All 15 Chapters Covered
SOLUTION MANUAL
, Table of Contents
Chapter 1… ............................................................................. 1
Chapter 2… ........................................................................... 14
Chapter 3… ........................................................................... 47
Chapter 4… ........................................................................... 72
Chapter 5… ........................................................................... 96
Chapter 6… ......................................................................... 128
Chapter 7… ......................................................................... 151
Chapter 8… ......................................................................... 169
Chapter 9… ......................................................................... 183
Chapter 10… ....................................................................... 203
Chapter 11… ....................................................................... 226
Chapter 12… ....................................................................... 249
Chapter 13… ....................................................................... 269
Chapter 14… ....................................................................... 288
Chapter 15… ....................................................................... 305
Sample Formula Sheet for Exams………………………….
viii
, Chapter 1
This chapter presents a review of some topics from classical physics. I have often
heard from instructors using the book that “my students have already studied a year of
introductory classical physics, so they don’t need the review.” This review chapter gives
the opportunity to present a number of concepts that I have found to cause difficulty for
students and to collect those concepts where they are available for easy reference. For
example, all students should know that kinetic energy is 12 mv2 , but few are readily
familiar with kinetic energy as pm , which is used more often in the text. The
expression connecting potential energy difference with potential difference for an electric
charge q, U = qV , zips by in the blink of an eye in the introductory course and is
rarely used there, while it is of fundamental importance to many experimental set-ups in
modern physics and is used implicitly in almost every chapter. Many introductory
courses do not cover thermodynamics or statistical mechanics, so it is useful to “review”
them in this introductory chapter.
I have observed students in my modern course occasionally struggling with
problems involving linear momentum conservation, another of those classical concepts
that resides in the introductory course. Although we physicists regard momentum
conservation as a fundamental law on the same plane as energy conservation, the latter is
frequently invoked throughout the introductory course while former appears and virtually
disappears after a brief analysis of 2-body collisions. Moreover, some introductory texts
present the equations for the final velocities in a one-dimensional elastic collision,
leaving the student with little to do except plus numbers into the equations. That is,
students in the introductory course are rarely called upon to begin momentum
conservation problems with pinitial = pfinal . This puts them at a disadvantage in the
application of momentum conservation to problems in modern physics, where many
different forms of momentum may need to be treated in a single situation (for example,
classical particles, relativistic particles, and photons). Chapter 1 therefore contains a
brief review of momentum conservation, including worked sample problems and end-of-
chapter exercises.
Placing classical statistical mechanics in Chapter 1 (as compared to its location in
Chapter 10 in the 2nd edition) offers a number of advantages. It permits the useful
expression Kav = 32 kT to be used throughout the text without additional explanation. The
failure of classical statistical mechanics to account for the heat capacities of diatomic
gases (hydrogen in particular) lays the groundwork for quantum physics. It is especially
helpful to introduce the Maxwell-Boltzmann distribution function early in the text, thus
permitting applications such as the population of molecular rotational states in Chapter 9
and clarifying references to “population inversion” in the discussion of the laser in
Chapter 8. Distribution functions in general are new topics for most students. They may
look like ordinary mathematical functions, but they are handled and interpreted quite
differently. Absent this introduction to a classical distribution function in Chapter 1, the
students’ first exposure to a distribution function will be ||2, which layers an additional
level of confusion on top of the mathematical complications. It is better to have a chance
to cover some of the mathematical details at an earlier stage with a distribution function
that is easier to interpret.
1
, Suggestions for Additional Reading
Some descriptive, historical, philosophical, and nonmathematical texts which give good
background material and are great fun to read:
A. Baker, Modern Physics and Anti-Physics (Addison-Wesley, 1970).
F. Capra, The Tao of Physics (Shambhala Publications, 1975).
K. Ford, Quantum Physics for Everyone (Harvard University Press, 2005).
G. Gamow, Thirty Years that Shook Physics (Doubleday, 1966).
R. March, Physics for Poets (McGraw-Hill, 1978).
E. Segre, From X-Rays to Quarks: Modern Physicists and their Discoveries (Freeman, 1980).
G. L. Trigg, Landmark Experiments in Twentieth Century Physics (Crane, Russak, 1975).
F. A. Wolf, Taking the Quantum Leap (Harper & Row, 1989).
G. Zukav, The Dancing Wu Li Masters, An Overview of the New Physics (Morrow, 1979).
Gamow, Segre, and Trigg contributed directly to the development of modern physics and
their books are written from a perspective that only those who were part of that
development can offer. The books by Capra, Wolf, and Zukav offer controversial
interpretations of quantum mechanics as connected to eastern mysticism, spiritualism, or
consciousness.
Materials for Active Engagement in the Classroom
A. Reading Quizzes
1. In an ideal gas at temperature T, the average speed of the molecules:
(1) increases as the square of the temperature.
(2) increases linearly with the temperature.
(3) increases as the square root of the temperature.
(4) is independent of the temperature.
2. The heat capacity of molecular hydrogen gas can take values of 3R/2, 5R/2, and 7R/2
at different temperatures. Which value is correct at low temperatures?
(1) 3R/2 (2) 5R/2 (3) 7R/2
Answers 1. 3 2. 1
B. Conceptual and Discussion Questions
1. Equal numbers of molecules of hydrogen gas (molecular mass = 2 u) and helium gas
(molecular mass = 4 u) are in equilibrium in a container.
(a) What is the ratio of the average kinetic energy of a hydrogen molecule to the
average kinetic energy of a helium molecule?
K H / K He = (1) 4 (2) 2 (3) 2 (4) 1 (5) 1/ 2 (6) 1/2 (7) 1/4
2
SOLUTION MANUAL
, Table of Contents
Chapter 1… ............................................................................. 1
Chapter 2… ........................................................................... 14
Chapter 3… ........................................................................... 47
Chapter 4… ........................................................................... 72
Chapter 5… ........................................................................... 96
Chapter 6… ......................................................................... 128
Chapter 7… ......................................................................... 151
Chapter 8… ......................................................................... 169
Chapter 9… ......................................................................... 183
Chapter 10… ....................................................................... 203
Chapter 11… ....................................................................... 226
Chapter 12… ....................................................................... 249
Chapter 13… ....................................................................... 269
Chapter 14… ....................................................................... 288
Chapter 15… ....................................................................... 305
Sample Formula Sheet for Exams………………………….
viii
, Chapter 1
This chapter presents a review of some topics from classical physics. I have often
heard from instructors using the book that “my students have already studied a year of
introductory classical physics, so they don’t need the review.” This review chapter gives
the opportunity to present a number of concepts that I have found to cause difficulty for
students and to collect those concepts where they are available for easy reference. For
example, all students should know that kinetic energy is 12 mv2 , but few are readily
familiar with kinetic energy as pm , which is used more often in the text. The
expression connecting potential energy difference with potential difference for an electric
charge q, U = qV , zips by in the blink of an eye in the introductory course and is
rarely used there, while it is of fundamental importance to many experimental set-ups in
modern physics and is used implicitly in almost every chapter. Many introductory
courses do not cover thermodynamics or statistical mechanics, so it is useful to “review”
them in this introductory chapter.
I have observed students in my modern course occasionally struggling with
problems involving linear momentum conservation, another of those classical concepts
that resides in the introductory course. Although we physicists regard momentum
conservation as a fundamental law on the same plane as energy conservation, the latter is
frequently invoked throughout the introductory course while former appears and virtually
disappears after a brief analysis of 2-body collisions. Moreover, some introductory texts
present the equations for the final velocities in a one-dimensional elastic collision,
leaving the student with little to do except plus numbers into the equations. That is,
students in the introductory course are rarely called upon to begin momentum
conservation problems with pinitial = pfinal . This puts them at a disadvantage in the
application of momentum conservation to problems in modern physics, where many
different forms of momentum may need to be treated in a single situation (for example,
classical particles, relativistic particles, and photons). Chapter 1 therefore contains a
brief review of momentum conservation, including worked sample problems and end-of-
chapter exercises.
Placing classical statistical mechanics in Chapter 1 (as compared to its location in
Chapter 10 in the 2nd edition) offers a number of advantages. It permits the useful
expression Kav = 32 kT to be used throughout the text without additional explanation. The
failure of classical statistical mechanics to account for the heat capacities of diatomic
gases (hydrogen in particular) lays the groundwork for quantum physics. It is especially
helpful to introduce the Maxwell-Boltzmann distribution function early in the text, thus
permitting applications such as the population of molecular rotational states in Chapter 9
and clarifying references to “population inversion” in the discussion of the laser in
Chapter 8. Distribution functions in general are new topics for most students. They may
look like ordinary mathematical functions, but they are handled and interpreted quite
differently. Absent this introduction to a classical distribution function in Chapter 1, the
students’ first exposure to a distribution function will be ||2, which layers an additional
level of confusion on top of the mathematical complications. It is better to have a chance
to cover some of the mathematical details at an earlier stage with a distribution function
that is easier to interpret.
1
, Suggestions for Additional Reading
Some descriptive, historical, philosophical, and nonmathematical texts which give good
background material and are great fun to read:
A. Baker, Modern Physics and Anti-Physics (Addison-Wesley, 1970).
F. Capra, The Tao of Physics (Shambhala Publications, 1975).
K. Ford, Quantum Physics for Everyone (Harvard University Press, 2005).
G. Gamow, Thirty Years that Shook Physics (Doubleday, 1966).
R. March, Physics for Poets (McGraw-Hill, 1978).
E. Segre, From X-Rays to Quarks: Modern Physicists and their Discoveries (Freeman, 1980).
G. L. Trigg, Landmark Experiments in Twentieth Century Physics (Crane, Russak, 1975).
F. A. Wolf, Taking the Quantum Leap (Harper & Row, 1989).
G. Zukav, The Dancing Wu Li Masters, An Overview of the New Physics (Morrow, 1979).
Gamow, Segre, and Trigg contributed directly to the development of modern physics and
their books are written from a perspective that only those who were part of that
development can offer. The books by Capra, Wolf, and Zukav offer controversial
interpretations of quantum mechanics as connected to eastern mysticism, spiritualism, or
consciousness.
Materials for Active Engagement in the Classroom
A. Reading Quizzes
1. In an ideal gas at temperature T, the average speed of the molecules:
(1) increases as the square of the temperature.
(2) increases linearly with the temperature.
(3) increases as the square root of the temperature.
(4) is independent of the temperature.
2. The heat capacity of molecular hydrogen gas can take values of 3R/2, 5R/2, and 7R/2
at different temperatures. Which value is correct at low temperatures?
(1) 3R/2 (2) 5R/2 (3) 7R/2
Answers 1. 3 2. 1
B. Conceptual and Discussion Questions
1. Equal numbers of molecules of hydrogen gas (molecular mass = 2 u) and helium gas
(molecular mass = 4 u) are in equilibrium in a container.
(a) What is the ratio of the average kinetic energy of a hydrogen molecule to the
average kinetic energy of a helium molecule?
K H / K He = (1) 4 (2) 2 (3) 2 (4) 1 (5) 1/ 2 (6) 1/2 (7) 1/4
2
