Chapter 4

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Table of Contents
Chapter 4 Arrangement of Electrons in Atoms
Section 1 The Development of a New Atomic Model
Section 2 The Quantum Model of the Atom
Section 3 Electron Configurations

Section 1 The Development of a New
Atomic Model
Objectives
• Explain the mathematical relationship among the
speed, wavelength, and frequency of
electromagnetic radiation.
• Discuss the dual wave-particle nature of light.
• Discuss the significance of the photoelectric effect
and the line-emission spectrum of hydrogen to the
development of the atomic model.
• Describe the Bohr model of the hydrogen atom.
Chapter 4

Atomic Model
Properties of Light
The Wave Description of Light
• Electromagnetic radiation is a form of energy that
exhibits wavelike behavior as it travels through
space.
• Together, all the forms of electromagnetic radiation
form the electromagnetic spectrum.
Chapter 4

Electromagnetic Spectrum
Atomic ModelChapter 4

Visual Concepts
Click below to watch the Visual Concept.
Visual Concept
Electromagnetic Spectrum
Chapter 4

Atomic Model
Properties of Light, continued
• Wavelength () is the distance between
corresponding points on adjacent waves.
• Frequency (v) is defined as the number of waves
that pass a given point in a specific time, usually one
second.
Chapter 4

Atomic Model
Properties of Light, continued
• Frequency and wavelength are mathematically related
to each other:
c = v
• In the equation, c is the speed of light (in m/s),  is the
wavelength of the electromagnetic wave (in m), and v
is the frequency of the electromagnetic wave (in s1).
Chapter 4

Wavelength and Frequency

Atomic Model
The Photoelectric Effect
• The photoelectric effect refers to the emission
of electrons from a metal when light shines on
the metal.
The Particle Description of Light
• A quantum of energy is the minimum quantity of
energy that can be lost or gained by an atom.
Chapter 4

Photoelectric Effect

Visual Concepts
Visual Concept
Photoelectric Effect
Chapter 4

Atomic Model
The Photoelectric Effect, continued
The Particle Description of Light, continued
• German physicist Max Planck proposed the following
relationship between a quantum of energy and the frequency
of radiation:
E = hv
• E is the energy, in joules, of a quantum of radiation, v is
the frequency, in s−1, of the radiation emitted, and h is a
fundamental physical constant now known as Planck’s
constant; h = 6.626  1034 J• s.
Chapter 4

Atomic Model
The Photoelectric Effect, continued
The Particle Description of Light, continued
• A photon is a particle of electromagnetic
radiation having zero mass and carrying a
quantum of energy.
• The energy of a particular photon depends on the
frequency of the radiation.
Ephoton = hv
Chapter 4

Visual Concepts
Visual Concept
Quantization of Energy
Chapter 4

Visual Concepts
Visual Concept
Energy of a Photon
Chapter 4

Atomic Model
The Hydrogen-Atom Line-Emission Spectrum
• The lowest energy state of an atom is its ground
state.
• A state in which an atom has a higher potential
energy than it has in its ground state is an
excited state.
Chapter 4

Atomic Model
The Hydrogen-Atom Line-Emission Spectrum,
continued
• When investigators passed electric current
through a vacuum tube containing hydrogen gas
at low pressure, they observed the emission of a
characteristic pinkish glow.
• When a narrow beam of the emitted light was
shined through a prism, it was separated into
four specific colors of the visible spectrum.
• The four bands of light were part of what is
known as hydrogen’s line-emission spectrum.
Chapter 4

Hydrogen’s Line-Emission Spectrum

Visual Concepts
Visual Concept
Absorption and Emission Spectra
Chapter 4

Atomic Model
Bohr Model of the Hydrogen Atom
• Niels Bohr proposed a hydrogen-atom model that
linked the atom’s electron to photon emission.
• According to the model, the electron can circle the
nucleus only in allowed paths, or orbits.
• The energy of the electron is higher when the
electron is in orbits that are successively farther
from the nucleus.
Chapter 4

Visual Concepts
Visual Concept
Bohr Model of the Atom
Chapter 4

Atomic Model
• When an electron falls to a lower energy level, a
photon is emitted, and the process is called
emission.
• Energy must be added to an atom in order to move
an electron from a lower energy level to a higher
energy level. This process is called absorption.
Chapter 4
Bohr Model of the Hydrogen Atom, continued

Photon Emission and Absorption

Visual Concepts
Visual Concept
Comparing Models of the Atom
Chapter 4

Section 2 The Quantum Model of
the Atom
Lesson Starter
• Write down your address using the format of street
name, house/apartment number, and ZIP Code.
• These items describe the location of your residence.
• How many students have the same ZIP Code? How
many live on the same street? How many have the
same house number?
Chapter 4

the Atom
Lesson Starter, continued
• In the same way that no two houses have the same
address, no two electrons in an atom have the same
set of four quantum numbers.
• In this section, you will learn how to use the
quantum-number code to describe the properties of
electrons in atoms.
Chapter 4

the Atom
Objectives
• Discuss Louis de Broglie’s role in the development
of the quantum model of the atom.
• Compare and contrast the Bohr model and the
quantum model of the atom.
• Explain how the Heisenberg uncertainty principle
and the Schrödinger wave equation led to the idea
of atomic orbitals.
Chapter 4

the Atom
Objectives, continued
• List the four quantum numbers and describe their
significance.
• Relate the number of sublevels corresponding to
each of an atom’s main energy levels, the number
of orbitals per sublevel, and the number of orbitals
per main energy level.
Chapter 4

the Atom
Electrons as Waves
• French scientist Louis de Broglie suggested that
electrons be considered waves confined to the
space around an atomic nucleus.
• It followed that the electron waves could exist only at
specific frequencies.
• According to the relationship E = hv, these
frequencies corresponded to specific energies—the
quantized energies of Bohr’s orbits.
Chapter 4

the Atom
Electrons as Waves, continued
• Electrons, like light waves, can be bent, or diffracted.
• Diffraction refers to the bending of a wave as it
passes by the edge of an object or through a small
opening.
• Electron beams, like waves, can interfere with each
other.
• Interference occurs when waves overlap.
Chapter 4

Visual Concepts
Visual Concept
De Broglie and the Wave-Particle Nature of
Electrons
Chapter 4

the Atom
The Heisenberg Uncertainty Principle
• German physicist Werner Heisenberg proposed that
any attempt to locate a specific electron with a
photon knocks the electron off its course.
• The Heisenberg uncertainty principle states that it
is impossible to determine simultaneously both the
position and velocity of an electron or any other
particle.
Chapter 4

Visual Concepts
Visual Concept
Heisenberg Uncertainty Principle
Chapter 4

the Atom
The Schrödinger Wave Equation
• In 1926, Austrian physicist Erwin Schrödinger
developed an equation that treated electrons in
atoms as waves.
• Together with the Heisenberg uncertainty principle,
the Schrödinger wave equation laid the foundation
for modern quantum theory.
• Quantum theory describes mathematically the
wave properties of electrons and other very small
particles.
Chapter 4

the Atom
The Schrödinger Wave Equation, continued
• Electrons do not travel around the nucleus in neat
orbits, as Bohr had postulated.
• Instead, they exist in certain regions called orbitals.
• An orbital is a three-dimensional region around the
nucleus that indicates the probable location of an
electron.
Chapter 4

Visual Concepts
Visual Concept
Electron Cloud
Chapter 4

the Atom
Atomic Orbitals and Quantum Numbers
• Quantum numbers specify the properties of atomic
orbitals and the properties of electrons in orbitals.
• The principal quantum number, symbolized by n,
indicates the main energy level occupied by the
electron.
• The angular momentum quantum number,
symbolized by l, indicates the shape of the orbital.
Chapter 4

the Atom
Atomic Orbitals and Quantum Numbers,
continued
• The magnetic quantum number, symbolized by m,
indicates the orientation of an orbital around the
nucleus.
• The spin quantum number has only two possible
values—(+1/2 , 1/2)—which indicate the two
fundamental spin states of an electron in an orbital.
Chapter 4

Visual Concepts
Visual Concept
Quantum Numbers and Orbitals
Chapter 4

Shapes of s, p, and d Orbitals
the AtomChapter 4

Electrons Accommodated in Energy Levels
and Sublevels
the AtomChapter 4

Quantum Numbers of the First 30 Atomic Orbitals
the AtomChapter 4

Objectives
• List the total number of electrons needed to fully
occupy each main energy level.
• State the Aufbau principle, the Pauli exclusion
principle, and Hund’s rule.
• Describe the electron configurations for the atoms of
any element using orbital notation, electron-
configuration notation, and, when appropriate, noble-
gas notation.
Chapter 4

Electron Configurations
• The arrangement of electrons in an atom is known
as the atom’s electron configuration.
• The lowest-energy arrangement of the electrons
for each element is called the element’s ground-
state electron configuration.
Chapter 4

Relative Energies of Orbitals
Chapter 4

Visual Concepts
Visual Concept
Electron Configuration
Chapter 4

Rules Governing Electron Configurations
• According to the Aufbau principle, an electron
occupies the lowest-energy orbital that can receive it.
• According to the Pauli exclusion principle, no two
electrons in the same atom can have the same set of
four quantum numbers.
Chapter 4

Visual Concepts
Visual Concept
Aufbau Principle
Chapter 4

Visual Concepts
Visual Concept
Pauli Exclusion Principle
Chapter 4

Rules Governing Electron Configurations,
continued
• According to Hund’s rule, orbitals of equal energy
are each occupied by one electron before any
orbital is occupied by a second electron, and all
electrons in singly occupied orbitals must have the
same spin state.
Chapter 4

Representing Electron Configurations
Orbital Notation
• An unoccupied orbital is represented by a line, with
the orbital’s name written underneath the line.
• An orbital containing one electron is represented as:

Chapter 4

Representing Electron Configurations,
continued
Orbital Notation
• An orbital containing two electrons is represented as:


1s
He
Chapter 4
• The lines are labeled with the principal quantum
number and sublevel letter. For example, the orbital
notation for helium is written as follows:

Visual Concepts
Visual Concept
Orbital Notation
Chapter 4

continued
Electron-Configuration Notation
• Electron-configuration notation eliminates the lines
and arrows of orbital notation.
• Instead, the number of electrons in a sublevel is
shown by adding a superscript to the sublevel
designation.
• The helium configuration is represented by 1s2.
• The superscript indicates that there are two electrons
in helium’s 1s orbital.
Chapter 4

Visual Concepts
Visual Concept
Reading Electron-Configuration Notation
Chapter 4

continued
Sample Problem A
The electron configuration of boron is 1s22s22p1.
How many electrons are present in an atom of
boron? What is the atomic number for boron?
Write the orbital notation for boron.
Chapter 4

continued
Sample Problem A Solution
The number of electrons in a boron atom is equal to
the sum of the superscripts in its electron-
configuration notation: 2 + 2 + 1 = 5 electrons. The
number of protons equals the number of electrons in
a neutral atom. So we know that boron has 5 protons
and thus has an atomic number of 5. To write the
orbital notation, first draw the lines representing
orbitals.
1 24 341s 2s
2p
Chapter 4

continued
Sample Problem A Solution, continued
Next, add arrows showing the electron locations.
The first two electrons occupy n = 1 energy level
and fill the 1s orbital.

1 24 34
1s 2s
2p
Chapter 4

continued
Sample Problem A Solution, continued
The next three electrons occupy the n = 2 main
energy level. Two of these occupy the lower-
energy 2s orbital. The third occupies a higher-
energy p orbital.
  
1 24 34
1s 2s
2p
Chapter 4

Elements of the Second Period
• In the first-period elements, hydrogen and helium,
electrons occupy the orbital of the first main
energy level.
• According to the Aufbau principle, after the 1s
orbital is filled, the next electron occupies the s
sublevel in the second main energy level.
Chapter 4

Elements of the Second Period, continued
• The highest-occupied energy level is the electron-
containing main energy level with the highest
principal quantum number.
• Inner-shell electrons are electrons that are not in
the highest-occupied energy level.
Chapter 4

Writing Electron Configurations
Chapter 4

Elements of the Third Period
• After the outer octet is filled in neon, the next
electron enters the s sublevel in the n = 3 main
energy level.
Noble-Gas Notation
• The Group 18 elements (helium, neon, argon,
krypton, xenon, and radon) are called the noble
gases.
• A noble-gas configuration refers to an outer
main energy level occupied, in most cases, by
eight electrons.
Chapter 4

Orbital Notation for Three Noble Gases
Chapter 4

Visual Concepts
Visual Concept
Noble-Gas Notation
Chapter 4

Elements of the Fourth Period
• The period begins by filling the 4s orbital, the
empty orbital of lowest energy.
• With the 4s sublevel filled, the 4p and 3d sublevels
are the next available vacant orbitals.
• The 3d sublevel is lower in energy than the 4p
sublevel. Therefore, the five 3d orbitals are next to
be filled.
Chapter 4

Orbital Notation for Argon and Potassium
Chapter 4

Elements of the Fifth Period
• In the 18 elements of the fifth period, sublevels fill
in a similar manner as in elements of the fourth
period.
• Successive electrons are added first to the 5s
orbital, then to the 4d orbitals, and finally to the 5p
orbitals.
Chapter 4

Sample Problem B
a. Write both the complete electron-configuration
notation and the noble-gas notation for iron, Fe.
b. How many electron-containing orbitals are in an atom
of iron? How many of these orbitals are completely
filled? How many unpaired electrons are there in an
atom of iron? In which sublevel are the unpaired
electrons located?
Chapter 4

Sample Problem B Solution
a. The complete electron-configuration notation of iron is
1s22s22p63s23p63d64s2. Iron’s noble-gas notation is
[Ar]3d64s2.
b. An iron atom has 15 orbitals that contain electrons.
They consist of one 1s orbital, one 2s orbital, three 2p
orbitals, one 3s orbital, three 3p orbitals, five 3d orbitals, and
one 4s orbital.
Eleven of these orbitals are filled, and there are four
unpaired electrons.
They are located in the 3d sublevel.
The notation 3d6 represents 3d      .
Chapter 4

Sample Problem C
a. Write both the complete electron-configuration
notation and the noble-gas notation for a rubidium
atom.
b. Identify the elements in the second, third, and
fourth periods that have the same number of
highest-energy-level electrons as rubidium.
Chapter 4

Sample Problem C Solution
a. 1s22s22p63s23p63d104s24p65s1, [Kr]5s1
b. Rubidium has one electron in its highest
energy level (the fifth). The elements with the
same outermost configuration are,
in the second period, lithium, Li;
in the third period, sodium, Na;
and in the fourth period, potassium, K.
Chapter 4

End of Chapter 4 Show

Standardized Test Preparation
Multiple Choice
1. Which of the following relationships is true?
A. Higher-energy light has a higher frequency
than lower-energy light does.
B. Higher-energy light has a longer
wavelength than lower-energy light does.
C. Higher-energy light travels at a faster
speed than lower-energy light does.
D. Higher-frequency light travels at a slower
Chapter 4

1. Which of the following relationships is true?
A. Higher-energy light has a higher frequency
than lower-energy light does.
B. Higher-energy light has a longer
wavelength than lower-energy light does.
C. Higher-energy light travels at a faster
D. Higher-frequency light travels at a slower
Chapter 4
Multiple Choice

2. The energy of a photon is greatest for
A. visible light.
B. ultraviolet light.
C. infrared light.
D. X-ray radiation.
Chapter 4
Multiple Choice

3. What is the wavelength of radio waves that
have a frequency of 88.5 MHz?
A. 3.4 m
B. 8.9 nm
C. 0.30 m
D. 300 nm
Chapter 4
Multiple Choice

4. Which transition in an excited hydrogen atom
will emit the longest wavelength of light?
A. E5 to E1
B. E4 to E1
C. E3 to E1
D. E2 to E1
Chapter 4
Multiple Choice

5. Which of the following quantum numbers is
often designated by the letters s, p, d, and f
instead of by numbers?
A. n
B. l
C. m
D. s
Chapter 4
Multiple Choice

6. Which quantum number is related to the shape
of an orbital?
A. n
B. l
C. m
D. s
Chapter 4
Multiple Choice

7. What is the maximum number of unpaired
electrons that can be placed in a 3p sublevel?
A. 1
B. 2
C. 3
D. 4
Chapter 4
Multiple Choice

8. What is the maximum number of electrons that
can occupy a 3s orbital?
A. 1
B. 2
C. 6
D. 10
Chapter 4
Multiple Choice

9. Which element has the noble-gas notation
[Kr]5s24d2?
A. Se
B. Sr
C. Zr
D. Mo
Chapter 4
Multiple Choice

10. When a calcium salt is heated in a flame, a photon
of light with an energy of 3.2  1019 J is emitted.
On the basis of this fact and the table below, what
color would be expected for the calcium flame?
Frequency, s–1 7.1 × 1014 6.4 × 1014 5.7 × 1014
Wavelength, nm 422 469 526
Color violet blue green
Frequency, s–1 5.2 × 1014 4.8 × 1014 4.3 × 1014
Wavelength, nm 577 625 698
Color yellow orange red
Chapter 4
Short Answer

10. When a calcium salt is heated in a flame, a
photon of light with an energy of 3.2  1019 J is
emitted. What color would be expected for the
calcium flame?
Answer: The color will be orange. Converting
energy into frequency gives 4.8  1014, which
corresponds to the frequency of orange light.
Chapter 4
Short Answer

11. The electron configuration of sulfur is
1s22s22p63s23p4. Write the orbital notation for
sulfur.
Chapter 4
Short Answer

11. The electron configuration of sulfur is
1s22s22p63s23p4. Write the orbital notation for
sulfur.
Answer:
    
1 24 34
   
1 24 34
1s 2s
2p
3s
3p
Chapter 4
Short Answer

12. Explain the reason for the hydrogen line-
emission spectrum.
Chapter 4
Extended Response

12. Explain the reason for the hydrogen line-
emission spectrum.
Answer: Electrons in atoms can occupy orbitals of
only specific energies. When an atom is
excited, the electron is no longer in the
ground state. When the electron returns to a
lower energy level, light is emitted. Because
only specific energies are allowed, certain
wavelengths of light are emitted, giving rise to
the individual lines in the spectrum.
Chapter 4
Extended Response

13. When blue light shines on potassium metal in
a photocell, electrons are emitted. But when
yellow light shines on the metal, no current is
observed. Explain.
Chapter 4
Extended Response

13. When blue light shines on potassium metal in
a photocell, electrons are emitted. But when
yellow light shines on the metal, no current is
observed. Explain.
Answer: Photons of blue light are higher energy
than photons of yellow light. Electrons can be
emitted only when a photon of sufficient
energy strikes the surface of the metal.
Therefore, the energy of blue light is greater
than the threshold energy, but the energy of
yellow light is not.
Chapter 4
Extended Response

Chapter 4

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