Electron Configuration
MAIN Idea A set of three rules
can be used to determine electron
arrangement in an atom.
ChemFacts
• Scientists use stellar absorption
spectra to identify a star’s elemental
composition and classify it into one
of the several spectral types.
• The properties of absorption spectra
are also related to a star’s surface
temperature.
• Stellar spectra revealed that stars
are made out of the same elements
as those found on Earth.
• There are around 600 dark lines in
the Sun’s absorption spectra.
Spectra Have students compare
and contrast the Betelgeuse and
Rigel emission spectra with the
visible portion of the electromagnetic
spectrum shown in Figure 5.5. The
stars’ emission spectra contain only certain
colors, while the visible portion of the electromagnetic spectrum contains all the colors.
Absorption
spectrum of Rigel
Interactive
C05_CO_874637.indd
Classroom
1
This DVD-ROM is an editable Microsoft® PowerPoint® presentation that includes:
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134
Chapter 5 • Electrons in Atoms
2/1/07
12:38:39
Start-Up Activities
LAUNCH Lab
RUBRIC available at glencoe.com
Purpose Students will make
LAUNCH Lab
Electron Configuration Make a
Foldable to help you summarize
the three rules that define how
electrons are arranged in an atom.
How do you know
what is inside an atom?
Imagine that it is your birthday, and there is one wrapped
present that is different from all the rest. Unlike the other
gifts that you can open, you can only guess what is inside
this package. In trying to determine the structure of the
atom, early chemists had a similar experience. How good
are your skills of observation and deduction?
observations using all the senses
except sight.
Safety Precautions Approve lab
safety forms before work begins.
STEP 1 Fold a sheet
of paper in half lengthwise.
Make the back edge about
2 cm longer than the
front edge.
Disposal Keep boxes for use
next year.
Teaching Strategies
• Try to use objects in the box that
are simple, but challenging.
• When students are through with
the lab, you might want to identify
the objects, or, to demonstrate that
chemists cannot always see what
they are looking for, you might
want to leave the object’s identity a
mystery!
STEP 2 Fold into thirds.
STEP 3 Unfold and
cut along the folds of the
top flap to make three tabs.
Procedure
1. Read and complete the lab safety form.
2. Obtain a wrapped box from your instructor.
3. Using as many observation methods as you can,
and without unwrapping or opening the box, try
to determine what is inside the box.
4. Record the observations you make throughout this
discovery process.
Analysis
1. Describe how you were able to determine
characteristcs such as the size, shape, and
composition of the object in the box.
2. Indicate what senses you used to make your
observations.
3. Discuss why it is hard to determine what type
of object is in the box without opening it.
Inquiry After reading the chapter, design another
investigation that illustrates the difficulties associated
with the study of subatomic particles.
Analysis
1. Answers will vary, but may include determining
9 PMC05_CO_874637.indd
2 whether the object inside has the same size and
shape as the box, lifting the box to estimate its
weight, shaking the box to sense any motion of the
object inside the box,trying to detect odors from the
box, and listening for sounds from inside the box.
2. Answers will will likely include include hearing,
touch, and smell
3. Students will determine that observations typically
rely heavily upon sight, although touch and hearing
are somewhat useful.
STEP 4 Label the
tabs as follows: Aufbau
Principle, Pauli Exclusion
Principle, and Hund’s Rule.
Expected Results Results will
vary. Students should try to use
senses other than sight to determine
the relative size, mass, shape, and
number of objects.
Electron Configuration
Aufbau
Principle
Pauli
Exclusion
Principle
Hund’s
Rule
&/,$!",%3 Use this Foldable with Sections 5.3. As
you read this section, summarize each rule under the
appropriate tab.
Customize this lab with
the LabManager™
CD-ROM.
Visit glencoe.com to:
υ study the entire chapter online
υ
explore
υ
take Self-Check quizzes
υ
use the Personal Tutor to work Example
Problems step-by-step
υ
access Web Links for more information,
projects, and activities
υ
find the Try at Home Lab, Observing
Light’s Wave Nature
Inquiry Answers will vary depending on what students choose to investigate.
2/1/07
12:39:24 PM
Chapter 5 • Electrons in Atoms
135
Section 5.1
1 Focus
Focus Transparency
Before presenting the lesson, project
Section Focus Transparency 17 and
have students answer the accompanying questions. BL EL
Section 5.1
Objectives
◗ Compare the wave and particle
natures of light.
◗ Define a quantum of energy, and
explain how it is related to an energy
change of matter.
◗ Contrast continous electromagnetic
spectra and atomic emission spectra.
Review Vocabulary
MAIN Idea
Electromagnetic Radiation’s
Dual Nature Ask students to
envision the way that water molecules
on a lake’s surface behave as a water
wave travels across the lake. The water
molecules move up and down as the wave
travels across the lake’s surface. Then, ask
what happens when the water wave
reaches the lake’s shore. Some of the
wave’s energy is transferred to the particles
that make up the shore, often shifting or moving them. Explain that as a ray of light
(a form of electromagnetic radiation)
travels from place to place, electric
and magnetic fields move from side
to side and up and down. Also,
explain that when light transfers
some of its energy to matter—for
example, when sunlight touches
one’s dark clothing—the energy is
absorbed in certain amounts, called
quanta. In other words, light seems
to travel as a wave but is emitted and
absorbed by matter in only certain,
definite amounts. OL
radiation: the rays and particles—
alpha particles, beta particles, and
gamma rays—that are emitted by
radioactive material
New Vocabulary
electromagnetic radiation
wavelength
frequency
amplitude
electromagnetic spectrum
quantum
Planck’s constant
photoelectric effect
photon
atomic emission spectrum
■ Figure 5.1 Different elements can
have similar reactions with water.
Light and Quantized Energy
MAIN Idea Light, a form of electromagnetic radiation, has
characteristics of both a wave and a particle.
Real-World Reading Link Have you ever come inside on a cold day, headed
for the kitchen, and popped a cold snack into the microwave oven? When the
microwaves reached your snack, small packets of energy warmed it in practically
no time at all.
The Atom and Unanswered Questions
After discovering three subatomic particles in the early 1900s, scientists
continued their quest to understand atomic structure and the arrangement of electrons within atoms.
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. 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. Rutherford’s nuclear model did
not begin to account for the differences and similarities in chemical
behavior among the various elements.
For example, consider the elements lithium, sodium, and potassium,
which are found in different periods on the periodic table but have similar chemical behaviors. All three elements appear metallic in nature,
and their atoms react vigorously with water to liberate hydrogen gas.
In fact, as shown in Figure 5.1, both sodium and potassium react so
violently that the hydrogen gas can ignite and even explode.
In the early 1900s, scientists began to unravel the puzzle of chemical
behavior. They 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. To understand this relationship and the nature of
atomic structure, it will be helpful to first understand the nature of light.
2 Teach
Concept Development
Matter Explain the concept that
matter is made up of atoms. For
example, water contains two atoms
of hydrogen for every atom of
oxygen and 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.
136 Chapter 5 • Electrons in Atoms
Lithium
Sodium
Potassium
Differentiated Instruction
1
Hearing Impaired
Help students visualize
C05_S1_874637.indd
the characteristics of various types of electromagnetic waves by writing the following
three items (A–C) and questions (1–3) on
the chalkboard:
A. Visible light;
B. Microwaves;
C. Radio waves
1. Which moves through air at such a speed
that it travels around Earth approximately
seven times in one second? A, B, and C. Note:
Visible light, microwaves, and radio waves are three
forms of electromagnetic radiation. All three travel at
a speed of 3.00 × 10 8 m/s in a vacuum and almost
the same speed in air.
2. Which might have a wavelength equal to
the length of three football fields? C, radio
waves
3. Which might have a wavelength equal to
the width of a pencil? B, microwaves OL
2/1/07
2:09:51
The Wave Nature of Light
Quick Demo
Visible light is a type of electromagnetic radiation—a form of energy
that exhibits wavelike behavior as it travels through space. Other examples of electromagnetic radiation include microwaves that cook your
food, X rays that doctors and dentists use to examine bones and teeth,
and waves that carry radio and television programs into homes.
Wave Characteristics Bring
in a coiled spring toy and attach
it securely to an object on one
side of the room. Demonstrate
wave characteristics, 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
more energy is needed 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 decreasing,
and energy is increasing. BL OL EL
Characteristics of waves All waves can be described by several
characteristics, a few of which you might be familiar with from everyday
experience. You might have seen concentric waves when dropping an
object into water, as shown in Figure 5.2a.
The wavelength (represented by λ, 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 × 10 -9 m).
The frequency (represented by ν, the Greek letter nu) is the number
of waves that pass a given 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, (1/s) or (s -1). When expressed
in this way, the term waves is understood. For example, 652 Hz =
652 waves/second = 652/s = 652 s -1.
The amplitude of a wave is the wave’s height from the origin to a
crest, or from the origin to a trough, as illustrated in Figure 5.2b.
Wavelength and frequency do not affect the amplitude of a wave.
All electromagnetic waves, including visible light, travel at a speed
of 3.00 × 10 8 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 (λ) and its frequency (ν).
Electromagnetic Wave Relationship
c = λν
c is the speed of light in a vacuum.
λ is the wavelength.
ν is the frequency.
■
The product of the frequency and the wavelength is equal to the speed of light in a vacuum.
a
1 PMC05_S1_874637.indd
Caption Question Fig. 5.2
Students should point to the correct parts of
the photo.
Content Background
Figure 5.2 a. The concentric waves in the water show the characteristic
properties of all waves. b. Amplitude, wavelength, and frequency are the main
characteristics of waves.
Identify a crest, a trough, and one wavelength in the photo.
■
Value of C In the formula c = λν, ν
(the frequency of an electromagnetic
wave) can be measured precisely
with lasers and atomic clocks. The λ
(wavelength) of an electromagnetic
wave, however, cannot be measured
with such extreme precision.
Accordingly, the International
Commission of Weights and
Measures decided in 1983 to make
the speed of light a defined quantity.
c, the speed of light in a vacuum, is
defined as exactly 299,792,458 m/s.
However, c = 3.00 × 10 8 is sufficiently accurate for most purposes.
b
Wavelength (λ)
Crest
Amplitude
Wavelength (λ)
Origin
Trough
Chemistry Project
2
Classical Physics and Electrons
in Atoms Have students research and
2/1/07
1:40:41 PM
explain how electrons in atoms should
behave according to classical physics.
Have them draw diagrams illustrating
their findings. Negatively charged electrons
orbiting the nucleus should spiral into the positively
charged nucleus, giving off energy in the process.
OL EL
Section 5.1 • Light and Quantized Energy
137
■
Caption Question Fig. 5.3
Wavelength and frequency do not affect the
amplitude of a wave.
Math in Chemistry
■ Figure 5.3 These waves illustrate
the relationship between wavelength and
frequency. As wavelength increases,
frequency decreases.
Infer Does frequency or wavelength
affect amplitude?
Wavelength and Frequency
Shorter
wavelength
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 = λν is valid only if the quantities
λ and ν are inversely related.
Lower frequency
Higher frequency
Although the speed of all electromagnetic waves in a vacuum is the
same, waves can have different wavelengths and frequencies. As you can
see from the equation on the previous page, wavelength and frequency
are inversely related; in other words, as one quantity increases, the other
decreases. To better understand this relationship, examine the two
waves illustrated in Figure 5.3. Although both waves travel at the speed
of light, you can see that the red wave has a longer wavelength and lower
frequency than the violet wave.
Visual Learning
Figure 5.3 Have students count
the number of wavelengths shown in
the two waves, both in the same total
length. One wave has four wavelengths;
the other has seven wavelengths. Ask
how the wavelength of the higherfrequency wave compares with that
of the lower-frequency wave. The
wavelength is 4/7 that of the lower-frequency
wave. Ask how the frequency of the
higher-frequency wave compares
with that of the lower-frequency
wave. The frequency is 7/4 that of the lowerfrequency wave. Use these answers to
reinforce the inverse relationship
between wavelength and frequency.
OL
Longer
wavelength
Electromagnetic spectrum Sunlight, which is one example of
white light, contains a nearly continuous range of wavelengths and
frequencies. White light passing through a prism separates into a
continuous spectrum of colors similar to the spectrum in Figure 5.4.
These are the colors of the visible spectrum. The spectrum is called continuous because each point of it corresponds to a unique wavelength
and frequency. You might be familiar with the colors of the visible spectrum. 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 spectrum that arches across the sky.
■ Figure 5.4 When white light passes
through a prism, it is separated into a continuous spectrum of its different components—red, orange, yellow, green, blue,
indigo, and violet light.
Chemistry Journal
C05_S1_874637.indd
3
Frequencies and Daily Living 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 phenomena
and, when possible, quantify the frequencies.
BL OL
138 Chapter 5 • Electrons in Atoms
2/1/07
1:40:44
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, includes 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 bend varies with the
wavelengths as they pass through the prism, resulting in the sequence of
the colors red, orange, yellow, green, blue, indigo, and violet. In examining the energy of the radiation shown in Figure 5.5, 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.
Because all electromagnetic waves travel at the same speed in a given
medium, you can use the formula c = λν to calculate the wavelength or
frequency of any wave.
Careers In chemistry
Quick Demo
Spectroscopist Spectroscopy is
the study of the spectra absorbed or
emitted by matter. Because each element’s spectrum is unique, it is like a
fingerprint. Astrophysicists use spectroscopy to investigate what a star,
such as the Sun, is made of. A star’s
absorption spectrum shows many
dark lines, which allow spectroscopists to identify the elements present
in the star. For more information on
chemistry careers, visit glencoe.com.
Reflection and Refraction
Project the beam from a highintensity projector onto 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 as they are
reflected and refracted by
raindrops.
Reading Check State the relationship between the energy and the
frequency of electromagnetic radiation.
to Physics
Electromagnetic radiation from diverse origins constantly bombards us. In addition to the radiation from the Sun,
human activities also produce radiation which include radio and TV
signals, phone relay stations, lightbulbs, medical X-ray equipment, and
particle accelerators. Natural sources on Earth, such as lightning, natural radioactivity, and even the glow of fireflies, also contribute. Our
knowledge of the universe is based on electromagnetic radiation emitted by distant objects and detected with instruments on Earth.
Connection
Figure 5.5 The electromagnetic spectrum covers a wide range of frequencies.
The visible-light section of the spectrum is very narrow. As frequency and energy increase,
wavelength decreases.
■
4 PMC05_S1_874637.indd
Reading Check The energy
increases when the frequency increases.
Content Background
Electromagnetic Waves An
electromagnetic wave consists of
oscillating electric and magnetic
fields. The two fields oscillate at right
angles to one another. For example,
if the electric field oscillates up and
down, the magnetic field oscillates
from side to side. Both the electric
and magnetic fields oscillate at right
angles to the direction of propagation of the electromagnetic wave.
Visible light
Wavelength increases
Wavelength (λ) in meters
4
3 × 10
3 × 10
2
3
−2
3 × 10
3 × 10
Radio
−4
−6
3 × 10
Infrared
−8
3 × 10
Ultraviolet
Microwaves
4
6
8
10
10
10
Frequency (ν) in hertz
10
10
3 × 10
−10
3 × 10
−12
3 × 10
−14
Gamma rays
X rays
12
10
14
10
16
10
18
10
20
10
22
10
Energy/frequency increases
Electromagnetic Spectrum
Chemistry Project
4
Electromagnetic Waves and Uses
2/1/07
1:40:49 PM
Have students research and discuss the
many ways humans use electromagnetic
waves to transmit information and carry
energy from place to place. OL
Section 5.1 • Light and Quantized Energy
139
EXAMPLE Problem 5.1
IN-CLASS Example
Question The red-colored light in
a fireworks display might be produced when strontium salts are
heated. What is the frequency of
such red light with a wavelength of
6.50 × 10 -7 m?
1
Solving Algebraic
Equations
pages 954–955
Analyze the Problem
You are given the frequency of a microwave. You also know that because microwaves are
part of the electromagnetic spectrum, their speeds, frequencies, and wavelengths are
related by the formula c = λν. The value of c is a known constant. First, solve the
equation for wavelength, then substitute the known values and solve.
Known
ν = 3.44 × 10 9 Hz
c = 3.00 × 10 8 m/s
Answer 4.62 × 10 14 s -1
ν = (3.00 × 10 8 m/s) ÷ 6.50 × 10 -7 m
= 4.62 × 10 14 s -1
Math Handbook
Calculating Wavelength of an EM Wave Microwaves are used to cook food
and transmit information. What is the wavelength of a microwave that has a
frequency of 3.44 × 10 9 Hz?
2
Unknown
λ=?m
Solve for the Unknown
Solve the equation relating the speed, frequency, and wavelength of an electromagnetic
wave for wavelength (λ).
PRACTICE Problems
Have students refer to p. 993 for
complete solutions to odd-numbered
problems. The complete solutions for
all problems can be found in the
Solutions Manual.
1.
2.
3.
4.
6.12 × 10 14 Hz
2.61 × 10 18 Hz
3.00 × 10 8 m/s
FM: λ = 3.17 m; AM: λ = 366 m
FM: drawing b; AM: drawing a
Reinforcement
Electromagnetic waves When
the people in a stadium do the
“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. Thus, the energy
travels around the stadium but
not the people. In the same way,
an electromagnetic wave carries
energy but not matter.
c = λν
State the electromagnetic wave relationship.
λ = c/ν
Solve for λ.
3.00 × 10 8 m/s
λ = __
3.44 × 10 9 Hz
Substitute c = 3.00 × 10 8 m/s and ν= 3.44 × 10 9 Hz.
Note that hertz is equivalent to 1/s or s -1.
3.00 × 10 8 m/s
λ = __
9 -1
Divide numbers and units.
3.44 × 10 s
λ = 8.72 × 10 -2 m
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.
PRACTICE Problems
Extra Practice Page 978 and glencoe.com
1. Objects get their colors from reflecting only certain wavelengths when hit with white light.
Light reflected from a green leaf is found to have a wavelength of 4.90 × 10 -7 m.
What is the frequency of the light?
2. X rays can penetrate body tissues and are widely used to diagnose and treat disorders
of internal body structures. What is the frequency of an X ray with a wavelength of
1.15 × 10 -10 m?
3. After careful analysis, an electromagnetic wave is found to have a frequency of
7.8 × 10 6 Hz. What is the speed of the wave?
4. Challenge While an FM radio station broadcasts at a frequency of 94.7 MHz, an
AM station broadcasts at a frequency of 820 kHz. What are the wavelengths of the
two broadcasts? Which of the drawings below corresponds to the FM station?
To the AM station?
a
b
Differentiated Instruction
C05_S1_874637.indd
5
English Learners Have English learners
look up and then explain the meanings
of several key English terms used in this
section: radiation, spectrum, constant,
effect, emission, quantum. Then, ask them
to use the terms in a paragraph about
waves. EL BL
140
Chapter 5 • Electrons in Atoms
2/1/07
1:40:51
The Particle Nature of Light
Assessment
While considering light as a wave explains 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 light of a specific frequency
shines on them. Scientists realized that a new model or a revision of
the wave model of light was needed to address these phenomena.
The quantum concept When objects are heated, they emit glowing light. Figure 5.6 illustrates this phenomenon with iron. A piece of
iron appears dark gray at room temperature, glows red when heated sufficiently, and turns orange, then bluish in color at even higher temperatures. As you will learn in later chapters, 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. In 1900, German physicist Max Planck (1858–1947) began
searching for an explanation of this phenomenon as he studied the light
emitted by heated objects. His study led him to a startling conclusion:
matter can gain or lose energy only in small, specific amounts called
quanta. A quantum is the minimum amount of energy that can be
gained or lost by an atom.
Performance Have students
develop an investigation 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. OL
VOCABULARY
ACADEMIC VOCABULARY
Phenomenon
an observable fact or event
During rainstorms, electric currents
often pass from the sky to Earth—
a phenomenon we call lightning.
Enrichment
Optical Pyrometer Have interest-
ed students research and make a
class presentation or report on the
operation of an optical pyrometer—a
device that measures extremely high
temperatures by the wavelengths of
light emitted by the objects. OL
Reading Check Explain why the color of heated objects changes with
their temperature.
Reading Check TThe temperature
of an object is a measure of the average
kinetic energy of its particles. As the
object becomes hotter, it emits light at
higher frequencies, and therefore of different colors.
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 think 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.
1 PMC05_S1_874637.indd
■
Caption Question Fig. 5.6
When the temperature increases, the energy
increases, thus the frequency increases.
This means that the wavelength decreases.
Cooler metal is red, hotter metal is bluish.
■ Figure 5.6 The wavelength of the
light emitted by heated metal, such as the
iron at left, depends on the temperature. At
room temperature, iron is gray. When heated,
it first turns red, then glowing orange.
Explain the relationship between the
color and the temperature of the metal.
Chemistry Journal
6
What’s
a quantum? Have students
2/1/07
1:40:55 PM
research the reactions of Planck’s contemporaries to his quantum concept. Have
them list and explain the reactions of
Planck’s contemporaries in their
chemistry journals. OL
Section 5.1 • Light and Quantized Energy
141
Planck proposed that the energy emitted by hot objects was quantized. He then went further and demonstrated mathematically that a
relationship exists between the energy of a quantum and the frequency
of the emitted radiation.
Concept Development
Chemical Behavior 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 to the
arrangement of electrons within
their atoms.
Build a Model
Energy of a Quantum
E quantum = hν
Reading Check The photoelectric
effect is the phenomenon of electron
emission from the surface of metals in
the presence of light whose frequency is
at or above a certain value.
ν represents frequency.
The energy of a quantum is given by the product of Planck’s constant and the frequency.
Real-World Chemistry
The Photoelectric Effect
Photoelectric Effect Have stu-
dent 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.
OL EL COOP LEARN
E quantum represents energy.
h is Planck’s constant.
Solar energy is sometimes used
to power road signs. Photovoltaic
cells use the photoelectric effect
to convert the energy of light into
electric energy.
Planck’s constant has a value of 6.626 × 10 -34 J·s, where J is the symbol for joule, the SI unit of energy. The equation shows that the energy
of radiation increases as the radiation’s frequency, v, increases.
According to Planck’s theory, for a given frequency, v, matter can
emit or absorb energy only in whole-number multiples of hv; that is,
1hv, 2hv, 3hv, 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 whole numbers of
blocks. Similarly, matter can have only certain amounts of energy—
quantities of energy between these values do not exist.
The photoelectric effect Scientists also knew that the wave model
of light 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, or higher than
a certain frequency, shines on the surface, as shown in Figure 5.7.
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. In reality, a metal will not eject photoelectrons below a specific frequency of incident light. For example, no
matter how intensely or how long it shines, light with a frequency less
than 1.14 × 10 15 Hz does not eject photoelectrons from silver. But even
dim light with a frequency equal to or greater than 1.14 × 10 15 Hz ejects
photoelectrons from silver.
Reading Check Describe the photoelectric effect.
■ Figure 5.7 The photoelectric
effect occurs when light of a certain
frequency strikes a metal surface
and ejects electrons. When the
intensity of the light increases,
the number of electrons ejected
increases. When the frequency
(energy) of the light increases, the
energy of the ejected electrons
increases.
Electron ejected
from surface
Incident beam of light
Metal surface
Electrons
Chemistry Project
C05_S1_874637.indd
7
Sunscreens Because the molecules
in sunscreens vibrate and absorb certain
frequencies of ultraviolet (UV) light, the
sunscreens can help protect people from
the harmful effects of sun exposure. Have
students research and write a description
of the newest types of sunscreens, the
molecules involved in each, and the
wavelengths of UV light absorbed. OL
142
Chapter 5 • Electrons in Atoms
2/1/07
1:40:57
Light’s dual nature To explain the photoelectric effect, Albert
Einstein proposed in 1905 that light has a dual nature. A beam of light
has wavelike and particlelike properties. It can be thought of as a beam
of bundles of energy called photons. A photon is a massless particle that
carries a quantum of energy. Extending Planck’s idea of quantized energy, Einstein calculated that a photon’s energy depends on its frequency.
IN-CLASS Example
Question A new sunscreen is
reputed to protect against the
UV-A waves that can cause skin cancer. How much energy is possessed
by a single photon of UV-A electromagnetic radiation with frequency
9.231 × 10 14 s -1?
Energy of a Photon
E photon represents energy.
h is Planck’s constant.
ν represents frequency.
E photon = hν
The energy of a photon is given by the product of Planck’s constant and the frequency.
Answer 6.116 × 10 -19 J
Einstein also proposed that the energy of a photon must have a certain
threshold value to cause the ejection of a photoelectron from the surface
of the metal. Thus, even small numbers of photons with energy above
the threshold value will cause the photoelectric effect. Einstein won the
Nobel Prize in Physics in 1921 for this work.
E photon = (6.626 × 10 -34 J·s)( 9.231 × 10 14 s -1)
= 6.116 × 10 -19 J
PRACTICE Problems
EXAMPLE Problem 5.2
Math Handbook
Calculate the Energy of a Photon Every object gets its color by reflecting a
certain portion of incident light. The color is determined by the wavelength of the
reflected photons, thus by their energy. What is the energy of a photon from the
violet portion of the Sun’s light if it has a frequency of 7.230 × 10 14 s -1?
1
Analyze the Problem
Known
ν = 7.230 × 10 14 s -1
h = 6.626 × 10 -34 J·s
2
5. a. 4.19 × 10 -13 J
b. 6.29 × 10 -20 J
c. 6.96 × 10 -18 J
6. 4.42 × 10 -17 J
7. 1.59 × 10 -24 J
Unknown
E photon = ? J
Solve for the Unknown
E photon = hν
E photon = (6.626 ×
State the equation for the energy of a photon.
10 -34
J·s)(7.230 ×
10 14
s -1)
E photon = 4.791 × 10 -19 J
3
Have students refer to p. 993 for
complete solutions to odd-numbered
problems. The complete solutions for
all problems can be found in the
Solutions Manual.
Operations with
Scientific Notation
page 948
Substitute h = 6.626 × 10 -34 J·s and ν = 7.230 × 10 14 s -1.
Multiply and divide numbers and units.
GLENCOE Technology
Evaluate the Answer
Virtual Labs CD-ROM
As expected, the energy of a single photon of light is extremely small. The unit is joules,
an energy unit, and there are four significant figures.
PRACTICE Problems
Chemistry: Matter and Change
Video: Flame Test
Video: The Aurora
Video: Atomic Emissions
Extra Practice Page 978 and glencoe.com
5. Calculate the energy possessed by a single photon of each of the following types of
electromagnetic radiation.
a. 6.32 × 10 20 s –1
b. 9.50 × 10 13 Hz
c. 1.05 × 10 16 s –1
6. The blue color in some fireworks occurs when copper(I) chloride is heated to
approximately 1500 K and emits blue light of wavelength 4.50 × 10 2 nm. How much
energy does one photon of this light carry?
7. Challenge The microwaves used to heat food have a wavelength of 0.125 m. What is the
energy of one photon of the microwave radiation?
7 PMC05_S1_874637.indd
Differentiated Instruction
8
Advanced
Learners Have students
2/1/07
1:41:10 PM
research and perhaps explain to the
class how astrophysicists determine which
elements make up Earth’s Sun and other
stars. In general, because a star is made of hot,
glowing gases, its emitted light can be gathered by
a telescope and analyzed. From the atomic emission
and absorption spectra of the light, the elements
present in the star can be determined. AL
Section 5.1 • Light and Quantized Energy
143
Atomic Emission Spectra
Reading Check When excited,
atoms return to their ground state
by emitting light, which corresponds
to a certain transition of electrons
between orbitals. The lines in the
emission spectrum of an element
correspond to the transitions.
See the MiniLab worksheet in your
FAST FILE.
RUBRIC available at glencoe.com
Purpose Students will observe the
colors of light emitted when certain
compounds are burned in a flame.
Process Skills classify, compare
and contrast, observe and infer
Safety Precautions Approve
lab safety forms before work begins.
Remind students to use caution with
the flame. Although the wet swab
will not burn easily, have a beaker of
tap water set out for students to
extinguish the hot swabs. Review
MSDS’s for all hazardous chemicals
used in this lab.
Disposal Swabs should be thrown
in the trash, not into the sink. Check
local regulations to determine if
the chemicals used in the lab are
permitted in the school trash. If
not, waste must be sent to a landfill
site approved for the disposal of
chemical and hazardous wastes.
Have you ever wondered how light is produced in the
glowing tubes of neon signs? This process is 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 atoms return to their
stable state by emitting light to release that energy.
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 corresponding to the frequencies of
the radiation emited by the atoms of neon. It is not a
continuous range of colors, as in the visible spectrum
of white light.
Identify Compounds
How do flame colors vary for different
elements?
Procedure
1. Read and complete the lab safety form.
2. Dip one of six cotton swabs into the lithium
chloride solution. Put the swab into the
flame of a Bunsen burner. Observe the color
of the flame, and record it in your data table.
3. Repeat Step 2 for each of the metallic chloride solutions (sodium chloride, potassium
chloride, calcium chloride, and strontium
chloride). Record the color of each flame in
your data table.
4. Compare your results to the flame tests
shown in the Elements Handbook.
5. Repeat Step 2 using a sample of unknown
solution obtained from your teacher. Record
the color of the flame produced.
6. Dispose of the used cotton swabs as directed
by your teacher.
Reading Check Explain how an emission
spectrum is produced.
Each element’s atomic emission spectrum is unique
and can be used to identify an element or determine
whether 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 by doing the MiniLab.
Figure 5.8 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.
Analysis
1. Suggest a reason why each compound produced a flame of a different color, even
though they each contain chlorine.
2. Explain how an element’s flame test might
be related to its atomic emission spectrum.
3. Infer the identity of the unknown crystals.
Explain your reasoning.
■ Figure 5.8 The purple
light emitted by hydrogen can
be separated into its different
components using a prism.
Hydrogen has an atomic emission spectrum that comprises
four lines of different
wavelengths.
Determine Which line has
the highest energy?
Slit
Prism separates light
into its components.
410 434
nm nm
Teaching Strategies
Hydrogen gas
discharge tube
emits light.
• Darken the room as much as
possible so that the flame colors
can be seen vividly.
λ (nm) 400
450
486
nm
500
656
nm
550
600
650
700
750
Hydrogen’s Atomic Emission Spectrum
Expected Results
See data table below:
Compound
Flame color
lithium chloride
red
sodium chloride
yellow
potassium chloride
violet
calcium chloride
red-orange
strontium chloride
bright red
unknown
depends on
compound
144 Chapter 5 • Electrons in Atoms
Analysis
1. The colors are due primarily to electron transitions
of the metal atoms.
The colors are characteristic of
C05_S1_874637.indd
9
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.
Customize this lab with
the LabManager™
CD-ROM.
Caption Question Fig. 5.8 The line corresponding to the 410 nm wavelength has the highest
energy.
■
2/1/07
1:41:13
3 Assess
■ Figure 5.9 The first spectrum is an
absorption spectrum. It is composed of black
lines on a continuous spectrum. The black
lines correspond to certain frequencies
absorbed by a given element, helium in this
case. They can be matched to the colored
lines present in helium’s emission spectrum,
shown below the absorption spectrum.
Check for Understanding
Ask students to explain why chemists
found Rutherford’s nuclear model of
the atom lacking. It did not explain or
account for the differences in the chemical
behavior of the elements. OL
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 10 g fluorescein
in 100 mL water in a 150 mL beaker.
Darken the room and shine a flashlight’s beam through a transparent
red cellophane sheet into the fluorescein solution. When the flashlight is
turned off, the solution will not fluoresce.
Then, repeat the process, but use a
blue cellophane sheet rather than a
red one. The solution will fluoresce when
the flashlight is turned off. 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 solution can be flushed down a drain with
water. OL
Connection to Astronomy 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 specific frequencies of light are
emitted. Because those emitted frequencies are related to energy by the
formula E photon = hν, only photons with specific energies are emitted.
This was not predicted by the laws of classical physics. Scientists had
expected to observe the emission of a continuous series of colors as
excited electrons lost energy. Elements absorb the same specific frequencies of light as the frequencies they emit, thus creating an absorption spectrum. In an absorption spectrum, the absorbed frequencies
appear as black lines, as shown in Figure 5.9. By comparing the black
lines to the emission spectrum of elements, scientists are able to determine the composition of the outer layers of stars.
Section 5.1
Assessment
MAIN Idea
Compare the dual nature of light.
Section Summary
8.
◗ All waves are defined by their wavelengths, frequencies, amplitudes,
and speeds.
9. Describe the phenomena that can be explained only by the particle model of
light.
10. Compare and contrast continuous spectrum and emission spectrum.
◗ In a vacuum, all electromagnetic
waves travel at the speed of light.
11. Assess Employ quantum theory to assess the amount of energy that matter
gains and loses.
◗ All electromagnetic waves have both
wave and particle properties.
12. Discuss the way in which Einstein utilized Planck’s quantum concept to explain
the photoelectric effect.
◗ Matter emits and absorbs energy
in quanta.
13. Calculate Heating 235 g of water from 22.6°C to 94.4°C in a microwave oven
requires 7.06 × 10 4 J of energy. If the microwave frequency is 2.88 × 10 10 s -1,
how many quanta are required to supply the 7.06 × 10 4 J?
Knowledge Ask students to
14. Interpret Scientific Illustrations Use Figure 5.5 and your knowledge of
electromagnetic radiation to match the numbered items with the lettered items.
The numbered items may be used more than once or not at all.
a. longest wavelength
1. gamma ray
b. highest frequency
2. infrared wave
c. greatest energy
3. radio waves
compare the wavelengths, frequencies,
and energies of microwaves and
X rays. Microwaves have longer wavelengths, lower frequencies, and lower energies than X rays. OL
◗ White light produces a continuous
spectrum. An element’s emission
spectrum consists of a series of
lines of individual colors.
3 PMC05_S1_874637.indd
Section 5.1
The ChemLab
located at the end of the chapter can
be used at this point in the lesson.
Assessment
Assessment
10
2/1/07
8. Light exhibits wavelike behavior as it travels through space. Light exhibits
particlelike behavior as it interacts with matter.
9. The particle model must be used to explain the photoelectric effect, the
color of hot objects, and atomic emission spectra.
10. A continuous spectrum shows the colors of all the wavelengths. An emission spectrum shows the wavelengths corresponding to a given element.
11. A single quantum is the minimum amount of energy that can be lost or
gained by an atom. Therefore, matter loses or gains energy only in multiples
of one quantum.
Self-Check Quiz glencoe.com
1:41:17 PM
12. Einstein proposed that electromagnetic radiation has a wave-particle
nature, that the energy of a quantum, or photon, depends on the frequency
of the radiation, and that the energy of the photon is given by the formula
E photon = hν.
13. 3.70 × 10 27
14. a: 3, b: 1, c: 1
Section 5.1 • Light and Quantized Energy
145
Section 5.2
1 Focus
Focus Transparency
Before presenting the lesson, project
Section Focus Transparency 18 and
have students answer the accompanying questions. BL EL
MAIN Idea
Waves and Quantized Energies
Draw a circle with a dot in the middle
on the board and explain that it is
one way of representing the circular
orbit of an electron around an atomic
nucleus. Then, explain that moving
particles, such as electrons, have
wavelike properties. Challenge three
students to come to the board, to
divide the circles into three, four, and
five equal segments, respectively, and
to draw the same number of standing waves on the circles. The standing
waves should resemble those in Figure 5.13c.
Ask which of the wave patterns represents the shortest wavelength, highest frequency, and greatest energy.
The one with five complete wavelengths.
Point out that when an electron with
wavelike motion is restricted to a circular orbit of fixed radius, only certain wavelength, frequencies, and
energies are possible. OL AL EL
2 Teach
Section 5.2
Objectives
◗ Compare the Bohr and quantum
mechanical models of the atom.
◗ Explain the impact of de Broglie’s
wave-particle duality and the
Heisenberg uncertainty principle
on the current view of electrons
in atoms.
◗ Identify the relationships among
a hydrogen atom’s energy levels,
sublevels, and atomic orbitals.
Quantum Theory
and the Atom
MAIN Idea Wavelike properties of electrons help relate atomic
emission spectra, energy states of atoms, and atomic orbitals.
Real-World Reading Link Imagine climbing a ladder and trying to stand
between the rungs. Unless you could stand on air, it would not work. When
atoms are in various energy states, electrons behave in much the same way as a
person climbing up the rungs of a ladder.
Review Vocabulary
Bohr’s Model of the Atom
atom: the smallest particle of an
element that retains all the properties
of that element; is composed of
electrons, protons, and neutrons
The dual wave-particle model of light accounted for several previously
unexplainable phenomena, but scientists still did not understand the
relationships among atomic structure, electrons, and atomic emission
spectra. Recall that hydrogen’s atomic emission spectrum is discontinuous; that is, it is made up of only certain frequencies of light. Why are
the atomic emission spectra of elements discontinuous rather than continuous? Niels Bohr, a Danish physicist working in Rutherford’s laboratory in 1913, proposed a quantum model for the hydrogen atom that
seemed to answer this question. Bohr’s model also correctly predicted
the frequencies of the lines in hydrogen’s atomic emission spectrum.
New Vocabulary
ground state
quantum number
de Broglie equation
Heisenberg uncertainty principle
quantum mechanical model of the atom
atomic orbital
principal quantum number
principal energy level
energy sublevel
■ Figure 5.10 The figure shows an
atom that has one electron. Note that the
illustration is not to scale. In its ground
state, the electron is associated with the
lowest energy level. When the atom is in
an excited state, the electron is associated with a higher energy level.
Visual Learning
Energy states of hydrogen Building on Planck’s and Einstein’s
concepts of quantized energy, 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.
Bohr also related the hydrogen atom’s energy states to the electron
within the atom. He suggested that the 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. Thus, a hydrogen atom can have many different excited states, although it contains only one electron. Bohr’s idea
is illustrated in Figure 5.10.
Electron
Electron
Nucleus
Nucleus
Ground state
Excited state
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). E n = n 2E 1 OL
Differentiated Instruction
1
Below Level
Demonstrate the electron transitions associated with energy-level
C05_S2-874637.indd
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 as the energy released when the electron
returns to its original orbit. BL EL
146
Chapter 5 • Electrons in Atoms
2/1/07
12:41:15
Table 5.1
Bohr’s Atomic Orbit
First
Assessment
Bohr’s Description of the Hydrogen Atom
Performance Have students
Quantum Number
Orbit Radius (nm)
Corresponding Atomic
Energy Level
Relative Energy
n=1
0.0529
1
E1
Second
n=2
0.212
2
E 2 = 4E 1
Third
n=3
0.476
3
E 3 = 9E 1
Fourth
n=4
0.846
4
E 4 = 16E 1
Fifth
n=5
1.32
5
E 5 = 25E 1
Sixth
n=6
1.90
6
E 6 = 36E 1
Seventh
n=7
2.59
7
E 7 = 49E 1
make a large copy of the hydrogen
atom’s Bohr orbits (as shown in
Figure 5.12) 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). OL EL
In order to complete his calculations, Bohr assigned a number, n,
called a quantum number, to each orbit. He also calculated the radius
of each orbit. 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 allowed orbits and energy levels is
given in Table 5.1.
The hydrogen line spectrum Bohr suggested that the hydrogen
atom is in the ground state, also called the first energy level, when its
single 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 5.11. 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 lower-energy orbit. As a result of this transition, the atom emits a photon corresponding to the energy difference
between the two levels.
Interactive Figure Students can
interact with the Balmer Series at
glencoe.com.
∆E = E higher-energy orbit - E lower-energy orbit = E photon = hv
■ Figure 5.11 When an electron
drops from a higher-energy orbit to a
lower-energy orbit, a photon is emitted.
The ultraviolet (Lyman), visible (Balmer),
and infrared (Paschen) series correspond
to electrons dropping to n = 1, n = 2,
and n = 3, respectively.
Visible series
(Balmer)
n=1 +
n=2
n=3
n=4
n=5
Ultraviolet
series
(Lyman)
5 PMC05_S2-874637.indd
n=6
n=7
Infrared
series
(Paschen)
Interactive Figure To see
an animation of the Balmer Series,
visit glencoe.com.
Differentiated Instruction
2
2/1/07
Advanced Learners Ask advanced students to work through Bohr’s use of Newton’s
12:41:20 PM
second law (F = ma), Coulomb’s constant (K), and Bohr’s own concept of quantized
angular momenta to derive the relationship r n = (h 2n 2)/(4π 2Kmq 2). Then, have them
use the equation to calculate the radii of the hydrogen atom’s first four Bohr orbits. AL
Section 5.2 • Quantum Theory and the Atom
147
return to their ground state from an
excited state, the atom emits photon
whose frequency corresponds to the
energy difference between the two
energy levels. Each frequency corresponds to a certain color.
Concept Development
The Real-World-Reading-Link analogy between electron energy states
and rungs on a ladder is useful in
helping students understand the
Bohr and Quantum Mechanical
Models of the atom. Remind students, however, that the analogy
has limitations. Ask students what is
correct and what is incorrect about
the ladder analogy. Correct: The atom has
only certain allowable energy states or energy
levels. Incorrect: Atomic energy states are not
evenly spaced, as are the rungs on a ladder.
BL OL
Interactive Figure Students can
interact with the animation of electron
transition at glencoe.com.
148
Chapter 5 • Electrons in Atoms
4
3
Interactive Figure To see
an animation of electron transitions, visit glencoe.com.
2
1
Because only certain atomic energies are possible, only certain frequencies of electromagnetic radiation can be emitted. You might compare hydrogen’s atomic energy states to 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, corresponding to the energy difference between the two orbits.
Figure 5.12 shows that, unlike rungs on a ladder, however, the
hydrogen atom’s energy levels are not evenly spaced. Figure 5.12 also
illustrates the four electron transitions that account for visible lines in
hydrogen’s atomic emission spectrum, shown in Figure 5.8. Electron
transitions from higher-energy orbits to the second orbit account for all
of hydrogen’s visible lines, which form 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.
Quick Demo
WARNING: Wear safety goggles
and conduct this demo behind
an explosion shield. Do not
allow the forks to touch. Do not
allow anyone to come near the
demo or touch any part of the
setup. Insert two forks into the
ends of a large dill pickle. With
the cord unplugged, attach leads
from a 110-V current to the two
forks. Plug in the cord. The electric current will produce a yellow glow in the pickle. Ask
students what may account for
the yellow glow. The pickle has been
brined with salt, and the electric current
excites sodium ions in the pickle. The
excited sodium ions produce the yellow
emission spectrum of sodium when they
drop back to lower energy states. Allow
students to use hand-held diffraction gratings to examine
the emission spectrum.
n
∞
6
5
■ Figure 5.12 Only certain energy levels
are allowed. The energy levels are similar to
the rungs of a ladder. The four visible lines
correspond to electrons dropping from a
higher n to the orbit n = 2. As n increases,
the hydrogen atom’s energy levels are closer
to each other.
Energy of hydrogen atom
Reading Check When electrons
Reading Check Explain why different colors of light result from electron behavior in the atom.
The limits of Bohr’s model Bohr’s model explained hydrogen’s
observed spectral lines. 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.
Differentiated Instruction
C05_S2-874637.indd
3
English Learners Have English learners
look up and then explain the meanings
of several key English terms used in
this section: state (as in ground state),
uncertainty, principal, level (noun). Ask
students to use each term in a sentence
or a paragraph. EL BL
2/1/07
12:41:23
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 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 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
describe 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 where the
electrons are and where they
are going.
Electrons as waves De Broglie had been thinking that Bohr’s
quantized electron orbits had characteristics similar to those of waves.
For example, as Figures 5.13a and 5.13b show, only multiples of halfwavelengths are possible on a plucked harp string because the string is
fixed at both ends. Similarly, de Broglie saw that only odd numbers of
wavelengths are allowed in a circular orbit of fixed radius, as shown in
Figure 5.13c. 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?
■ Figure 5.13 a. The string on the harp vibrates between
two fixed endpoints. b. The vibrations of a string between the
two fixed endpoints labeled A and B are limited to multiples of
half-wavelengths. c. Electrons on circular orbits can only have
odd numbers of wavelengths.
a
3 PMC05_S2-874637.indd
n=1
A
B
n = 3 wavelengths
1 half–wavelength
n=2
Content Background
A
B
A
In the Bohr model of the hydrogen
atom, each possible electron orbit
has a definite radius, as described in
Table 5.1. The quantum mechanical
(QM) model, however, predicts
only the probability of finding the
electron at a specific location in
the atom. Interestingly, the QM
model’s most probable distance of
the electron from the nucleus in the
hydrogen atom matches the radius
of the Bohr orbit.
n = 5 wavelengths
2 half–wavelengths
n=3
The Bohr Model and the
Quantum Mechanical Model
B
3 half–wavelengths
b Vibrating guitar string
Only multiples of half-wavelengths allowed
n ≠ whole number (not allowed)
c Orbiting electron
Only whole numbers of wavelengths allowed
Chemistry Journal
4
Gases
for IR and UV Have students
2/1/07
2:13:11 PM
research the types of gases used to emit
infrared and ultraviolet electromagnetic
radiation. Have them summarize their
findings in their chemistry journals. OL
Section 5.2 • Quantum Theory and the Atom
149
The de Broglie equation predicts that all moving particles have
wave characteristics. It also explains why it is impossible to notice the
wavelength of a fast-moving car. An automobile moving at 25 m/s
and having a mass of 910 kg has a wavelength of 2.9 × 10 -38 m, a
wavelength far too small to be seen or detected. By comparison, an
electron moving at the same speed has the easily measured wavelength
of 2.9 × 10 -5 m. Subsequent experiments have proven that electrons
and other moving particles do indeed have wave characteristics. De
Broglie knew that if an electron has wavelike motion and is restricted
to circular orbits of fixed radius, only certain wavelengths, frequencies,
and energies are possible. Developing his idea, de Broglie derived the
following equation.
Problem-Solving Lab
Purpose Students will learn
how to relate emission-spectrum
wavelengths to electron-orbit transitions in the Bohr atomic model, calculate the wavelengths using the
1 = 1.09678 × 10 7 m -1
equation _
λ
1 -_
1 , and determine the
_
nf2 ni2
energy per quantum for a given
wavelength with the equation
hc
E = _.
λ
Process Skills interpret scientific illustrations, use numbers, think
critically
(
)
Teaching Strategies
• Balmer found his famous series for
hydrogen in 1886. Point out to students that experimental constraints
at that time limited his ability to
determine wavelengths to those in
the visible and near ultraviolet,
from approximately 250 nm to
700 nm. Thus, all Balmer’s lines lie
in that region.
• You may wish to run through a set
of example calculations with students to ensure that they can perform the calculations properly.
• Emphasize to students that the
absorption and emission spectra of
hydrogen are particularly important in astronomy because most of
the Universe is made of hydrogen.
Think Critically
1. a. λ = 6.565 × 10 -7 m
b. λ = 4.863 × 10 -7 m
c. λ = 4.342 × 10 -7 m
d. λ = 4.103 × 10 -7 m
2. n i = 3, n f = 2: calculated wavelength
of 6.565 × 10 -7 m closely matches
experimental wavelength of 6562 Å;
the n i = 4 , n f = 2: calculated wavelength of 4.863 × 10 -7 m closely
matches experimental wavelength
of 4861 Å; n i = 5, n f = 2: calculated
wavelength of 4.342 × 10 -7 m closely
matches experimental wavelength
of 4340 Å; n i = 6, n f = 2: calculated
wavelength of 4.103 × 10 -7 m closely
matches experimental wavelength
of 4101 Å
150
Chapter 5 • Electrons in Atoms
Particle Electromagnetic–Wave Relationship
λ represents wavelength.
h is Planck’s constant.
m represents mass of the particle.
ν represents frequency.
h
λ=_
mν
The wavelength of a particle is the ratio of Planck’s constant, and the product of the
particle’s mass by its frequency.
Problem-solving lab
Interpret Scientific
Illustrations
What electron transitions account for the
Balmer series? Hydrogen’s emission spectrum
comprises three series of lines. Some wavelengths are ultraviolet (Lyman series) and infrared (Paschen series). Visible wavelengths
comprise the Balmer series. The Bohr atomic
model attributes these spectral lines to transitions from higher-energy states with electron
orbits in which n = n i to lower-energy states
with smaller electron orbits in which n = n f.
Analysis
The image at right illustrates some of the transitions in hydrogen’s Balmer series. These Balmer
lines are designated H α (6562 Å), H β (4861 Å),
H γ (4340 Å), and H δ (4101 Å). Each wavelength
(λ) is related to an electron transition within a
hydrogen atom by the following equation, in
which 1.09678 × 10 7 m –1 is known as the
Rydberg constant.
(
)
1
1
1
_
= 1.09678 × 10 7 _
-_
m –1
2
2
λ
nf
ni
For hydrogen’s Balmer series, electron orbit transitions occur from larger orbits to the n = 2
orbit; that is, n f = 2.
3. a. 3.027 × 10 -19 J
b. 4.087 × 10 -19 J
-19
C05_S2-874637.indd
5
c. 4.577 × 10
J
d. 4.844 × 10 -19 J
4. 1.549 × 10 -19 J
Series
limit
Hδ Hγ
4000
Hβ
Hα
5000
6000
7000
λ (Å)
Think Critically
1. Calculate the wavelengths for the following
electron orbit transitions.
a. n i = 3; n f = 2
c. n i = 5; n f = 2
b. n i = 4; n f = 2
d. n i = 6; n f = 2
2. Relate the Balmer-series wavelengths you
calculated in Question 1 to those determined
experimentally. Allowing for experimental
error and calculation uncertainty, do the
wavelengths match? Explain your answer.
One angstrom (Å) equals 10 –10 m.
3. Apply the formula E = hc/λ to determine the
energy per quantum for each of the orbit
transitions in Question 1.
4. Extend the Bohr model by calculating the
wavelength and energy per quantum for the
electron orbit transition for which n f = 3 and
n i = 5. This transition accounts for a spectral
line in hydrogen’s Paschen series.
Assessment
Skill Have the students extend the
ideas presented here to make a prediction
concerning the spectrum that would be
emitted from hydrogen-like atoms, such as
He + or Li 2+. Or, have them predict what
would happen to the continuous spectrum
of light if it passed through a cell containing
hydrogen gas. OL
2/1/07
12:41:33
The Heisenberg uncertainty principle 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) proved to have
profound implications for atomic models.
Heisenberg showed that it is impossible to take any measurement of
an object without disturbing the object. Imagine trying to locate a hovering, helium-filled balloon in a darkened room. If you wave your hand
about, you can locate the balloon’s position when you touch it. However,
when you touch the balloon, you transfer energy to it and change its
position. You could also detect the balloon’s position by turning on a
flashlight. Using this method, photons of light reflected from the balloon would reach your eyes and reveal the balloon’s location. Because
the balloon is a macroscopic object, the effect of the rebounding photons on its position is very small and not observable.
Imagine trying to determine an electron’s location by “bumping” it
with a high-energy photon. 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 5.14. 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.
Enrichment
Uncertainty Principle Make a
sign labeled Heisenberg Might 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 (momentum) and position at the
same time. OL
Reading Check 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.
■
Reading Check Explain the Heisenberg uncertainty principle.
Although scientists of the time found Heisenberg’s principle difficult
to accept, it has been proven to describe the fundamental limitations of
what can be observed. The interaction of a photon with a macroscopic
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 is
not the case with an electron moving at 6 × 10 6 m/s near an atomic
nucleus. The uncertainty of the electron’s position is at least 10 -9 m,
about 10 times greater than the diameter of the entire atom.
The Heisenberg uncertainty principle also means that is impossible
to assign fixed paths for electrons like the circular orbits in Bohr’s
model. The only quantity that can be known is the probability for an
electron to occupy a certain region around the nucleus.
3 PMC05_S2-874637.indd
y
Photon
λ
y
Photon’s
wavelength
increases.
λ
Electron
x
x
Speed = 0
Before collision
Electron’s speed
increases.
Quick Demo
Photons and Electrons
Give a heavy ball to a blindfolded
student in the middle of an open
space (about a 1.5-m radius).
Quietly, set a 50-mL, plastic
graduated cylinder about 3 m
from the student. Surround the
blindfolded student with a ring
of other students about 3 m 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 no
longer where it was before being hit
with the ball. Then describe the
analogy to the photon and
electron. BL EL
■ Figure 5.14 When a photon interacts with an electron at rest, both the
velocity and the position of the electron
are modified. This illustrates the
Heisenberg uncertainty principle. It is
impossible to know at the same time the
position and the velocity of a particle.
Explain Why has the photon’s
energy changed?
After collision
Differentiated Instruction
6
Advanced
Learners Have students
Caption Question Fig. 5.14
It transferred some energy to the electron.
2/1/07
12:41:35 PM
investigate and report on whether quantum
mechanics invalidates the laws and models
of classical physics. In general, classical 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
to accurately describe and explain atomic and
subatomic behavior. AL
Section 5.2 • Quantum Theory and the Atom 151
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. 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, the quantum mechanical model of the atom.
Like Bohr’s model, 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.
Apply Chemistry
Lasers 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-to-crest 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 small diameters, they can be used
for internal surgeries, destroying target tissue without adversely affecting
surrounding tissue. In addition, 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.
Reading Check Both models limit
an electron’s energy to certain values.
Unlike the Bohr model, the quantum
mechanical model makes no attempt to
describe the electron’s path around the
nucleus.
Reading Check Electrons are located around the nucleus at a position that
can be described only by a probability
map. A boundary surface is chosen to
contain the region that the electron can
be expected to occupy 90% of the time.
Reading Check Compare and contrast Bohr’s model and the
quantum mechanical model.
The Schrödinger wave equation is too complex to be considered
here. However, each solution to the equation is known as a wave function, which is related to the probability of finding the electron within a
particular volume of space around the nucleus. Recall from your study
of mathematics that an event with a high probability is more likely to
occur than one with a low probability.
Electron’s probable location The wave function predicts a three-
dimensional region around the nucleus, called an atomic orbital,
which describes the electron’s probable location. An atomic orbital is like
a fuzzy cloud in which the density at a given point is proportional to the
probability of finding the electron at that point. Figure 5.15a illustrates
the probability map that describes the electron in the atom’s lowest
energy state. The probability map can be thought of 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. The high
density of dots near the nucleus indicates the electron’s most probable
location. However, because the cloud has no definite boundary, it is
also possible that the electron might be found at a considerable distance
from the nucleus.
Reading Check Describe where electrons are located in an atom.
■ Figure 5.15 The density map
represents the probability of finding
an electron at a given position
around the nucleus. a. The higher
density of points near the nucleus
shows that the electron is more
likely to be found close to the nucleus. b. At any given time, there is
a 90% probability of finding the
electron within the circular region
shown. This surface is sometimes
chosen to represent the boundary
of the atom. In this illustration, the
circle corresponds to a projection of
the 3-dimensional sphere that contains the electrons.
a
b
Boundary
Nucleus
Density Maps
Differentiated Instruction
7
English Learners
Have English Learners investigate two acronyms related to the
C05_S2-874637.indd
quantum mechanical model and emission spectra, MASER and LASER. MASER is an
acronym for Microwave Amplification by Stimulated Emission of Radiation (Masers
differ from lasers in that maser emissions involve vibrational energy states of molecules and laser emissions involve energy-level transitions of atoms.). LASER is an
acronym for Light Amplification by Stimulated Emission of Radiation. Demonstrate
a low-powered laser that is safe to use in the classroom by aiming the beam in a safe
direction and clapping chalkboard erasers over the beam. The beam becomes visible
as the light reflects from chalk particles in the air. EL
152
Chapter 5 • Electrons in Atoms
2/1/07
12:41:37
Hydrogen’s Atomic Orbitals
Identify
Misconceptions
Because the boundary of an atomic orbital is fuzzy, the orbital does
not have an exact 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.
This means that the probability of finding the electron within the
boundary is 0.9 and the probability of finding it outside the boundary
is 0.1. In other words, it is more likely to find the electron close to the
nucleus and within the volume defined by the boundary, than to find it
outside the volume. The circle shown in Figure 5.15b encloses 90% of
the lowest-energy orbital of hydrogen.
Students might think that the
hydrogen atom’s energy levels
are evenly spaced.
Uncover the Misconception
Have students compare hydrogen’s
energy levels shown in Figure
5.12 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 E n/E n-1 from E 2
through E 7. E 2 /E 1 = 4, E 3 /E 2 = 2.25,
E 4 /E 3 = 1.78, E 5 /E 4 = 1.56, E 6 /E 5 = 1.44,
E 7 /E 6 = 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 become more
closely spaced as n increases. OL
Principal quantum number Recall that the Bohr atomic model
assigns quantum numbers to electron orbits. Similarly, the quantum
mechanical model assigns four quantum numbers to atomic orbitals.
The first one is the principal quantum number (n) and indicates the
relative size and energy of atomic orbitals. As n increases, the orbital
becomes larger, the electron spends more time farther from the nucleus,
and the atom’s energy increases. Therefore, n specifies the atom’s major
energy levels. Each major energy level is called a principal energy level.
An atom’s lowest principal energy level is assigned a principal quantum
number of 1. When the hydrogen atom’s single electron occupies an
orbital with n = 1, the atom is in its ground state. Up to 7 energy levels
have been detected for the hydrogen atom, giving n values ranging from
1 to 7.
Energy sublevels Principal energy levels contain energy sublevels.
Principal energy level 1 consists of a single sublevel, principal energy
level 2 consists of two sublevels, principal energy level 3 consists of three
sublevels, and so on. To better understand the relationship between the
atom’s energy levels and sublevels, picture the seats in a wedge-shaped
section of a theater, as shown in Figure 5.16. As you move away from
the stage, the rows become higher and contain more seats. Similarly,
the number of energy sublevels in a principal energy level increases
as n increases.
Reading Check Explain the relationship between energy levels
and sublevels.
Reading Check The number of
energy sublevels in a principal energy
level increases as n increases.
Figure 5.16 Energy levels can be thought of as rows of seats in a theater. The rows
that are higher up and farther from the stage contain more seats. Similarly, energy levels
related to orbitals farther from the nucleus contain more sublevels.
■
7 PMC05_S2-874637.indd
n = 4 (4 sublevels)
n = 3 (3 sublevels)
n = 2 (2 sublevels)
n = 1 (1 sublevel )
Chemistry Project
8
Models of the Atom Have students
2/1/07
12:41:39 PM
research and explain 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. OL
Section 5.2 • Quantum Theory and the Atom
153
Shapes of orbitals Sublevels are labeled s, p, d, or f according to the
Reading Check s orbitals
shapes of the atom’s orbitals. All s orbitals are spherical, and all p orbitals are dumbbell-shaped; however, not all d or f orbitals have the same
shape. Each orbital can contain, at most, two electrons. The single sublevel in principal energy level 1 corresponds to a spherical orbital called
the 1s orbital. The two sublevels in principal energy level 2 are designated 2s and 2p. The 2s sublevel corresponds to the 2s orbital, which is
spherical like the 1s orbital but larger in size, as shown in Figure 5.17a.
The 2p sublevel corresponds to three dumbbell-shaped p orbitals designated 2p x, 2p y, and 2p z. 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 5.17b. Each of the p orbitals related to an energy sublevel has
the same energy.
are spherical. p orbitals are
dumbbell-shaped.
Enrichment
Sublevels Students might think
that the letters s, p, d, and f, which
represent sublevels, are arbitrary and
perhaps mysterious. Explain that the
letters originated from descriptions
of spectral lines as sharp, principal,
diffuse, and fundamental.
Reading Check Describe the shapes of s and p orbitals.
Principal energy level 3 consists of three sublevels designated 3s, 3p,
and 3d. Each d sublevel relates to five orbitals of equal energy. Four of
the d orbitals have identical shapes but different orientations along the
x, y, and z coordinate axes. However, the fifth orbital, d z 2, is shaped and
oriented differently than the other four. The shapes and orientations of
the five d orbitals are illustrated in Figure 5.17c. The fourth principal
energy level (n = 4) contains a fourth sublevel, called the 4f sublevel,
which relates to seven f orbitals of equal energy. The f orbitals have
complex, multilobed shapes.
Concept Development
Hydrogen’s Orbitals Show students the radial probability distributions of hydrogen’s 1s, 2s, and 3s
orbitals. Explain that such distributions show where the electron is
most likely to be found.
Point out that the 1s orbital’s radial probability distribution (rpd) has a
single maximum near the nucleus.
This maximum represents a region
of high electron density. The larger
2s orbital’s rpd has two regions of
electron density, the more distant
region having the higher density.
The two regions are separated by
a spherical node where the probability of finding the electron is zero. The
3s orbital’s rpd has three regions of
electron density and two nodes. As
with the 2s orbital, the region of
highest electron density is the one
farthest from the nucleus.
■
Figure 5.17 Each energy sublevel relates to orbitals of different shape.
z
z
z
x
x
x
y
x
x
y
y
y
y
px
1s orbital
z
z
pz
py
2s orbital
b. The three p orbitals are dumbshell-shaped and are oriented along the three
a. All s orbitals are spherical, and their size increases
perpendicular x, y, and z axes.
with increasing principal quantum number.
z
z
z
z
z
y
y
Assessment
x
Knowledge Ask students
which hydrogen energy-level transition accounts for the violet line in its
emission spectrum. n = 6 → n = 2
OL
dxy
y
y
x
x
dxz
dyz
x
y
x
dx2-y2
dz2
c. Four of the five d orbitals have the same shape but lie in
different planes. The d z orbital has its own unique shape.
2
Chemistry Journal
9
Orbital Shapes
Have students sketch the
C05_S2-874637.indd
shapes and orientations of hydrogen’s 3s,
3p, and 3d orbitals. Have them label the
orbital sketches and include them in their
chemistry journals. OL EL
154
Chapter 5 • Electrons in Atoms
2/1/07
12:41:45
Table 5.2
3 Assess
Hydrogen’s First Four Principal Energy Levels
Principal Quantum
Number (n)
Sublevels (Types of
Orbitals) Present
Number of Orbitals
Related to Sublevel
Total Number of Orbitals
Related to Principal
Energy Level (n 2)
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
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. OL
Extension
Assessment
MAIN Idea Explain the reason, according to Bohr’s atomic model, why atomic
emission spectra contain only certain frequencies of light.
Section Summary
15.
◗ Bohr’s atomic model attributes hydrogen’s emission spectrum to electrons
dropping from higher-energy to
lower-energy orbits.
16. Differentiate between the wavelength of visible light and the wavelength
of a moving soccer ball.
◗ The de Broglie equation relates a
particle’s wavelength to its mass,
its velocity, and Planck’s constant.
19. Calculate Use the information in Table 5.1 to calculate how many times larger
the hydrogen atom’s seventh Bohr radius is than its first Bohr radius.
◗ Electrons occupy three-dimensional
regions of space called atomic orbitals.
5 PMC05_S2-874637.indd
Section 5.2
17. Enumerate the sublevels contained in the hydrogen atom’s first four energy
levels. What orbitals are related to each s sublevel and each p sublevel?
18. Explain why the location of an electron in an atom is uncertain using the
Heisenberg uncertainty principle and de Broglie’s wave-particle duality. How is
the location of electrons in atoms defined?
◗ The quantum mechanical model
assumes that electrons have wave
properties.
Ask students to explain why higher
energy levels are made of sublevels
associated with more electrons than
lower energy levels. Higher energy levels
are associated with larger volumes, which can
contain more orbitals than smaller volumes. It
is reasonable, therefore, that more electrons
can be contained in the greater number of
orbitals associated with higher energy levels.
OL
Reteach
Hydrogen’s first four principal energy levels, sublevels, and related
atomic orbitals are summarized in Table 5.2. Note that the number of
orbitals related to each sublevel is always an odd number, and that the
maximum number of orbitals related to each principal energy level
equals n 2.
At any given time, the electron in a hydrogen atom can occupy just
one orbital. 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, when the atom gains a quantum of
energy, the electron is excited to one of the unoccupied orbitals.
Depending on the amount of energy available, the electron can move
to the 2s orbital, to one of the three 2p orbitals, or to any other orbital
that is vacant.
Section 5.2
Check for Understanding
20. Compare and contrast Bohr’s model and the quantum mechanical model
of the atom.
According to quantum mechanics,
each electron in an atom can be
described by four quantum numbers.
Three of these (n, l, and m l) are
related to the probability of finding
the electron at various points in
space. The fourth (m s) 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. m l specifies the
orientation in space of the orbital
containing the electron. m s specifies
the orientation of the electron’s
spin axis. AL
Assessment
10
2/1/07
15. Because only certain atomic energies are possible, only certain frequencies
of radiation can be emitted from an atom.
16. The wavelength of the moving soccer ball is much smaller than the
wavelengths of visible light. The moving soccer ball’s wavelength is
too small to see or detect.
17. First energy level, s; second energy level, s and p; third energy level, s, 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 (p x, p y, and p z).
18. An electron has wave-particle characteristics and does not have a single,
Self-Check Quiz glencoe.com
12:41:48 PM
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.
19. n = 7: radius: 2.59 nm; n = 1: radius: 0.0529 nm
2.59 nm ÷ 0.0529 nm = 49.0 times larger
20. Bohr model: the electron is a particle; the hydrogen atom has only certain
allowable energy states. Quantum mechanical model: the electron is
a wave-particle 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.
Section 5.2 • Quantum Theory and the Atom
155
Before presenting the lesson, project
Section Focus Transparency 19 and
have students answer the accompanying questions. BL EL
MAIN Idea
Learning the Aufbau Sequence
Draw a sublevel diagram on the
chalkboard, listing each sublevel
and drawing the diagonal arrows
that reflect the aufbau sequence.
Ask students to write the sequence
of sublevels by following the arrows
in sequence from top to bottom. 1s,
2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d,
6p, 7s, 5f, 6d, 7p Point out that they can
construct and use such a sublevel
diagram whenever they need to
follow the Aufbau sequence in
determining an atom’s electron
arrangement. OL
2 Teach
Use Science Terms
Aufbau Principle Explain that the
name aufbau is derived from the
German aufbauen, which means to
build up.
■
Objectives
Electron Configuration
◗ Apply the Pauli exclusion principle,
the aufbau principle, and Hund’s rule
to write electron configurations using
orbital diagrams and electron
configuration notation.
◗ Define valence electrons, and draw
electron-dot structures representing
an atom’s valence electrons.
MAIN Idea A set of three rules can be used to determine electron
arrangement in an atom.
Real-World Reading Link As students board a bus, they each sit in a separate
bench seat until they are all full. Then, they begin sharing seats. Electrons fill
atomic orbitals in a similar way.
Ground-State Electron Configuration
Review Vocabulary
When you consider that atoms of the heaviest elements contain more
than 100 electrons, the idea of determining electron arrangements in
atoms with many electrons seems daunting. Fortunately, all atoms can
be described with orbitals similar to hydrogen’s. This allows us to
describe arrangements of electrons in atoms using a few specific rules.
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 energy possible. The most
stable, lowest-energy arrangement of the electrons 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.
electron: a negatively charged, fastmoving particle with an extremely small
mass that is found in all forms of matter
and moves through the empty space
surrounding an atom’s nucleus
New Vocabulary
electron configuration
aufbau principle
Pauli exclusion principle
Hund’s rule
valence electron
electron-dot structure
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 5.18. In the diagram, each box represents an atomic orbital.
■ Figure 5.18 The aufbau diagram
shows the energy of each sublevel relative to the energry of other sublevels.
Each box on the diagram represents an
atomic orbital.
Determine Which sublevel has
the greater energy, 4d or 5p?
Caption Question Fig. 5.18 5p
7p
7s
6s
6p
5p
5s
Increasing energy
Focus Transparency
Section 5.3
Orbital filling sequence
Section 5.3
1 Focus
6d
5d
5f
4f
4d
4p
3d
4s
3p
3s
2p
2s
1s
$EMONSTRATION
Emission Spectra
Purpose
to illustrate the relationship between
the electron configurations of nonmetals and their emission spectra
Materials
Spectrum tubes (H and Ne); spectrum
tube supply; Flinn C-Spectra diffraction grating; colored pencils or chalk
156 Chapter 5 • Electrons in Atoms
C05_S3_874637.indd
1
Safety Precautions
Use care around the spectrum tube highvoltage power supply. Spectrum tubes become
hot when used.
Procedure
An inexpensive alternative to a spectro-scope
can be created by taping 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.
Because hydrogen has 1 electron, ask students
to predict if there will be more or fewer lines
in hydrogen’s spectrum.
2/1/07
12:43:51
Table 5.3
Features of the Aufbau Diagram
Example
Feature
All orbitals related to an energy sublevel are of equal energy.
All three 2p orbitals are of equal energy.
In a multi-electron atom, the energy sublevels within
a principal energy level have different energies.
The three 2p orbitals are of higher energy than the 2s orbital.
In order of increasing energy, the sequence of energy
sublevels within a principal energy level is s, p, d, and f.
If n = 4, then the sequence of energy sublevels is
4s, 4p, 4d, and 4f.
Orbitals related to energy sublevels within one principal
energy level can overlap orbitals related to energy sublevels
within another principal level.
The orbital related to the atom’s 4s sublevel has a lower energy
than the five orbitals related to the 3d sublevel.
Reading Check The aufbau principle
states that each electron occupies the
lowest energy orbital available. The Pauli
exclusion principle states that a maximum of two electrons can occupy a single atomic orbital. Hund’s rule states
that single electrons with the same spin
must occupy each equal-energy orbital
before additional electrons with opposite spin can occupy the same orbital.
&/,$!",%3
RUBRIC available at glencoe.com
Table 5.3 summarizes several features of the aufbau diagram.
Although the aufbau principle describes the sequence in which orbitals
are filled with electrons, it is important to know that atoms are not built
up electron by electron.
The Pauli exclusion principle Electrons in orbitals can be represented by arrows in boxes. Each electron has an associated spin, similar
to the way a top spins on its point. 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, and an arrow pointing down ↓
represents the electron spinning in the opposite direction. 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.
The Pauli exclusion principle states that a maximum of two electrons can occupy a single atomic orbital, but only if the electrons have
opposite spins. Austrian physicist Wolfgang Pauli (1900–1958) proposed this principle after observing atoms in excited states. An atomic
orbital containing paired electrons with opposite spins is written as ↑↓ .
Because each orbital can contain, at most, two electrons, the maximum
number of electrons related to each principal energy level equals 2n 2.
→
→
→
→
→
→
→
→
Reading Check State the three rules that define how electrons are
arranged in atoms.
2
Results
1 PMC05_S3_874637.indd
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: 1s 22s 22p 6, H: 1s 1
WORD ORIGIN
Aufbau
comes from the German word
aufbauen, which means to
configure or arrange
&/,$!",%3
Incorporate information
from this section into
your Foldable.
Build a Model
Use this activity to help students
understand how the orbitals related
to a neon-or-beyond atom’s lowest
two energy levels relate to one another. Have students work in groups to
build a model that shows the atomic
orbitals of a neon atom. Have them
use cellular polystyrene (Styrofoam)
models for neon’s 1s, 2p x, 2p y, and
2p z orbitals and metal rods to connect the orbital models. Have them
use a see-through material such as
netting for the 2s orbital. Ask each
group to demonstrate their model
for the class. Be sure to point out that
an actual atomic orbital does not
have the well-defined boundaries of
such a model. OL COOP LEARN
GLENCOE Technology
Virtual Labs CD-ROM
→
6.
→
3.
→
→
→
→
→
→
→
→
5.
→
4.
2.
→
1.
→
Hund’s rule The fact that negatively charged electrons repel each
other has an important impact on the distribution of electrons in equalenergy 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.
VOCABULARY
Chemistry: Matter and Change
Animation: Electrons and
Energy Levels
Exploration: Building Atoms
2/1/07
12:43:56 PM
2. What is the appearance of neon in the
excited
Assessment
state? In the ground state, neon is a clear, colorless
Skill Have students view
gas. In the excited state it gives off a red-orange light.
the excited spectral tube of another
element such as mercury. Ask them
3. Of the two spectra viewed, did hydrogen
to predict if Hg will have more lines
or neon have more lines? Explain why. Neon
has more lines than hydrogen because its ten electrons than neon and hydrogen because it
has 80 electrons. No, Hg has fewer lines in
have a greater number of possible energy transitions.
the visible spectrum. However, there are many
additional lines in mercury’s IR and UV spectra.
OL
Section 5.3 • Electron Configuration
157
■
Caption Question Fig. 5.19 10
Electron Arrangement
1s
2s
You can represent an atom’s electron configuration using one of two
convenient methods: orbital diagrams or electron configuration
notation.
2px
Visual Learning
Table 5.4 Have students write an
electron configuration notation that
shows the orbital occupancy related
to a phosphorus atom’s 3p sublevel.
3p x 13p y 13p z 1 A chlorine atom’s 3s and
3p sublevels. 3s 23p x 23p y 23p z 1 OL
Orbital diagrams As mentioned earlier, electrons in orbitals can be
represented by arrows in boxes. 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 one electron in two of three separate 2p orbitals, is shown below.
2py
2pz
→
→
→
→
→
Neon atom
→
→
→
→
→
2p
→
→
2s
→
→
1s
→
→
Concept Development
Hund’s Rule 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. Passengers tend to 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. BL OL
1s
■
2p orbitals of a neon atom overlap.
Determine how many electrons
a neon atom has.
Table 5.4
Interactive Table Students
can interact with the table at
glencoe.com.
2s
2p
Figure 5.19 The 1s, 2s, and
Electron configuration notation The electron configuration
notation 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 1s 22s 22p 2. Orbital diagrams and electron configuration notations
for the elements in periods one and two of the periodic table are shown
in Table 5.4. Figure 5.19 illustrates how the 1s, 2s, 2p x, 2p y, and 2p z
orbitals of the neon atom, previously illustrated in Figure 5.17, overlap.
Interactive Table Explore electron
configurations and orbital diagrams
at glencoe.com.
Electron Configurations
and Orbital Diagrams
for Elements 1–10
Orbital Diagram
2s 2p x 2p y 2p z
Element
Atomic Number
Hydrogen
1
↑
1s 1
Helium
2
↑↓
1s 2
Lithium
3
↑↓
↑
1s 2 2s 1
Beryllium
4
↑↓
↑↓
1s 2 2s 2
Boron
5
↑↓
↑↓
↑
Carbon
6
↑↓
↑↓
↑
↑
Nitrogen
7
↑↓
↑↓
↑
↑
↑
1s 2 2s 2 2p 3
Oxygen
8
↑↓
↑↓
↑↓ ↑
↑
1s 2 2s 2 2p 4
Fluorine
9
↑↓
↑↓
↑↓ ↑↓ ↑
1s 2 2s 2 2p 5
Neon
10
↑↓
↑↓
↑↓ ↑↓ ↑↓
1s 2 2s 2 2p 6
1s
Electron Configuration Notation
1s 2 2s 2 2p 1
1s 2 2s 2 2p 2
Differentiated Instruction
C05_S3_874637.indd
3
Below Level Look for ways to encourage
and help these students as they learn to
write electron configuration notations.
One way is to have each of them make an
aufbau diagram on one side of a 4 × 6 or
5 × 7 card and a sublevel diagram on the
other side. Increase students’ confidence by
having them use the cards as they practice
writing electron configurations for various
elements. BL
158
Chapter 5 • Electrons in Atoms
2/1/07
12:43:58
Note that the electron configuration notation does not usually show
the orbital distributions of electrons related to a sublevel. It is understood that a designation such as nitrogen’s 2p 3 represents the orbital
occupancy 2p x 12p y 12p z 1.
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 as follows.
Assessment
Personal Tutor For an online tutorial
on electron configuration notation,
visit glencoe.com.
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. OL
→
→
→
→
→
→
1s22s22p63s1
Knowledge Ask students
→
→
→
→
→
1s
2s
2p
Content Background
3s
Noble-gas notation is a method of representing electron configura-
VOCABULARY
tions of noble gases. Noble gases are the elements in the last column of
the periodic table. They have eight electrons in their outermost orbital
and they are unusually stable. You will learn more about noble gases in
Chapter 6. The noble-gas notation uses bracketed symbols. For example,
[He] represents the electron configuration for helium, 1s 2, and [Ne]
represents the electron configuration for neon, 1s 22s 22p 6. 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]3s 1. The electron configuration for an element can be represented using the noblegas notation for the noble gas in the previous period and the electron
configuration for the additional orbitals being filled. The complete and
abbreviated (using noble-gas notation) electron configurations of the
period 3 elements are shown in Table 5.5.
SCIENCE USAGE V. COMMON USAGE
Period
Science usage: a horizontal row
of elements in the current
periodic table
There are seven periods in the
current periodic table.
Common usage: an interval of time
determined by some recurring
phenomenon
The period of Earth’s orbit is one year.
Reading Check Explain how to write the noble-gas notation for an
element. What is the noble-gas notation for calcium?
Table 5.5
Electron Configurations for
Elements 11–18
Element
Atomic
Number
Complete
Electron
Configuration
Electron
Configuration
Using Noble Gas
Sodium
11
1s 22s 22p 63s 1
[Ne]3s 1
Magnesium
12
1s 22s 22p 63s 2
[Ne]3s 2
Aluminum
13
1s 22s 22p 63s 23p 1
[Ne]3s 23p 1
Silicon
14
1s 22s 22p 63s 23p 2
[Ne]3s 23p 2
Phosphorus
15
1s 22s 22p 63s 23p 3
[Ne]3s 23p 3
Sulfur
16
1s 22s 22p 63s 23p 4
[Ne]3s 23p 4
Chlorine
17
1s 22s 22p 63s 23p 5
[Ne]3s 23p 5
Argon
18
1s 22s 22p 63s 23p 6
[Ne]3s 23p 6 or [Ar]
8 PMC05_S3_874637.indd
More Exceptions to Predicted
Configurations The exceptions to
predicted ground-state electron configurations become more numerous
among the transition elements
in periods 5 and 6. Period 5:
Niobium, [Kr]5s 14d 4; Molybdenum,
[Kr]5s 14d 5; Ruthenium, [Kr]5s 14d 7;
Rhodium, [Kr]5s 14d 8; Palladium,
[Kr]4d 10; silver, [Kr]5s 14d 10.
Period 6: Lanthanum, [Xe]6s 24f 05d 1;
Platinum, [Xe]6s 14f 145d 9; Gold,
[Xe]6s 14f 145d 10
Interactive Figure Students can
interact with the electron configuration
at glencoe.com.
Interactive Figure To see an
animation of electron configurations,
visit glencoe.com.
Reading Check Ca: [Ar]4s 2
Cultural Diversity
4
The
Development of Fireworks Explain
that the Chinese may have 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 these crackers to frighten off
evil spirits and to celebrate weddings, births,
battle victories, and eclipses of the Moon.
Fireworks became much more interesting
2/1/07
12:44:02 PM
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.
The colors in fireworks are due to energylevel transitions of electrons in the metal
atoms of these inorganic compounds.
Section 5.3 • Electron Configuration
159
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]4s 23d 4, and copper, [Ar]4s 23d 9, would be incorrect.
The correct configurations for these two elements are [Ar]4s 13d 5 for
chromium and [Ar]4s 13d 10 for copper. The electron configurations for
these two elements, as well as those of several other elements, illustrate
the increased stability of half-filled and filled sets of s and d orbitals.
Reinforcement
Energy-Level Sequence 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 energy-level sequence for
electron configurations does not
render the aufbau sequence invalid.
PRACTICE Problems
Have students refer to p. 993 for
complete solutions to odd-numbered
problems. The complete solutions for
all problems can be found in the
Solutions Manual.
21. a. [Ar]4s 23d 104p 5
b. [Kr]5s 2
c. [Kr]5s 24d 105p 3
d. [Xe]6s 24f 145d 5
e. [Xe]6s 24f 9
f. [Ar]4s 23d 2
22. 5; 11
23. 6
24. indium
25. [Xe]6s 2; barium
Problem-Solving Strategy
Apply the Strategy
2
[Kr]5s 4d
2
Problem-Solving Strategy
Filling Atomic Orbitals
By drawing a sublevel diagram and following the arrows,
you can write the ground-state electron configuration for
any chemical element.
1s
1. Sketch the sublevel diagram on a blank piece of paper.
2. Determine the number of electrons in one atom of the element
for which you are writing the electron configuration. The
number of electrons in a neutral atom equals the element’s
atomic number.
3. Starting with 1s, write the aufbau sequence of atomic orbitals
by following the diagonal arrows from the top of the sublevel
diagram to the bottom. When you complete one line of arrows,
move to the right, to the beginning of the next line of arrows.
As you proceed, add superscripts indicating the numbers of
electrons in each set of atomic orbitals. Continue only until you
have sufficient atomic orbitals to accommodate the total number
of electrons in one atom of the element.
4. Apply noble-gas notation.
Apply the Strategy
Write the ground-state electron configuration for zirconium.
PRACTICE Problems
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
The sublevel diagram shows the order in
which the orbitals are usually filled.
Extra Practice Page 978 and glencoe.com
21. Write ground-state electron configurations for the following elements.
a. bromine (Br)
c. antimony (Sb)
e. terbium (Tb)
b. strontium (Sr)
d. rhenium (Re)
f. titanium (Ti)
22. A chlorine atom in its ground state has a total of seven electrons in orbitals related to the
atom’s third energy level. How many of the seven electrons occupy p orbitals? How many
of the 17 electrons in a chlorine atom occupy p orbitals?
23. When a sulfur atom reacts with other atoms, electrons in orbitals related to the atom’s
third energy level are involved. How many such electrons does a sulfur atom have?
24. An element has the ground-state electron configuration [Kr]5s 24d 105p 1. It is part of some
semiconductors and used in various alloys. What element is it?
25. Challenge In its ground state, an atom of an element has two electrons in all orbitals
related to the atom’s highest energy level for which n = 6. Using noble-gas notation,
write the electron configuration for this element, and identify the element.
Differentiated Instruction
C05_S3_874637.indd
5
Visually Impaired Make or purchase
cellular polystyrene or papier-mâché models of s, p, and d orbitals. Allow visually
impaired students to feel the models and
trace their contours to gain a better appreciation of their shapes and orientations.
BL EL
160
Chapter 5 • Electrons in Atoms
2/1/07
12:44:07
Valence Electrons
Use 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.
S
Valence Explain to students that
some textbooks and reference books
use the term valence in place of oxidation number. For example, some
books might indicate that oxygen has
a valence of 2-.
[Ne]3s 23p 4
Similarly, although a cesium atom contains 55 electrons, it has just one
valence electron, the 6s electron shown in cesium’s electron configuration.
Cs
Content Background
Valence Electrons Explain to
students that some inner-level
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 can be involved
in bonding.
[Xe]6s 1
Electron-dot structures Because valence electrons are involved in
forming chemical bonds, chemists often represent them visually using a
simple shorthand method, called electron-dot structure. 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 all of the atom’s valence electrons. 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 ground-state electron configurations and electron-dot structures
for the elements in the second period are shown in Table 5.6.
Table
5.6
Electron
Configurations
and Dot Structures
Interactive Table Explore
electron-dot structures at
glencoe.com.
Atomic
Number
Electron
Configuration
Electron-Dot
Structure
Lithium
3
1s 22s 1
Li
Beryllium
4
1s 22s 2
Be
Boron
5
1s 22s 22p 1
B
Carbon
6
1s 22s 22p 2
C
Nitrogen
7
1s 22s 22p 3
N
Oxygen
8
1s 22s 22p 4
O
Fluorine
9
1s 22s 22p 5
F
Neon
10
1s 22s 22p 6
Ne
Element
7 PMC05_S3_874637.indd
Interactive Table Students
can interact with the electron-dot
structures at glencoe.com.
Chemistry Journal
6
Another
Solar System—What if?
2/1/07
12:44:09 PM
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
might contain up to three electrons rather
than just two. Their speculation should
focus on the characteristics of the elements
on this new planet. OL
Section 5.3 • Electron Configuration
161
EXAMPLE Problem 5.3
IN-CLASS Example
Question How many electrons are
shown in the electron-dot structures
for atoms of lithium and potassium?
Atoms of fluorine and iodine? Atoms
of boron and thallium?
Electron-Dot Structures Some toothpastes contain stannous fluoride,
a compound of tin and fluorine. What is tin’s electron-dot structure?
1
Consult the periodic table to determine the total number of electrons in a tin atom. Write
out tin’s electron configuration, and determine its number of valence electrons. Then use
the rules for electron-dot structures to draw the electron-dot structure for tin.
2
one dot. Fluorine and iodine have seven dots.
Boron and thallium have three dots.
Have students refer to p. 993 for
complete solutions to odd-numbered
problems. The complete solutions for
all problems can be found in the
Solutions Manual.
26. Refer to Solutions Manual
27. aluminum; 3 electrons
28. helium
3 Assess
Solve for the Unknown
Tin has an atomic number of 50. Thus, a tin atom has 50 electrons.
[Kr]5s 24d 105p 2
Answer Lithium and potassium have
PRACTICE Problems
Analyze the Problem
Write out tin’s electron configuration using
noble-gas notation. The closest noble gas is Kr.
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 the four valence electrons around tin’s chemical symbol (Sn) to show
tin’s electron-dot structure. Sn
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
Extra Practice Page 978 and glencoe.com
26. Draw electron-dot structures for atoms of the following elements.
a. magnesium
b. thallium
c. xenon
27. An atom of an element has a total of 13 electrons. What is the element, and how many
electrons are shown in its electron-dot structure?
28. Challenge An element exists in the gaseous state at room temperature and normal
atmospheric pressure and is known to be one of the following: hydrogen, helium,
nitrogen, oxygen, fluorine, chlorine, or neon. Identify the element based on the electrondot structure at right.
X
Check for Understanding
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. Give students the
formula 2n2, which can be used to
calculate the number of electrons
related to each value of n. 32 and 50
electrons, respectively OL
Reteach
Have students write the electron-dot
structure of strontium. The 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. Then, ask what the
electron-dot structure does not
communicate about the strontium
atom’s electrons. It does not specify which
orbital contains the two electrons, nor does
it give any information about strontium’s
inner level electrons. OL
Extension
Ask students to identify the elements
that have the following ground-state
electron configurations.
[Ar]4s 23d 5 manganese
[Xe]6s 24f 145d 106p 3 bismuth OL
162
Chapter 5 • Electrons in Atoms
Section 5.3
Assessment
Section Summary
◗ The arrangement of electrons in an
atom is called the atom’s electron
configuration.
29.
MAIN Idea 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.
a. silicon
b. fluorine
c. calcium
d. krypton
◗ Electron configurations are defined
by the aufbau principle, the Pauli
exclusion principle, and Hund’s rule.
30. Define valence electron.
◗ An element’s valence electrons determine the chemical properties of the
element.
32. Extend the aufbau sequence through an element that has not yet been identified, but whose atoms would completely fill 7p orbitals. How many electrons such
an atom would have? Write its electron configuration using noble-gas notation
for the previous noble gas, radon.
◗ Electron configurations can be represented using orbital diagrams, electron configuration notation, and
electron-dot structures.
Section 5.3
C05_S3_874637.indd
31. Illustrate and describe the sequence in which ten electrons occupy the five
orbitals related to an atom’s d sublevel.
33. Interpret Scientific Illustrations Which is the correct electron-dot structure
for an atom of selenium? Explain.
a.
Se
b.
Se
c.
Se
d.
S
Assessment
7
29. a. Si 1s 22s 22p 63s 23p 2 c. Ca 1s 22s 22p 63s 23p 64s 2
b. F 1s 22s 22p 5
d. Kr 1s 22s 22p 63s 23p 64s 2
3d 104p 6
30. electrons in an atom’s outermost orbital
31. See Solutions Manual for illustrations.
Single electrons with the same spin occupy each
equal-energy orbital before additional electrons
with opposite spins occupy the same orbital.
2/1/07
32. 118 electrons. [Rn]7s 25f 146d 107p 6
33. c is correct; a shows three two-electron orbitals; b
shows one three-electron orbital; d has the wrong
symbol
Self-Check Quiz glencoe.com
12:44:14
Tiny Tweezers
Peering through a microscope, a cell biologist
can grasp a single cell with a pair of “tweezers.”
But these are not the kind of tweezers you
might find in a medicine cabinet. These tweezers
are made from two laser beams and can hold
very tiny things such as cells and even individual
atoms.
You might have heard that lasers can be used
to cut things. Laser “scissors” are used in some
surgeries. But surprisingly, lasers can also trap
living cells and other microscopic objects in their
beams without damaging them. How can beams
of light hold things in place?
Gripping with light When light rays pass
through a cell, they change direction slightly.
This is similar to how light rays bend when
passing through water in an aquarium. When
light rays are bent, they exert a force. Large
objects, such as aquariums, are too massive to
be affected by this miniscule force, but tiny
cells respond to the force. If the light rays are
positioned in just the right way, they can hold
a small object in place, as shown in Figure 1.
Microscope lens
Laser beam
Ray 1
Ray 2
2
1
Cell
F
F2
Scissors
beam
Tweezers
beam
Purpose
Students will learn how lasers can
be used as microscopic tweezers and
scissors in the smallest of surgeries.
Lens
Tweezers
beam
Background
Laser is an acronym for Light
Amplification by the Stimulated
Emission of Radiation. Laser light
can be contrasted with other sorts of
colored light, such as that produced
by neon lightbulbs. In a laser beam,
all the bits of light (called photons)
are the same wavelength (wavelength
determines the color of the light)
and are in phase with one another.
This property, called coherence, is
the crucial difference between laser
light and other light sources.
Spindle
Chromosome
Cell
Figure 2 Organelles found within living cells are accessible to
the smallest lasers.
Lasers and cancer So what use do scientists
have for these tiny tweezers? One group of
scientists is using them to study cell organelles.
They are studying the forces exerted by mitotic
spindles—the grouping of microtubules that
coordinates cell division. The spindles guide replicated chromosomes to opposite sides of the
cell—a key role in cell division. However, scientists do not know exactly how the spindles perform this function.
Tiny laser scissors have been used to cut off
pieces of chromosomes during cell division. Laser
tweezers were then used to move the pieces
around the cell and the spindles, as shown in
Figure 2. Knowing the force with which the
tweezers grasp the chromosomes, scientists can
measure the opposing force exerted by the spindles. Scientists hope that learning how spindles
function during cell division will help them learn
more about diseases related to cell division, such
as cancer—a disease in which cells divide
uncontrollably.
Teaching Strategies
Model the size of a cell, a molecule,
and an atom as a classroom exercise.
For instance, if an atom were the size
of a dot, perhaps 1 cm in diameter,
then a typical sugar molecule would
be about 10 cm in diameter and an
average human cell would be around
200,000 cm (or 2 km) wide. Such
a comparison might make students
think that cells are large; on the
contrary, it shows that atoms are
amazingly small. On this same scale,
a human being would be about
150,000 km long, stretching nearly
halfway from Earth to the Moon.
F1
Chemistry
2
1
Figure 1 As the laser passes through the cell, the beam is bent.
The cell feels a force in the opposite direction of bending and so is
held within the beam of light.
Laser Light Lasers can be found in a wide variety
of everyday settings. Research the different types
of lasers you might encounter daily, and find out
what kind of light each laser uses. Summarize the
results of your research in a journal. For more
information about how laser light is made, visit
glencoe.com.
Chemistry
C05_CH_874637.indd
RUBRIC available at glencoe.com
1
2/1/07
2:17:23 PM
Summarize Some of the lasers students might list
from their everyday lives include: Laser scanners found in
stores and libraries to read barcodes; CD players and CDROM; laser pointers; Police forces use invisible infrared
laser beams rather than radar systems to watch for speeding motorists.
Chemistry & Health
163
See the ChemLab worksheet in your
FAST FILE.
RUBRIC available at glencoe.com
Preparation
Time Allotment one class period
Process Skills compare and
contrast, predict, think critically,
classify, observe and infer, sequence
Safety Precautions Approve lab
safety forms before work begins.
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. Plug into wall receptacles only protected by GFI circuits.
Disposal The flasks of food coloring solutions can be reused.
Preparation of Materials
• Set up light sockets with lightbulbs
prior to class and have them
plugged in.
• Set up spectrum power supplies
and tubes prior to class.
Procedure
• Have several groups of students
start their observations of the gas
discharge tubes first, so that the
area does not become crowded
by the end of the class period.
• 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
• A possible source for the gas spectrum tubes and power supplies
would be the physics lab.
164 ChemLab
ANALYZE LINE SPECTRA
Background: Emission spectra are produced
when excited atoms return to a more stable state
by emitting radiation of specific wavelengths. When
white light passes through a sample, atoms in the
sample absorb specific wavelengths. This produces
dark lines in the continuous spectrum of white light
and is called an absorption spectrum.
Question: What absorption and emission spectra
do various substances produce?
Materials
ring stand with clamp
40-W tubular lightbulb
light socket with grounded power cord
275-mL polystyrene culture flask
Flinn C-Spectra® or similar diffraction grating
red, green, blue, and yellow food coloring
set of colored pencils
spectrum tubes (hydrogen, neon, and sodium)
spectrum-tube power supply (3)
7. With the room lights darkened, view the light using
the Flinn C-Spectra®. The top spectrum viewed will
be a continuous spectrum from the white lightbulb.
The bottom spectrum will be the absorption spectrum of the red solution. Use colored pencils to make
a drawing of the absorption spectra you observe.
8. Repeat Steps 6 and 7 using the green, blue, and
yellow solutions.
9. Cleanup and Disposal Turn off the light and
spectrum-tube power supplies. Wait several minutes
for the lightbulb and spectrum tubes to cool.
Dispose of the liquids and store the lightbulb
and spectrum tubes as directed by your teacher.
Safety Precautions
WARNING: Use care around the spectrum-tube power
supplies. Spectrum tubes will become hot when used.
Procedure
Analyze and Conclude
1. Read and complete the lab safety form.
2. Use a Flinn C-Spectra or similar diffraction grating
to view an incandescent lightbulb. Draw the
observed spectrum using colored pencils.
®
3. Use the Flinn C-Spectra® to view the emission
spectra from tubes of gaseous hydrogen, neon,
and sodium. Use colored pencils to draw the
observed spectra.
4. Fill a 275-mL culture flask with about 100 mL of
water. Add two or three drops of red food coloring
to the water. Shake the solution.
5. Repeat Step 4 for the green, blue, and yellow food
coloring.
6. Set up the 40-W lightbulb so that it is near eye level.
Place the flask with red food coloring about 8 cm
from the lightbulb so that you are able to see light
from the bulb above the solution and light from the
bulb projecting through the solution.
Analyze and Conclude
1. At any given time, the electron occupies a single
C05_CL_874637.indd
1
orbital. However,
it can move into other vacant orbitals as the atom absorbs or releases energy.
2. 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.
3. The spectrum of each element is unique. Thus,
the presence of a unique atomic spectrum indicates
the presence of that element.
4. Answers will vary.
1. Think Critically How can the single electron in a
hydrogen atom produce all of the lines found in its
emission spectrum?
2. Predict How can you predict the absorption
spectrum of a solution by looking at its color?
3. Apply How can spectra be used to identify the
presence of specific elements in a substance?
4. Error Analysis Name a potential source of error in
this experiment. Choose one of the elements you
observed, and research its absorption spectrum.
Compare your findings with the results of your
experiment.
INQUIRY EXTENSION
Hypothesize What would happen if you mixed
more than one color of food coloring with water
and repeated the experiment? Design an experiment
to test your hypothesis.
Inquiry Extension
Answers will vary.
2/1/07
Customize this lab with
the LabManager™
CD-ROM.
12:37:29
Download quizzes, key
terms, and flash cards
from glencoe.com.
BIG Idea The atoms of each element have a unique arrangement of electrons.
Study Guide
Section 5.1 Light and Quantized Energy
MAIN Idea Light, a form of
electromagnetic radiation, has
characteristics of both a wave
and a particle.
Key Concepts
• All waves are defined by their wavelengths, frequencies, amplitudes, and speeds.
Vocabulary
• In a vacuum, all electromagnetic waves travel at the speed of light.
• All electromagnetic waves have both wave and particle properties.
•
•
•
•
•
•
•
•
•
•
Use the Vocabulary
To reinforce chapter vocabulary,
have students write a sentence using
each term. OL EL
c = λν
amplitude (p. 137)
atomic emission spectrum (p. 144)
electromagnetic radiation (p. 137)
electromagnetic spectrum (p. 139)
frequency (p. 137)
photoelectric effect (p. 142)
photon (p. 143)
Planck’s constant (p. 142)
quantum (p. 141)
wavelength (p. 137)
• Matter emits and absorbs energy in quanta.
Review Strategies
E quantum = hν
• Ask students to write the equation
that relates frequency and wavelength. OL
• Have students write the equation
that relates the energy of a quantum
to the associated frequency. OL
• Ask students to relate Heisenberg’s
uncertainty principle to electrons
in atoms. OL
• Have students explain the relationship between an atom’s orbitals
and its energy levels. OL
• Problems from p. 978 or the
Supplemental Problems booklet
can be used for review. OL
• White light produces a continuous spectrum. An element’s emission spectrum
consists of a series of lines of individual colors.
Section 5.2 Quantum Theory and the Atom
MAIN Idea Wavelike properties
of electrons help relate atomic
emission spectra, energy states of
atoms, and atomic orbitals.
Key Concepts
• Bohr’s atomic model attributes hydrogen’s emission spectrum to electrons
dropping from higher-energy to lower-energy orbits.
∆E = E higher-energy orbit - E lower-energy orbit = E photon = hν
Vocabulary
•
•
•
•
•
•
•
•
•
atomic orbital (p. 152)
de Broglie equation (p. 150)
energy sublevel (p. 153)
ground state (p. 146)
Heisenberg uncertainty
principle (p. 151)
principal energy level (p. 153)
principal quantum number (p.153)
quantum mechanical model
of the atom (p. 152)
quantum number (p. 147)
• The de Broglie equation relates a particle’s wavelength to its mass, its velocity,
and Planck’s constant.
λ = h / mν
• The quantum mechanical model of the atom assumes that electrons have wave
properties.
• Electrons occupy three-dimensional regions of space called atomic orbitals.
Students can visit glencoe.com to:
• study the entire chapter online
• access Web links for more information, projects, and activities
• review content online with
the Interactive Tutor and take
Self-Check Quizzes
• take Chapter Tests and
Standardized Test Practice
• use Study to Go to download
content onto a PDA
Section 5.3 Electron Configuration
MAIN Idea A set of three rules can
be used to determine electron
arrangement in an atom.
Vocabulary
•
•
•
•
•
•
aufbau principle (p. 156)
electron configuration (p. 156)
electron-dot structure (p. 161)
Hund’s rule (p. 157)
Pauli exclusion principle (p. 157)
valence electron (p. 161)
C05_CA_874637.indd
1
Key Concepts
• The arrangement of electrons in an atom is called the atom’s electron
configuration.
• Electron configurations are defined by the aufbau principle, the Pauli exclusion
principle, and Hund’s rule.
• An element’s valence electrons determine the chemical properties of the element.
• Electron configurations can be represented using orbital diagrams, electron
configuration notation, and electron-dot structures.
What’s CHEMISTRY
Got To Do With It?
DVD Driving Into The Future
Use the ExamView®
Assessment Suite
CD-ROM to:
Vocabulary PuzzleMaker
2/1/07
2:19:07 PM
For additional practice with vocabulary, have
students access the Vocabulary PuzzleMaker
online at glencoe.com.
Vocabulary Puzzlemaker glencoe.com
• create multiple versions of tests
• create modified tests with one
mouse click
• edit existing questions and add
your own questions
• build tests aligned with state standards using built-in state curriculum tags
• change English tests to Spanish
with one mouse click
• track students’ progress using the
Teacher Management System
Chapter 5 • Study Guide
165
Assessment
Section 5.1
Mastering Concepts
34. a. Frequency is the number 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.
35. d. X-rays, a. ultraviolet light, b. microwaves, c. radio waves
36. 2.88 × 10 21 gamma-ray electromagnetic
waves of this frequency pass a given
point per second.
37. A phenomenon in which a metal emits
electrons when light of a sufficient
frequency shines on it.
38. The light from a neon sign contains only
certain visible colors, while sunlight
contains the full spectrum of colors.
39. According to Planck, for a given frequency,
ν, matter can emit or absorb energy
only in discrete quanta that are wholenumber multiples of hν.
40. He proposed that photons must have
a certain minimum, or threshold, value
to cause the ejection of a photoelectron.
41. The red waves have a longer wavelength
and a lower frequency.
42. The color of the light changes as the
object acquires more energy.
43. The wave model does not explain the
photoelectric effect, atomic emission
spectra, and why matter emits different
frequencies of light at different
temperatures.
44. Both types of waves travel at the same
speed in a vacuum, 3.00 × 10 8 m/s.
Radio waves have a longer wavelength
and lower frequency than ultraviolet
waves.
166 Chapter 5 • Assessment
Section 5.1
48. What is the speed of an electromagnetic wave with a
frequency of 1.33 × 10 17 Hz and a wavelength of 2.25 nm?
Mastering Concepts
49. What is the energy of a photon of red light that has a
frequency of 4.48 × 10 14 Hz?
34. Define the following terms.
a. frequency
b. wavelength
c. quantum
d. ground state
Hg
35. Arrange the following types of electromagnetic radiation
in order of increasing wavelength.
a. ultraviolet light
c. radio waves
b. microwaves
d. X rays
λ (nm) 400
■
450
500
550
600
650
700
Figure 5.21
50. Mercury Mercury’s atomic emission spectrum is shown
in Figure 5.21. Estimate the wavelength of the orange
36. A gamma ray has a frequency of 2.88 × 10 21 Hz. What
does this mean?
line. What is its frequency? What is the energy of a photon corresponding to the orange line emitted by the
mercury atom?
37. What is the photoelectric effect?
38. Neon Sign How does light emitted from a neon sign
differ from sunlight?
51. What is the energy of an ultraviolet photon that has a
39. Explain Planck’s quantum concept as it relates to energy
wavelength of 1.18 × 10 -8 m?
lost or gained by matter.
52. A photon has an energy of 2.93 × 10 -25 J. What is its
40. How did Einstein explain the photoelectric effect?
frequency? What type of electromagnetic radiation is
the photon?
41. Rainbow What are two differences between the red and
green electromagnetic waves in a rainbow?
53. A photon has an energy of 1.10 × 10 -13 J. What is the
42. Temperature What happens to the light emitted by a
photon’s wavelength? What type of electromagnetic
radiation is it?
heated, glowing object as its temperature increases?
54. Spacecraft How long does it take a radio signal from
43. What are three deficiencies of the wave model of light
the Voyager spacecraft to reach Earth if the distance
between Voyager and Earth is 2.72 × 10 9 km?
related to light’s interaction with matter?
44. How are radio waves and ultraviolet waves similar? How
are they different?
55. Radio Waves If your favorite FM radio station
broadcasts at a frequency of 104.5 MHz, what is the
wavelength of the station’s signal in meters? What is
the energy of a photon of the station’s electromagnetic
signal?
Mastering Problems
Radio
Infrared
Ultraviolet Gamma rays
X rays
12
10
Microwaves
56. Platinum What minimum frequency of light is needed
4
10
10
6
10
8
10
10
10
14
10
16
10
18
10
20
10
to eject a photoelectron from atoms of platinum, which
require at least 9.08 × 10 -19 J/photon?
22
Frequency (ν) in hertz
57. Eye Surgery The argon fluoride (ArF) laser used in
Electromagnetic Spectrum
■
some refractive eye surgeries emits electromagnetic
radiation of 193.3 nm wavelength. What is the frequency
of the ArF laser’s radiation? What is the energy of a single quantum of the radiation?
Figure 5.20
45. Radiation Use Figure 5.20 to determine the following
types of radiation.
a. radiation with a frequency of 8.6 × 10 11 s -1
b. radiation with a wavelength of 4.2 nm
c. radiation with a frequency of 5.6 MHz
d. radiation that travels at a speed of 3.00 × 10 8 m/s
410 434
nm nm
λ (nm) 400
46. What is the wavelength of electromagnetic radiation
■
500
550
600
650
700
750
Figure 5.22
58. Hydrogen One line in hydrogen’s emission spectrum
has a wavelength of 486 nm. Examine Figure 5.22 to
47. What is the frequency of electromagnetic radiation
with a wavelength of 3.33 × 10 -8 m? What type of
electromagnetic radiation is this?
45. a. infrared
C05_CA_874637.indd
2
b. X ray
c. AM radio
d. any EM wave
46. λ = 6.00 × 10 -5 m; infrared radiation
47. ν = 9.01 × 10 15 s -1; ultraviolet radiation
48. ν = 3.00 × 10 8 m/s
49. E photon = 2.97 × 10 -19 J
50. λ = 615 nm, ν =4.88 × 10 14 s −1,
E photon = 3.23 × 10 −19 J
51. E photon = 1.68 × 10 −17 J
52. ν = 4.42 × 10 8 s -1; TV or FM wave
53. λ = 1.81 × 10 -12 m; an X ray or gamma-ray
450
656
nm
Hydrogen’s Atomic Emission Spectrum
with a frequency of 5.00 × 10 12 Hz? What kind of
electromagnetic radiation is this?
Mastering Problems
486
nm
determine the line’s color. What is the line’s frequency?
54.
55.
56.
57.
58.
t = 9070 s, or 151 min
λ = 2.87 m, E photon = 6.92 × 10 -26 J
1.37 × 10 15 Hz
ν = 1.55 × 10 15 s -1; E = 1.03 × 10 –18 J
The line is blue-green. Its frequency is 6.17 × 10 14 s -1.
Chapter Test glencoe.com
2/1/07
2:19:17
Section 5.2
Section 5.2
Section 5.3
Mastering Concepts
Mastering Concepts
59. According to the Bohr model, how do electrons move
76. In what sequence do electrons fill the atomic orbitals
in atoms?
related to a sublevel?
60. What does n designate in Bohr’s atomic model?
7p
61. What is the difference between an atom’s ground state
7s
trons are treated as waves? Who first wrote the electron
wave equations that led to this model?
63. What is an atomic orbital?
64. What does n represent in the quantum mechanical
model of the atom?
6s
5s
Increasing energy
62. What is the name of the atomic model in which elec-
Orbital filling sequence
and an excited state?
Ultraviolet series (Lyman)
5p
6d
5f
5d
4f
4d
4p
3d
3p
3s
2p
2s
n=1+ n=2
n=3
n=4
n=5
n=6
n=7
6p
4s
Visible series (Balmer)
■
Mastering Concepts
1s
■
Figure 5.24
77. Rubidium Using Figure 5.24, explain why one electron
in a rubidium atom occupies a 5s orbital rather than a
4d or 4f orbital.
Infrared series (Paschen)
78. What are valence electrons? How many of a magnesium
Figure 5.23
atom’s 12 electrons are valence electrons?
65. Electron Transition According to the Bohr model
shown in Figure 5.23, what type of electron-orbit
transitions produce the ultraviolet lines in hydrogen’s
Lyman series?
66. How many energy sublevels are contained in each of the
79. Light is said to have a dual wave-particle nature. What
does this statement mean?
80. Describe the difference between a quantum and
a photon.
81. How many electrons are shown in each element’s elec-
hydrogen atom’s first three energy levels?
tron-dot structure?
a. carbon
b. iodine
67. What atomic orbitals are related to a d sublevel?
68. What do the sublevel designations s, p, d, and f specify
with respect to the atom’s orbitals?
c. calcium
d. gallium
82. When writing the electron configuration notation for an
atom, what three principles or rules should you follow?
69. How are the five orbitals related to an atom’s d sublevel
83. Write the electron configuration and draw the orbital
designated?
notation for atoms of oxygen and sulfur.
70. What is the maximum number of electrons an orbital
can contain?
71. Describe the relative orientations of the orbitals related
to an atom’s 2p sublevel.
72. How many electrons can be contained in all the orbitals
Mastering Problems
84. List the aufbau sequence of orbitals from 1s to 7p.
85. Write each element’s orbital notation and complete
electron configuration.
a. beryllium
b. aluminum
related to an argon atom’s third energy level?
73. How does the quantum mechanical model of the atom
describe the paths of an atom’s electrons?
74. Macroscopic Objects Why do we not notice the wave-
c. nitrogen
d. sodium
86. Use noble-gas notation to describe the electron
lengths of moving objects such as automobiles?
75. Why is it impossible to know precisely the velocity and
position of an electron at the same time?
81. a: 4; b: 7; c: 2; d: 3
82. Pauli exclusion principle, aufbau principle, and
7 PMC05_CA_874637.indd
3 Hund’s rule
83. oxygen: 1s 22s 22p 4; The orbital diagram has five boxes
with two arrows in the first three and single arrows in
the last two. sulfur: [Ne]3s 23p 4; The orbital diagram
has nine boxes with two arrows in the first seven and
single arrows in the last two.
Mastering Problems
84. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p,
7s, 5f, 6d, 7p
Chapter Test glencoe.com
configurations of the elements represented by the
following symbols.
a. Kr
c. Zr
b. P
d. Pb
59. Electrons move in circular orbits around
the nucleus.
60. The quantum number n specifies the
electron’s orbit.
61. An atom’s ground state is its lowest energy
state, while any energy state higher than
the ground state is an excited state.
62. the quantum mechanical model of the
atom; Erwin Schrödinger
63. a three-dimensional region around
the nucleus describing an electron’s
probable location
64. n represents an orbital’s principal quantum
number, which indicates the relative size
and energy of the orbital.
65. The Lyman series is caused by electron
transitions from Bohr’s higher energy
orbits to the n = 1 orbit.
66. Energy level 1 has one sublevel, energy
level 2 has two sublevels, energy level 3
has three sublevels
67. d sublevel: xy, xz, yz, x 2 - y 2, and z 2
orbitals
68. their shapes
69. xy, xz, yz, x 2 - y 2, z 2
70. two electrons
71. Lying along the x, y, and z coordinate
axes, the three p orbitals are mutually
perpendicular.
72. eight electrons
73. The quantum mechanical gives no
description of the electrons’ paths.
74. Their wavelengths are too small to be seen.
75. The photon required to measure an
electron’s velocity or position changes
both the position and velocity of
the electron.
Section 5.3
Mastering Concepts
76.
85. a. Be 1s 22s 2
b. Al 1s 22s 22p 63s 23p 1
↑↓ ↑↓ ↑↓↑↓↑↓ ↑↓ ↑
↑↓ ↑↓
1s 2s
2p2/1/07 3s12:34:43
3p PM 77.
1s 2s
c. N 1s 22s 22p 3
d. Na 1s 22s 22p 63s 1
↑↓ ↑↓ ↑ ↑ ↑
↑↓ ↑↓ ↑↓↑↓↑↓ ↑
78.
1s 2s 2p
1s 2s
2p 3s
86. a. Kr [Ar]4s 23d 104p 6
79.
b. P [Ne]3s 23p 3
c. Zr [Kr]5s 24d 2
d. Pb [Xe]6s 24f 145d 106p 2
80.
Each orbital must contain a single
electron before any orbital contains
two electrons.
The orbital related to the 5s sublevel has
a lower energy than orbitals related to
the 4d and 4f sublevels.
Valence electrons are the electrons in an
atom’s outermost orbitals; 2.
Light exhibits wavelike behavior in
some situations and particlelike
behavior in others.
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.
Chapter 5 • Assessment
167
F
Ca
Nd
Te
Br
87. What element is represented by each electron
configuration?
a. 1s 22s 22p 5
b. [Ar]4s 2
c. [Xe]6s 24f 4
d. [Kr]5s 24d 105p 4
e. [Rn]7s 25f 13
f. 1s 22s 22p 63s 23p 64s 23d 104p 5
C
95. What is the wavelength of light with a frequency of
→
→
→
→
→
→
→
5.77 × 10 14 Hz?
1.
3.
2.
4.
→
→
→
→
→
Figure 5.27
→
■
→
→
→
→
3d
→
4s
→
→
3p
→
→
3s
96. Waves Using the waves shown in Figure 5.27, identify
→
→
→
→
the wave or waves with the following characteristics.
a. longest wavelength
b. greatest frequency
c. largest amplitude
d. shortest wavelength
→
→
→
→
3d
4s
→
Mixed Review
3p
→
3s
→
Sn
→
c. Po
d. K
e. Ba
91. 18; 15; 4
92. b
93. [Kr]5s 24d 105p 2
contained in an atom’s orbitals having the following
principal quantum numbers?
a. 3
c. 6
b. 4
d. 7
atom in an excited state?
a. [Ar]4s 23d 104p 2
b. [Ne]3s 23p 5
c. [Kr]5s 24d 1
d. [Ar]4s 23d 84p 1
b. As
Mixed Review
94. What is the maximum number of electrons that can be
88. Which electron configuration notation describes an
→
87. a.
b.
c.
d.
f.
88. d
89. a
90. a.
→
→
→
→
→
3d
→
→
→
4s
→
→
→
→
3p
97. How many orientations are possible for the orbitals
→
94. a. 18
c. 72
b. 32
d. 98
95. ν = 5.20 × 10 -7 m
96. a. longest wavelength: 4
b. greatest frequency: 3
c. largest amplitude: 1 and 3
d. shortest wavelength: 3
97. a. 1
c. 5
b. 3
d. 7
98. helium, calcium, cobalt, barium
99. n = 4 → n = 2
100. The two dots are the atom’s two 4s
valence electrons.
101. ν = 4.54 × 10 15 s -1;
λ = 6.60 × 10 -8 m
102. francium
103. Bohr proposed that atoms emit light
of certain wavelengths and energies
when electrons move from higherenergy orbits to lower-energy orbits.
104. 3.10 × 10 19 photons
105. Its wavelength decreases.
106. The energy of the atom increases
as one or more electrons move into
orbitals farther from the nucleus.
3s
→
→
→
→
→
3s
■
Chapter 5 • Assessment
3d
4s
Figure 5.25
89. Which orbital diagram in Figure 5.25 is incorrect for an
atom in its ground state?
90. Draw an electron-dot structure for an atom of each
element.
a. carbon
b. arsenic
c. polonium
d. potassium
e. barium
98. Which elements have only two electrons in their electron-
dot structures: hydrogen, helium, lithium, aluminum,
calcium, cobalt, bromine, krypton, or barium?
produces the blue-green line in hydrogen’s atomic emission spectrum?
100. Zinc A zinc atom contains a total of 18 electrons in its
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?
X
■
3s, 3p, and 3d orbitals. Why does its electron-dot structure show only two dots?
101. X Ray An X-ray photon has an energy of 3.01 × 10 -18 J.
What is its frequency and wavelength?
102. Which element has the ground-state electron configura-
tion represented by the noble-gas notation [Rn]7s 1?
103. How did Bohr explain atomic emission spectra?
Figure 5.26
92. Which element could have the ground-state
electron-dot notation shown in Figure 5.26?
a. manganese
b. antimony
related to each sublevels?
a. s
c. d
b. p
d. f
99. In Bohr’s atomic model, what electron-orbit transition
91. Arsenic An atom of arsenic has how many electron-
c. calcium
d. samarium
93. For an atom of tin in the ground state, write the electron
configuration using noble-gas notation, and draw its
electron-dot structure.
C05_CA_874637.indd
168
3p
104. Infrared Radiation How many photons of infrared
radiation with a fre-quency of 4.88 × 10 13 Hz are
required to provide an energy of 1.00 J?
105. Light travels slower in water than it does in air; however,
its frequency remains the same. How does the wavelength of light change as it travels from air to water?
106. According to the quantum mechanical model of the
atom, what happens when an atom absorbs a quantum
of energy?
4
2/1/07
Chapter Test glencoe.com
12:34:57
7
Think Critically
Think Critically
Additional Assessment
107. Compare and Contrast Briefly discuss the difference
between an orbit in Bohr’s model of the atom and an
orbital in the quantum mechanical view of the atom.
Chemistry
115. Neon Signs To make neon signs emit different col-
108. Calculate It takes 8.17 × 10 -19 J of energy to remove
ors, manufacturers often fill the signs with gases other
than neon. Write an essay about the use of gases in
neon signs and the colors produced by the gases.
one electron from a gold surface. What is the maximum
wavelength of light capable of causing this effect?
z
z
z
116. Rutherford’s Model Imagine that you are a scientist
in the early twentieth century, and you have just
learned the details of a new, nuclear model of the atom
proposed by the prominent English physicist Ernest
Rutherford. After analyzing the model, you discern
what you believe to be important limitations. Write a
letter to Rutherford in which you express your concerns regarding his model. Use diagrams and examples
of specific elements to help you make your point.
y
x
x
x
y
y
py
1s orbital
■
p orbital
dxz
d orbital
Document-Based Questions
Figure 5.28
109. Describe the shapes of the atomic orbitals shown in
Figure 5.28. Specify their orientations and relate each
orbital to a particular type of energy sublevel.
110. Infer Suppose that you live in a universe in which
the Pauli exclusion principle states that a maximum
of three, rather than two, electrons can occupy a single
atomic orbital. Evaluate and explain the new chemical
properties of the elements lithium and phosphorus.
Challenge Problem
Sodium Vapor When sodium metal is vaporized in a gasdischarge lamp, two closely spaced, bright yellow-orange lines
are produced. Because sodium vapor lamps are electrically
efficient, they are used widely for outdoor lighting, such as
streetlights and security lighting.
Figure 5.29 shows the emission spectrum of sodium metal.
The entire visible spectrum is shown for comparison.
Data obtained from: Volland, W. March 2005. Spectroscopy: Element
Identification and Emission Spectra.
Challenge Problem
111. Hydrogen Atom The hydrogen atom’s energy is
111. λ = 9.38 × 10 -8 m
-6.05 × 10 –20 J when the electron is in the n = 6 orbit
and -2.18 × 10 –18 J when the electron is in the n = 1.
Calculate the wavelength of the photon emitted when
the electron drops from the n = 6 orbit to the n = 1
orbit. Use the following values: h = 6.626 × 10 –34 J•s
and c = 3.00 × 10 8 m/s.
Cumulative Review
112. Round 20.56120 g to three significant figures. (Chapter 2)
Cumulative Review
Na
■
Figure 5.29
117. Differentiate between the two spectra shown above.
118. Sodium’s two bright lines have wavelengths of
588.9590 nm and 589.9524 nm. What is the groundstate electron configuration notation for sodium, and
how does sodium’s electron configuration relate to
the lines?
113. Identify whether each statement describes a chemical
property or a physical property. (Chapter 3)
a. Mercury is a liquid at room temperature.
b. Sucrose is a white, crystalline solid.
c. Iron rusts when exposed to moist air.
d. Paper burns when ignited.
107. In the Bohr model, an orbit is a circular
path taken by an electron as it moves
around the atomic nucleus. In the
quantum mechanical model, an orbital
is a three-dimensional region around
the nucleus that describes the electron’s
probable location.
108. λ = 2.43 × 10 -7 m
109. The first orbital is spherical and related
to an s sublevel. The second orbital
is dumbbell-shaped, oriented along
the y-axis, and related to a p sublevel.
The third orbital consists of two,
perpendicular dumbbell-shaped parts,
lies in the xz plane, and is related to
a d sublevel.
110. Both lithium and phosphorus would be
noble gases. Lithium, with an electron
configuration notation of 1s 3, would be
analogous to helium (1s 2). Phosphorus,
with an electron configuration notation
of 1s 32s 32p 9, would be analogous to
neon (1s 2, 2s 2, 2p 6).
112. 20.6 g
113. a. physical property
b. physical property
c. chemical property
d. chemical property
114. 64 electrons, 64 protons, 89 neutrons
Additional Assessment
119. Calculate the energies of photons related to the
114. An atom of gadolinium has an atomic number of 64 and
a mass number of 153. How many electrons, protons,
and neutrons does it contain? (Chapter 4)
two lines using the relationships expressed in the
following equations.
Chemistry
RUBRIC available at glencoe.com
E photon = hv; c = λv; E = hc/λ
Document-Based Questions
Data obtained from: Dr. Walt Volland. March, 2005. Spectroscopy:
PMC05_CA_874637.indd
5
Element
Identification and Emission Spectra
117. One shows all the colors of the complete visible
spectrum; the other shows just certain colors
emitted by sodium atoms, known as sodium’s
atomic emission spectrum.
118. 1s 22s 22p 63s 1; The two lines are produced when
sodium atoms drop from excited states to lowerenergy states. This occurs when electrons in
higher-energy orbitals drop into lower-energy
orbitals.
119. 3.38 × 10 -19 J and 3.37 × 10 -19 J
Chapter Test glencoe.com
2/1/07
115. Students answers might include the
following elements and colors: helium
(yellow); neon (orange-red); sodium
(yellow); argon (lavender); krypton
(white); xenon (blue).
12:35:07 PM
116. Answers will vary.
Chapter 5 • Assessment 169
Cumulative
Standardized Test Practice
Multiple Choice
1.
2.
3.
4.
5.
6.
7.
8.
9.
D
C
B
C
D
C
D
A
D
Standardized Test Practice
Multiple Choice
1. Cosmic rays are high-energy radiation from outer
space. What is the frequency of a cosmic ray that has
a wavelength of 2.67 × 10 -13 m when it reaches
Earth? (The speed of light is 3.00 × 10 8 m/s.)
A. 8.90 × 10 -22 s -1
B. 3.75 × 10 12 s -1
C. 8.01 × 10 −5 s -1
D. 1.12 × 10 21 s -1
In
C.
In
D.
In
z
z
x
y
x
x
y
y
3. To which sublevel do all of these orbitals belong?
A. s
B. p
C. d
D. f
4. How many electrons total can reside in this sublevel?
A. 2
B. 3
C. 6
D. 8
5. What is the maximum theoretical number of
electrons related to the fifth principal energy level
of an atom?
A. 10
B. 20
C. 25
D. 50
C05_STP_874637.indd
170
Chapter 5 • Assessment
Symbol
Atomic
Number
Vanadium
V
23
[Ar]4s 23d 3
Yttrium
Y
39
[Kr]5s 24d 1
Element
Electron
Configuration
Scandium
Sc
21
Cadmium
Cd
48
[Ar]4s 23d 1
6. Using noble-gas notation, what is the ground-state
electron configuration of Cd?
A. [Kr]4d 104f 2
B. [Ar]4s 23d 10
C. [Kr]5s 24d 10
D. [Xe]5s 24d 10
Use the figure below to answer Questions 3 and 4.
z
Electron Configurations for Selected Transition Metals
[Xe]6s 24f 145d 6
2. Which is the electron-dot structure for indium?
A. In
B.
Use the periodic table and the table below to answer
Questions 6 to 8.
7. What is the element that has the ground-state
electron configuration [Xe]6s 24f 145d 6?
A. La
B. Ti
C. W
D. Os
8. What is the complete electron configuration of a
scandium atom?
A. 1s 22s 22p 63s 23p 64s 23d 1
B. 1s 22s 22p 73s 23p 74s 23d 1
C. 1s 22s 22p 53s 23p 54s 23d 1
D. 1s 22s 12p 73s 13p 74s 23d 1
9. Which is NOT evidence that a chemical change has
occurred?
A. The properties of the substances involved in the
reaction have changed.
B. An odor is produced.
C. The composition of the substances involved in
the reaction have changed.
D. The total mass of all substances involved has
changed.
1
2/1/07
Standardized Test Practice glencoe.com
12:45:24
Short Answer
Short Answer
10. Check that the graph is approximately
linear, with time on the x-axis and temperature on the y-axis.
11. This process is occurring at a constant
rate. One can tell because there is only
one constant slope; the best-fit line
is linear.
12. Use slope = rise/run to find the slope;
students should select two points on
the line of best fit to compare (not two
points from the data table) such as
(45 s, 22°) and (220 s, 45°). With
these points, slope = (45 - 22) ÷
(220 - 45) = 0.13 degrees per second.
Multiply by 60 seconds per minute
to convert this value into degrees
per minute.
13. 39.6 + 273 = 313 K; (9/5)(39.6) + 32
= 103°F
SAT Subject Test: Chemistry
Use the data below to answer Questions 10 to 13.
27.8
32.0
150
35.3
180
39.6
210
43.3
240
48.1
2
1s 2s
1
→
→
→
→
→
→
→
→
→
D.
2
→
→
→
2
1s 2s
2p
→
90
120
B.
3
→
24.2
2p
→
19.7
60
2
→
30
2
1s 2s
→
16.3
1s
→
0
C.
2
→
A.
Temperature (°C)
→
Time (s)
→
Temperature of Water with Heating
→
Use the diagram below to answer Questions 17 and 18.
6
16. Which shows an orbital diagram that violates the
aufbau principle?
A. A
D. D
B. B
E. none
C. C
17. Which shows the orbital diagram for the element
beryllium?
A. A
D. D
B. B
E. none
C. C
10. Make a graph showing temperature versus time.
11. Is the heating of this sample of water a linear
process? Explain how you can tell.
18. A student performs an experiment to measure the
boiling point of pentane and measures it at 37.2°C.
The literature reports this value as 36.1°C. What is
the student’s percent error?
A. 97.0%
B. 2.95%
C. 1.1%
D. 15.5%
E. 3.05%
12. Use your graph to find the approximate rate of
heating in degrees per second. What is this value in
degrees per minute?
13. Show the equation to convert the temperature at
180 s from degrees Celsius to Kelvin and to degrees
Fahrenheit.
Extended Response
19. Which method of separating components of a
mixture
14.X depends on the different boiling points of
the components of the mixture?
A. chromatography
B. filtration
C. crystallization
D. distillation
E. sublimation
14. Compare the information provided in an electrondot structure with the information in an electron
configuration.
15. Explain why 1s 22s 22p 63s 23p 64s 24d 104p 2 is not the
correct electron configuration for germanium (Ge).
Write the correct electron configuration for
Germanium.
Extended Response
14. An electron-dot structure provides information about how many valence or outer
energy level electrons are in the atom,
whereas the electron configuration
shows the energy level and sublevel
for all electrons in the atom.
15. The electrons in the d sublevel are in
the third energy level, not the fourth.
The correct electron configuration would
be 1s 22s 22p 63s 23p 64s 23d 104p 2.
SAT Subject Test: Chemistry
16.
17.
18.
19.
NEED EXTRA HELP?
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Question . . .
Review Section . . .
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
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18
19
5.1
5.3
5.2
5.2
5.2
5.3
5.3
5.3
3.2
2.4
2.4
2.4
2.1
5.3
5.3
5.3
5.3
2.3
3.3
2
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D
B
E
D
12:45:31 PM
Chapter 5 • Assessment 171