Solution Manual for Modern Physics, 4th Edition by Krane

All 15Chapters Covered
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SOLUTIONMANUAL
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, Table of Contents
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Chapter 1….............................................................................. 1
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Chapter 2…............................................................................ 14
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Chapter 3…............................................................................ 47
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Chapter 4…............................................................................ 72
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Chapter 5…............................................................................ 96
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Chapter 6….......................................................................... 128
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Chapter 7….......................................................................... 151
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Chapter 8….......................................................................... 169
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Chapter 9….......................................................................... 183
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Chapter 10…........................................................................ 203
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Chapter 11…........................................................................ 226
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Chapter 12…........................................................................ 249
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Chapter 13…........................................................................ 269
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Chapter 14…........................................................................ 288
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Chapter 15…........................................................................ 305
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Sample Formula Sheet for Exams………………………….
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viii

, Chapter 1 k




This chapter presents a review of some topics from classical physics. I have often
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heard from instructors using the book that “my students have already studied a year of
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introductory classical physics, so they don’t need the review.” This review chapter gives the
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opportunity to present a number of concepts that I have found to cause difficulty for students
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and to collect those concepts where they are available for easy reference. For
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2
example, all students should know that kinetic energy is 1 mv
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2 , but few are readily
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familiar with kinetic energy as p2 /2m, which is used more often in the text. The
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expression connecting potential energy difference with potential difference for an electric
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charge q, U = qV , zips by in the blink of an eye in the introductory course and is
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rarely used there, while it is of fundamental importance to many experimental set-ups in
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modern physics and is used implicitly in almost every chapter. Many introductory courses
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do not cover thermodynamics or statistical mechanics, so it is useful to “review” them in this
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introductory chapter.
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I have observed students in my modern course occasionally struggling with problems
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involving linear momentum conservation, another of those classical concepts that resides in
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the introductory course. Although we physicists regard momentum conservation as a
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fundamental law on the same plane as energy conservation, the latter is frequently invoked
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throughout the introductory course while former appears and virtually disappears after a brief
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analysis of 2-body collisions. Moreover, some introductory texts present the equations for
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the final velocities in a one-dimensional elastic collision, leaving the student with little to do
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except plus numbers into the equations. That is, students in the introductory course are
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rarely called upon to begin momentum
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conservation problems with pinitial = pfinal . This puts them at a disadvantage in the k k k
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application of momentum conservation to problems in modern physics, where many
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different forms of momentum may need to be treated in a single situation (for example,
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classical particles, relativistic particles, and photons). Chapter 1 therefore contains a brief
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review of momentum conservation, including worked sample problems and end-of- chapter
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exercises.
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Placing classical statistical mechanics in Chapter 1 (as compared to its location in k k k k k k k k k k k k




Chapter 10 in the 2nd edition) offers a number of advantages. It permits the useful
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expression Kav = 23 kT to be used throughout the text without additional explanation. The
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failure of classical statistical mechanics to account for the heat capacities of diatomic gases
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(hydrogen in particular) lays the groundwork for quantum physics. It is especially helpful to
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introduce the Maxwell-Boltzmann distribution function early in the text, thus permitting
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applications such as the population of molecular rotational states in Chapter 9 and clarifying
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references to “population inversion” in the discussion of the laser in Chapter 8. Distribution
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functions in general are new topics for most students. They may look like ordinary
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mathematical functions, but they are handled and interpreted quite differently. Absent this
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introduction to a classical distribution function in Chapter 1, the students’ first exposure to a
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distribution function will be ||2, which layers an additional level of confusion on top of the
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mathematical complications. It is better to have a chance to cover some of the mathematical
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details at an earlier stage with a distribution function that is easier to interpret.
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1

, Suggestions for Additional Reading k k k




Some descriptive, historical, philosophical, and nonmathematical texts which give good
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background material and are great fun to read:
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A. Baker, Modern Physics and Anti-Physics (Addison-Wesley, 1970).
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F. Capra, The Tao of Physics (Shambhala Publications, 1975).
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K. Ford, Quantum Physics for Everyone (Harvard University Press, 2005).
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G. Gamow, Thirty Years that Shook Physics (Doubleday, 1966).
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R. March, Physics for Poets (McGraw-Hill, 1978).
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E. Segre, From X-Rays to Quarks: Modern Physicists and their Discoveries (Freeman, 1980).
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G. L. Trigg, Landmark Experiments in Twentieth Century Physics (Crane, Russak, 1975).
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F. A. Wolf, Taking the Quantum Leap (Harper & Row, 1989).
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G. Zukav, The Dancing Wu Li Masters, An Overview of the New Physics (Morrow, 1979).
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Gamow, Segre, and Trigg contributed directly to the development of modern physics and
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their books are written from a perspective that only those who were part of that development
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can offer. The books by Capra, Wolf, and Zukav offer controversial interpretations of
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quantum mechanics as connected to eastern mysticism, spiritualism, or consciousness.
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Materials for Active Engagement in the Classroom k k k k k k




A. Reading Quizzes
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1. In an ideal gas at temperature T, the average speed of the molecules:
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(1) increases as the square of the temperature. k k k k k k




(2) increases linearly with the temperature. k k k k




(3) increases as the square root of the temperature. k k k k k k k




(4) is independent of the temperature. k k k k




2. The heat capacity of molecular hydrogen gas can take values of 3R/2, 5R/2, and 7R/2 at
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different temperatures. Which value is correct at low temperatures?
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(1) 3R/2 (2) 5R/2
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Answers 1. 3 k 2. 1 k




B. Conceptual and Discussion Questions
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1. Equal numbers of molecules of hydrogen gas (molecular mass = 2 u) and helium gas
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(molecular mass = 4 u) are in equilibrium in a container.
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(a) What is the ratio of the average kinetic energy of a hydrogen molecule to the
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average kinetic energy of a helium molecule?
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K H / K He = (1) 4 (2) 2
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2