..
PHYSICAL CHEMISTRY
A MOLECULAR APPROACH
Donald A. McQuarrie
UNIVERSITY OF CALIFORNIA, DAVIS
john D. Simon
George B. Geller Professor of Chemistry
DUKE UNIVERSITY
~
University Science Books
Sausalito, California
J
, c;Lf/.3
Mt1'5 University Science Books
,~ 55D Gate Five Road
. ~'',.~Sausalito, CA 94965
~~~....,:~ · Fax: (415) 332-5393
Production manager: Susanna Tadlock
Manuscript editor: Ann McGuire
Designer: Robert Ishi
Illustrator: John Choi
Compositor: Eigentype
Printer & Binder: Edwards Brothers, Inc.
This book is printed on acid-free paper.
Copyright ©1997 by University Science Books
Reproduction or translation of any part of this work beyond that
permitted by Section 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is
unlawful. Requests for permission or further information should
be addressed to the Permissions Department, University Science
Books.
Library of Congress Cataloging-in-Publication Data
McQuarrie, Donald A. (Donald Allen)
Physical chemistry : a molecular approach I Donald A.
McQuarrie, John D. Simon.
p. em.
Includes bibliographical references and index.
ISBN 0-935702-99-7
I. Chemistry, Physical and theoretical. I. Simon, John
D. (John Douglas), 1957- . II. Title.
QD453.2.M394 1997
541-dc21 97-142
CIP
Printed in the United States of America
10987654321
, Contents
Preface xvii
To the Student xv11
To the Instructor xix
Acknowledgment xx111
CHAPTER 1 I The Dawn of the Quantum Theory
1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2
1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4
1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7
1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10
1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13
1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15
1-7. de Broglie Waves Are Observed Experimentally 16
1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg
Formula 18
1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum
of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23
Problems 25
MATHCHAPTER A I Complex Numbers 31
Problems 35
CHAPTER 2 I The Classical Wave Equation 39
2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39
2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40
2-3. Some Differential Equations Have Oscillatory Solutions 44
2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46
2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49
Problems 54
MATHCHAPTER 8 I Probability and Statistics 63
Problems 70
v
, PHYSICAL CHEMISTRY
CHAPTER l I The Schrodinger Equation and a Particle In a Box 73
3-1. The Schri:idinger Equation Is the Equation for Finding the Wave Function
of a Particle 73
3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in
Quantum Mechanics 75
3-3. The Schri:idinger Equation Can Be Formulated As an Eigenvalue Problem 77
3-4. Wave Functions Have a Probabilistic Interpretation 80
3-5. The Energy of a Particle in a Box Is Quantized 81
3-6. Wave Functions Must Be Normalized 84
3-7. The Average Momentum of a Particle in a Box Is Zero 86
3-8. The Uncertainty Principle Says That upux > h/2 88
3-9. The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension
of the One-Dimensional Case 90
Problems 96
MATHCHAPTER C I Vectors 105
Problems 11 3
CHAPTER 4 I Some Postulates and General Principles of
Quantum Mechanics 115
4-1. The State of a System Is Completely Specified by Its Wave Function 115
4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118
4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122
4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent
Schri:idinger Equation 125
4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127
4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured
Simultaneously to Any Precision 131
Problems 134
/Z")MATHCHAPTER D I Spherical Coordinates 147
{.__;Y Problems 153
CHAPTER 5 I The Harmonic Oscillator and the Rigid Rotator:
Two Spectroscopic Models 157
5-1. A Harmonic Oscillator Obeys Hooke's Law 157
-s=2.The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the
Reduced Mass of the Molecule 161
5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear
Potential Around Its Minimum 163
>K 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + ~)
with v=O, 1, 2, ... 166
5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic
Molecule 167
/5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169
/.5-7. Hermite Polynomials Are Either Even or Odd Functions 1 72
B The Energy Levels of a Rigid Rotator Are E = h 2 J(J + 1)/21 173
/ vi
PHYSICAL CHEMISTRY
A MOLECULAR APPROACH
Donald A. McQuarrie
UNIVERSITY OF CALIFORNIA, DAVIS
john D. Simon
George B. Geller Professor of Chemistry
DUKE UNIVERSITY
~
University Science Books
Sausalito, California
J
, c;Lf/.3
Mt1'5 University Science Books
,~ 55D Gate Five Road
. ~'',.~Sausalito, CA 94965
~~~....,:~ · Fax: (415) 332-5393
Production manager: Susanna Tadlock
Manuscript editor: Ann McGuire
Designer: Robert Ishi
Illustrator: John Choi
Compositor: Eigentype
Printer & Binder: Edwards Brothers, Inc.
This book is printed on acid-free paper.
Copyright ©1997 by University Science Books
Reproduction or translation of any part of this work beyond that
permitted by Section 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is
unlawful. Requests for permission or further information should
be addressed to the Permissions Department, University Science
Books.
Library of Congress Cataloging-in-Publication Data
McQuarrie, Donald A. (Donald Allen)
Physical chemistry : a molecular approach I Donald A.
McQuarrie, John D. Simon.
p. em.
Includes bibliographical references and index.
ISBN 0-935702-99-7
I. Chemistry, Physical and theoretical. I. Simon, John
D. (John Douglas), 1957- . II. Title.
QD453.2.M394 1997
541-dc21 97-142
CIP
Printed in the United States of America
10987654321
, Contents
Preface xvii
To the Student xv11
To the Instructor xix
Acknowledgment xx111
CHAPTER 1 I The Dawn of the Quantum Theory
1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2
1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4
1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7
1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10
1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13
1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15
1-7. de Broglie Waves Are Observed Experimentally 16
1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg
Formula 18
1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum
of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23
Problems 25
MATHCHAPTER A I Complex Numbers 31
Problems 35
CHAPTER 2 I The Classical Wave Equation 39
2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39
2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40
2-3. Some Differential Equations Have Oscillatory Solutions 44
2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46
2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49
Problems 54
MATHCHAPTER 8 I Probability and Statistics 63
Problems 70
v
, PHYSICAL CHEMISTRY
CHAPTER l I The Schrodinger Equation and a Particle In a Box 73
3-1. The Schri:idinger Equation Is the Equation for Finding the Wave Function
of a Particle 73
3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in
Quantum Mechanics 75
3-3. The Schri:idinger Equation Can Be Formulated As an Eigenvalue Problem 77
3-4. Wave Functions Have a Probabilistic Interpretation 80
3-5. The Energy of a Particle in a Box Is Quantized 81
3-6. Wave Functions Must Be Normalized 84
3-7. The Average Momentum of a Particle in a Box Is Zero 86
3-8. The Uncertainty Principle Says That upux > h/2 88
3-9. The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension
of the One-Dimensional Case 90
Problems 96
MATHCHAPTER C I Vectors 105
Problems 11 3
CHAPTER 4 I Some Postulates and General Principles of
Quantum Mechanics 115
4-1. The State of a System Is Completely Specified by Its Wave Function 115
4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118
4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122
4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent
Schri:idinger Equation 125
4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127
4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured
Simultaneously to Any Precision 131
Problems 134
/Z")MATHCHAPTER D I Spherical Coordinates 147
{.__;Y Problems 153
CHAPTER 5 I The Harmonic Oscillator and the Rigid Rotator:
Two Spectroscopic Models 157
5-1. A Harmonic Oscillator Obeys Hooke's Law 157
-s=2.The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the
Reduced Mass of the Molecule 161
5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear
Potential Around Its Minimum 163
>K 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + ~)
with v=O, 1, 2, ... 166
5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic
Molecule 167
/5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169
/.5-7. Hermite Polynomials Are Either Even or Odd Functions 1 72
B The Energy Levels of a Rigid Rotator Are E = h 2 J(J + 1)/21 173
/ vi
