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SECTION 4.2
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Chapter 3
Visual Concepts
Avogadro’s Number
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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?
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Visual Concepts
De Broglie and the Wave-Particle Nature of
Electrons
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4.2
Physics and the Quantum
Mechanical Model
>
Quantum Mechanics
Classical mechanics adequately
describes the motions of bodies much
larger than atoms, while quantum
mechanics describes the motions of
subatomic particles and atoms as
waves.
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Chapter 4
Section 2 The Quantum Model of
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.
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4.2
Physics and the Quantum
Mechanical Model
>
Quantum Mechanics
The Heisenberg uncertainty principle states
that it is impossible to know exactly both the
velocity and the position of a particle at the same
time.
• This limitation is critical in dealing with small
particles such as electrons.
• This limitation does not matter for ordinarysized object such as cars or airplanes.
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Chapter 4
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Heisenberg Uncertainty Principle
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4.2
Physics and the Quantum
Mechanical Model
>
Quantum Mechanics
The Heisenberg Uncertainty Principle
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Visual Concepts
Electron Cloud
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Chapter 4
Section 2 The Quantum Model of
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.
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Chapter 4
Section 2 The Quantum Model of
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.
1, 2, 3, etc. as n increases the electron’s energy level and
its distance from the nucleus increases.
• The angular momentum quantum number, symbolized by
l, indicates the shape of the orbital.
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4.2
Models of the Atom
>
Atomic Orbitals
Different atomic orbitals are denoted by letters.
The s orbitals are spherical, and p orbitals are
dumbbell-shaped.
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4.2
Models of the Atom
>
Atomic Orbitals
Four of the five d orbitals have the same shape
but different orientations in space.
f orbitals are more complex in nature as well.
There are seven f-orbitals.
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4.2
Models of the Atom
>
Atomic Orbitals
An atomic orbital is often thought of as a region
of space in which there is a high probability of
finding an electron.
Each energy sublevel corresponds to
an orbital of a different shape, which
describes where the electron is likely
to be found.
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4.2
Models of the Atom
>
Atomic Orbitals
The numbers and kinds of atomic orbitals
depend on the energy sublevel.
The number of orbitals in each the first 4 main energy levels equals n2.
22
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4.2
Models of the Atom
>
Atomic Orbitals
The number of electrons allowed in each of the
first four energy levels are shown here.
The maximum number of electrons in
each of the energy levels is equal to
2n2.
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Chapter 4
Section 2 The Quantum Model of
the Atom
Atomic Orbitals and Quantum Numbers,
continued
• The magnetic quantum number, symbolized by m,
indicates the orientation of an orbital around the
nucleus & can be an integer from - l to + l where l is
the angular momentum. (This is a little “L” notation)
• 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.
• A single orbital can hold a maximum of 2 electrons
which must have opposite spin states.
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Chapter 4
Visual Concepts
Quantum Numbers and Orbitals
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Chapter 4
Section 2 The Quantum Model of
the Atom
Shapes of s, p, and d Orbitals
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Chapter 4
Section 2 The Quantum Model of
the Atom
Electrons Accommodated in Energy Levels
and Sublevels
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Chapter 4
Section 2 The Quantum Model of
the Atom
Electrons Accommodated in Energy Levels
and Sublevels
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Chapter 4
Section 2 The Quantum Model of
the Atom
Quantum Numbers of the First 30 Atomic Orbitals
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5.3 Section Quiz.
Assess students’ understanding of
the concepts in Section
5.3.
Continue to:
-or-
Launch:
Section Quiz
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Online Self-Check Quiz
Complete the online Quiz and record answers.
Ask if you have any questions about your
answers.
click here for online Quiz 4.2
(10 questions)
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VIDEOS FOR ADDITIONAL INSTRUCTION
Additional Videos for Section 4.2: The Quantum Model of the Atom
•Atomic Orbitals (4:27)
•Quantum Numbers (3:12)
•Orbital Diagrams (4:58)
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