Transcription

INSTRUCTOR SOLUTIONS MANUAL

Instructor’s Manualto accompanyModern Physics, 3rd EditionKenneth S. KraneDepartment of PhysicsOregon State University 2012 John Wiley & Sons

PrefaceThis Instructor’s Manual accompanies the 3rd edition of the textbook ModernPhysics (John Wiley & Sons, 2012). It includes (1) explanatory material for eachchapter; (2) suggested outside readings for instructor or student; (3) references to websites or other generally available simulations of phenomena; (4) exercises that can beused in various active-engagement classroom strategies; (5) sample exam questions; and(6) complete solutions to the end-of-chapter problems in the text.Perhaps the greatest influence on my teaching in the time since the publication ofthe 2nd edition of this textbook (1996) has been the growth into maturity of the field ofphysics education research (PER). Rather than indicating specific areas ofmisunderstanding, PER has demonstrated that student comprehension is enhanced by anyof a number of interactive techniques that are designed to engage the students and makethem active participants in the learning process. The demonstrated learningimprovements are robust and replicable, and they transcend differences among instructorsand institutional types. In my own trajectory in this process, I have been especiallyinfluenced by the work of Lillian McDermott and her group at the University ofWashington1 and Eric Mazur at Harvard University.2 I am grateful to them not only fortheir contributions to PER but also for their friendship over the years.With the support of a Course, Curriculum, and Laboratory Improvement grantfrom the National Science Foundation3, I have developed and tested a set of exercisesthat can be used either in class as group activities or outside of class (for example, in aPeer Instruction mode following Mazur’s format or in a Just-In-Time Teaching4 mode).These exercises are included in this Instructor’s Manual. I am grateful for the support ofthe National Science Foundation in enabling this project to be carried out. Two OregonState University graduate students assisted in the implementations of these reformedteaching methods: K. C. Walsh helped with producing several simulations and illustrativematerials, with implementing an interactive web site, and with correspondingdevelopments in the laboratory that accompanies our course, and PornratWattanakasiwich undertook a PER project5 for her Ph.D. that involved the observation ofstudent reasoning about probability, which lies at the heart of most topics in modernphysics.One of the major themes that has emerged from PER in the past two decades isthat students can often learn successful algorithms for solving problems while lacking afundamental understanding of the underlying concepts. The importance of the in-class orpre-class exercises is to force students to consider these concepts and to apply them todiverse situations that often cannot be analyzed with an equation. It is absolutelyessential to devote class time to these exercises and to follow through with examquestions that require similar analysis and a similar articulation of the conceptualreasoning. I strongly believe that conceptual understanding is a necessary prerequisite tosuccessful problem solving. In my own classes at Oregon State University I haverepeatedly observed that improved conceptual understanding leads directly to improvedproblem-solving skills.In training students to reason conceptually, it is necessary to force them toverbalize their reasons for selecting a particular answer to a conceptual or qualitativequestion, and you will learn much from listening to or reading their arguments. A simpleii

multiple-choice conceptual question, either as a class exercise or a test problem, givesyou insufficient insight into the students’ reasoning patterns unless you also ask them tojustify their choice. Even when I have teaching assistants grade the exams in my class, Ialways grade the conceptual questions myself, if only to gather insight into how studentsreason. To save time I generally grade such questions with either full credit (correctchoice of answer and more-or-less correct reasoning) or no credit (wrong choice orcorrect choice with incorrect reasoning).Here’s an example of why it is necessary to require students to provide conceptualarguments. After a unit on the Schrödinger equation, I gave the following conceptual testquestion: Consider a particle in the first excited state of a one-dimensional infinitepotential energy well that extends from x 0 to x L. At what locations is the particlemost likely to be found? The students were required to state an answer and to give theirreasoning. One student drew a nice sketch of the probability density in the first excitedstate, correctly showing maxima at x L/4 and x 3L/4, and stated that those locationswere the most likely ones at which to find the particle. Had I not required the reasoning,the student would have received full credit, and I would have been satisfied with thestudent’s understanding of the material. However, in stating the reasoning, the studentdemonstrated what turned out to be a surprisingly common incorrect mode of reasoning.The student apparently confused the graph of probability density with a similar sort ofroller-coaster potential energy diagram from introductory physics and reasoned asfollows: The particle is moving more slowly at the peaks of the distribution, so it spendsmore time at those locations and is thus more likely to be found there. PER follow-upwork indicated that the confusion was caused in part by combining probabilitydistributions with energy level diagrams – students were unsure of what the ordinaterepresented. As a result, I adopted a policy in class (and in this edition of the textbook)of never showing the wave functions or probability distributions on the same plot as theenergy levels.The overwhelming majority of PER work has concerned the introductory course,but the effective pedagogic techniques revealed by that research carry over directly intothe modern physics course. The collection of research directly linked to topics in modernphysics is much smaller but no less revealing. The University of Washington group hasproduced several papers impacting modern physics, including the understanding ofinterference and diffraction of particles,, time and simultaneity in special relativity, andthe photoelectric effect (see the papers listed on their web site, ref. 1). The PER group ofEdward F. Redish at the University of Maryland has also been involved in studying thelearning of quantum concepts, including the student’s prejudices from classical physics,probability, and conductivity.6 (Further work on the learning of quantum concepts hasbeen carried out by the research groups of two of Redish’s Ph.D. students, Lei Bao atOhio State University7 and Michael Wittmann at the University of Maine.8) DeanZollman’s group at Kansas State University has developed tutorials and visualizations toenhance the teaching of quantum concepts at many levels (from pre-college throughadvanced undergraduate).9 The physics education group at the University of Colorado,led by Noah Finkelstein and Carl Wieman, is actively pursuing several research areasinvolving modern physics and has produced numerous research papers as well assimulations on topics in modern physics.10 Others who have conducted research on theteaching of quantum mechanics and developed interactive or evaluative materials includeiii

Chandralekha Singh at the University of Pittsburgh11 and Richard Robinett atPennsylvania State University.12Classroom Materials for Active Engagement1. Reading QuizzesI started developing the interactive classroom materials for modern physics aftersuccessfully introducing Eric Mazur’s Peer Instruction techniques into my calculus-basedintroductory course. Daily reading quizzes were a part of Mazur’s original classroomstrategy, but recently he has adopted a system that is more like Just-in-Time Teaching.Nevertheless, I have found the reading quizzes to work effectively in both myintroductory and modern physics classes, and I have continued using them. We useelectronic classroom communication devices (“clickers”) to collect the responses, but in asmall class paper quizzes work just as well. Originally the quizzes were intended to getstudents to read the textbook before coming to class, and I have over the years collectedevidence that the quizzes in fact accomplish that goal. The quizzes are given just at thestart of class, and I have found that they have two other salutary effects: (1) In the fewminutes before the bell rings at the start of class, the students are not reading the campusnewspaper or discussing last week’s football game – they are reading their physics books.(2) It takes no time at the start of class for me to focus the students’ attention or put them“in the mood” for physics; the quiz gets them settled into class and thinking aboutphysics. The multiple-choice quizzes must be very straightforward – no complexthinking or reasoning should be required, and if a student has done the assigned readingthe quiz should be automatic and should take no more than a minute or so to read andanswer. Nearly all students get at least 80% of the quizzes correct, so ultimately theyhave little impact on the grade distribution. The quizzes count only a few percent towardthe student’s total grade, so even if they miss a few their grade is not affected.2. Conceptual QuestionsI spend relatively little class time “lecturing” in the traditional sense. I prefer anapproach in which I prod and coach the students into learning and understanding thematerial. The students’ reading of the textbook is an important component of this process– I do not see the need to repeat orally everything that is already written in the textbook.(Of course, there are some topics in any course that can be elucidated only by a wellconstructed and delivered lecture. Separating those topics from those that the studentscan mostly grasp from reading the text and associated in-class follow-ups comes onlyfrom experience. Feedback obtained from the results of the conceptual exercises andfrom student surveys is invaluable in this process.) I usually take about 10 minutes at thebeginning of class to summarize the important elements from that day’s reading. In theprocess I list on the board new or unfamiliar words and important formulas. Theseremain visible during the entire class so I can refer back to them as often as necessary. Iexplain any special or restrictive circumstances that accompany the use of any equation.I do not do formal mathematical derivations in class – they cause a rapid drop-off instudent attention. However, I do discuss or explain mathematical processes or techniquesiv

that might be unfamiliar to students. I encourage students to e-mail me with questionsabout the reading before class, and at this point I answer those questions and any newquestions that may puzzle the students.The remainder of the class period consists of conceptual questions and workedexamples. I follow the Peer Instruction model for the conceptual questions: an individualanswer with no discussion, then small group discussions, and finally a second individualanswer. On my computer I can see the histograms of the responses using the clickers, andif there are fewer than 30% or more than 70% correct answers on the first response, thegroup discussions normally don’t provide much benefit so I abandon the question andmove on to another. During the group discussion time, I wander throughout the classlistening to the comments and occasionally asking questions or giving a small nudge if Ifeel a particular group is moving in the wrong direction. After the second response I aska member of the class to give the answer and an explanation, and I will supplement thestudent’s explanation as necessary. I generally do not show the histograms of the clickerresponses to the class, neither upon the first response nor the second. The daily quiz,summary, two conceptual questions or small group projects, and one or two workedexamples will normally fill a 50-minute class period, with a few minutes at the end forrecapitulation or additional questions. I try to end each class period with a brief teaserregarding the next class.Some conceptual questions listed for class discussion may appear similar to thosegiven on exams. I never use the same question for both class discussion and examinationduring any single term. However, conceptual questions used during one term forexaminations may find use for in-class discussions during a subsequent term.3. JITT Warm-up ExercisesJust-in-Time Teaching uses web-based “warm-up” exercises to assess the student’s priorknowledge and misconceptions. The instructor can use the responses to the warm-upexercises to plan the content of the next class. The reading quizzes and conceptualquestions intended for in-class activities can in many cases be used equally well for JiTTwarm-up exercises.Lecture DemonstrationsDemonstrations are an important part of teaching introductory physics, and physicseducation research has shown that learning from the demos is enhanced if they are madeinteractive. (For example, you can ask students to predict the response of the apparatus,discuss the predictions with a neighbor, and then to reconcile an incorrect prediction withthe observation.) Unfortunately, there are few demos that can be done in the modernphysics classroom. Instead, we must rely on simulations and animations. There aremany effective and interesting instructional software packages on the web that can bedownloaded for your class, and you can make them available for the students to useoutside of class. I have listed in this Manual some of the modern physics software that Ihave used in my classes. Of particular interest is the open-source collection of Physlets(physics applets) covering relativity and qu