[Donald A. McQuarrie, John D. Simon] Physical Chem(BookZZ.org)
1279 pág.

[Donald A. McQuarrie, John D. Simon] Physical Chem(BookZZ.org)


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P H Y S I C A L C H E M I S T R Y 
A M O L E C U L A R A P P R O A C H 
D o n a l d A . M c Q u a r r i e 
U N I V E R S I T Y O F C A L I F O R N I A , D A V I S 
j o h n D . S i m o n 
G e o r g e B . G e l l e r P r o f e s s o r o f C h e m i s t r y 
D U K E U N I V E R S I T Y 
~ 
U n i v e r s i t y S c i e n c e B o o k s 
S a u s a l i t o , C a l i f o r n i a 
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M t1'5 
University Science Books 
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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 
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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 
Printed in the United States of America 
10987654321 
CIP 
P r e f a c e x v i i 
T o t h e S t u d e n t x v 1 1 
T o t h e I n s t r u c t o r x i x 
A c k n o w l e d g m e n t x x 1 1 1 
C H A P T E R 1 I T h e D a w n o f t h e Q u a n t u m T h e o r y 
1 - 1 . B l a c k b o d y R a d i a t i o n C o u l d N o t B e E x p l a i n e d b y C l a s s i c a l P h y s i c s 2 
C o n t e n t s 
1 - 2 . P l a n c k U s e d a Q u a n t u m H y p o t h e s i s t o D e r i v e t h e B l a c k b o d y R a d i a t i o n L a w 4 
1 - 3 . E i n s t e i n E x p l a i n e d t h e P h o t o e l e c t r i c E f f e c t w i t h a Q u a n t u m H y p o t h e s i s 7 
1 - 4 . T h e H y d r o g e n A t o m i c S p e c t r u m C o n s i s t s o f S e v e r a l S e r i e s o f L i n e s 1 0 
1 - 5 . T h e R y d b e r g F o r m u l a A c c o u n t s f o r A l l t h e L i n e s i n t h e H y d r o g e n A t o m i c S p e c t r u m 1 3 
1 - 6 . L o u i s d e B r o g l i e P o s t u l a t e d T h a t M a t t e r H a s W a v e l i k e P r o p e r t i e s 1 5 
1 - 7 . d e B r o g l i e W a v e s A r e O b s e r v e d E x p e r i m e n t a l l y 1 6 
1 - 8 . T h e B o h r T h e o r y o f t h e H y d r o g e n A t o m C a n B e U s e d t o D e r i v e t h e R y d b e r g 
F o r m u l a 1 8 
1 - 9 . T h e H e i s e n b e r g U n c e r t a i n t y P r i n c i p l e S t a t e s T h a t t h e P o s i t i o n a n d t h e M o m e n t u m 
o f a P a r t i c l e C a n n o t B e S p e c i f i e d S i m u l t a n e o u s l y w i t h U n l i m i t e d P r e c i s i o n 2 3 
P r o b l e m s 2 5 
M A T H C H A P T E R A I C o m p l e x N u m b e r s 3 1 
P r o b l e m s 3 5 
C H A P T E R 2 I T h e C l a s s i c a l W a v e E q u a t i o n 3 9 
2 - 1 . T h e O n e - D i m e n s i o n a l W a v e E q u a t i o n D e s c r i b e s t h e M o t i o n o f a V i b r a t i n g S t r i n g 3 9 
2 - 2 . T h e W a v e E q u a t i o n C a n B e S o l v e d b y t h e M e t h o d o f S e p a r a t i o n o f V a r i a b l e s 4 0 
2 - 3 . S o m e D i f f e r e n t i a l E q u a t i o n s H a v e O s c i l l a t o r y S o l u t i o n s 4 4 
2 - 4 . T h e G e n e r a l S o l u t i o n t o t h e W a v e E q u a t i o n I s a S u p e r p o s i t i o n o f N o r m a l M o d e s 4 6 
2 - 5 . A V i b r a t i n g M e m b r a n e I s D e s c r i b e d b y a T w o - D i m e n s i o n a l W a v e E q u a t i o n 4 9 
P r o b l e m s 5 4 
M A T H C H A P T E R 8 I P r o b a b i l i t y a n d S t a t i s t i c s 6 3 
P r o b l e m s 7 0 
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 
{.__;Y Problems 153 
147 
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 
/.5-7. Hermite Polynomials Are Either Even or Odd Functions 1 72 B The Energy Levels of a Rigid Rotator Are E = h2 J(J + 1)/21 173 
/ vi 
169 
C o n t e n t s 
/~The R i g i d R o t a t o r I s a M o d e l f o r a R o t a t i n g D i a t o m i c M o l e c u l e 1 7 7 
P r o b l e m s 1 7 9 
C H A P T E R 6 I T h e H y d r o g e n A t o m 1 9 1 
6 - 1 . T h e S c h r o d i n g e r E q u a t i o n f o r t h e H y d r o g e n A t o m C a n B e S o l v e d E x a c t l y 1 9 1 
6 - 2 . T h e W a v e F u n c t i o n s o f a R i g i d R o t a t o r A r e C a l l e d S p h e r i c a l H a r m o n i c s 1 9 3 
6 - 3 . T h e P r e c i s e V a l u e s o f t h e T h r e e C o m p o n e n t s o f A n g u l a r M o m e n t u m C a n n o t B e 
M e a s u r e d S i m u l t a n e o u s l y 2 0 0 
6 - 4 . H y d r o g e n A t o m i c O r b i t a l s D e p e n d u p o n T h r e e Q u a n t u m N u m b e r s 2 0 6 
6 - 5 . s O r b i t a l s A r e S p h e r i c a l l y S y m m e t r i c 2 0 9 
6 - 6 . T h e r e A r e T h r e e p O r b i t a l s f o r E a c h V a l u e o f t h e P r i n c i p a l Q u a n t u m N u m b e r , 
n ~ 2 2 1 3 
6 - 7 . T h e S c h r o d i n g e r E