University Physics with Modern Physics 14th Edition PDF

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== Download for free here: http://bit.ly/UnivModPhy14thPDF == University Physics with Modern Physics PDF assimilates the best ideas from education research with enhanced problem-solving instruction, pioneering visual and conceptual pedagogy, all-new categories of end-of-chapter problems, and the most pedagogically proven and widely used online homework and tutorial system in the world. == Get it for free here: http://bit.ly/UnivModPhy14thPDF == Additional tags: best physics books, best physics textbook, University Physics 14th edition, university physics 14th edition pdf, university physics book, university physics by young and freedman, University Physics with Modern Physics, University Physics with Modern Physics 14th edition, University Physics with Modern Physics 14th edition pdf, University Physics with Modern Physics pdf, university physics young, young and freedman university physics

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T HI S I S ONL Y A PRE VI E W OF T HE BOOK. DOWNL OAD T HE F UL L BOOK I N PDF USI NG T HE DOWNL OAD L I NK I N T HE DE SCRI PT I ON OR VI SI T www. book s i npdf . c om BOOKS i n PDF . c om

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HugH D. Young RogeR A. FReeDmAn University of California Santa Barbara ContRibuting AutHoR A. LeWiS FoRD Texas AM University univeRSitY PHYSiCS WitH moDeRn PHYSiCS 14tH eDition SearS and ZemanSky’S Z07_YOUN3610_14_SE_EXTENDED_FM.indd 1 08/11/14 11:35 AM

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VOLUME 1: Chapters 1–20 • VOLUME 2: Chapters 21–37 • VOLUME 3: Chapters 37–44 26 Direct-Current Circuits 848 27 Magnetic Field and Magnetic Forces 881 28 Sources of Magnetic Field 921 29 Electromagnetic Induction 955 30 Inductance 990 31 Alternating Current 1020 32 Electromagnetic Waves 1050 Optics 33 The Nature and Propagation of Light 1078 34 Geometric Optics 1111 35 Interference 1160 36 Diffraction 1186 MOdern physics 37 Relativity 1218 38 Photons: Light Waves Behaving as Particles 1254 39 Particles Behaving as Waves 1279 40 Quantum Mechanics I: Wave Functions 1321 41 Quantum Mechanics II: Atomic Structure 1360 42 Molecules and Condensed Matter 1407 43 Nuclear Physics 1440 44 Particle Physics and Cosmology 1481 Appendices A The International System of Units A-1 B Useful Mathematical Relations A-3 C The Greek Alphabet A-4 D Periodic Table of the Elements A-5 E Unit Conversion Factors A-6 F Numerical Constants A-7 Answers to Odd-Numbered Problems A-9 Credits C-1 Index I-1 MechAnics 1 Units Physical Quantities and Vectors 1 2 Motion Along a Straight Line 34 3 Motion in Two or Three Dimensions 67 4 Newton’s Laws of Motion 101 5 Applying Newton’s Laws 130 6 Work and Kinetic Energy 172 7 Potential Energy and Energy Conservation 203 8 Momentum Impulse and Collisions 237 9 Rotation of Rigid Bodies 273 10 Dynamics of Rotational Motion 303 11 Equilibrium and Elasticity 339 12 Fluid Mechanics 369 13 Gravitation 398 14 Periodic Motion 433 WAves/AcOustics 15 Mechanical Waves 468 16 Sound and Hearing 505 therMOdynAMics 17 Temperature and Heat 545 18 Thermal Properties of Matter 584 19 The First Law of Thermodynamics 618 20 The Second Law of Thermodynamics 647 electrOMAgnetisM 21 Electric Charge and Electric Field 683 22 Gauss’s Law 722 23 Electric Potential 752 24 Capacitance and Dielectrics 785 25 Current Resistance and Electromotive Force 816 bRieF ContentS Z07_YOUN3610_14_SE_EXTENDED_FM.indd 3 08/11/14 11:35 AM

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Roger A. Freedman is a Lecturer in Physics at the University of California Santa Barbara. He was an undergraduate at the University of California campuses in San Diego and Los Angeles and did his doctoral research in nuclear theory at Stanford University under the direction of Professor J. Dirk Walecka. Dr. Freedman came to UCSB in 1981 after three years of teaching and doing research at the University of Washington. At UCSB Dr. Freedman has taught in both the Department of Physics and the College of Creative Studies a branch of the university intended for highly gifted and motivated undergraduates. He has published research in nuclear physics elementary particle physics and laser physics. In recent years he has worked to make physics lectures a more interactive experience through the use of classroom response systems and pre-lecture videos. In the 1970s Dr. Freedman worked as a comic book letterer and helped organize the San Diego Comic-Con now the world’s largest popular culture convention during its first few years. Today when not in the classroom or slaving over a computer Dr. Freedman can be found either flying he holds a commercial pilot’s license or with his wife Caroline cheering on the rowers of UCSB Men’s and Women’s Crew. in MeMOriAM: hugh yOung 1930–2013 Hugh D. Y oung was Emeritus Professor of Physics at Carnegie Mellon University. He earned both his undergraduate and graduate degrees from that university. He earned his Ph.D. in fundamental particle theory under the direction of the late Richard Cutkosky. Dr. Young joined the faculty of Carnegie Mellon in 1956 and retired in 2004. He also had two visiting professorships at the University of California Berkeley. Dr. Young’s career was centered entirely on undergraduate education. He wrote several undergraduate-level textbooks and in 1973 he became a coauthor with Francis Sears and Mark Zemansky for their well-known introductory textbooks. In addition to his role on Sears and Zemansky’s University Physics he was the author of Sears and Zemansky’s College Physics. Dr. Young earned a bachelor’s degree in organ performance from Carnegie Mellon in 1972 and spent several years as Associate Organist at St. Paul’s Cathedral in Pittsburgh. He often ventured into the wilderness to hike climb or go caving with students in Carnegie Mellon’s Explorers Club which he founded as a graduate student and later advised. Dr. Young and his wife Alice hosted up to 50 students each year for Thanksgiving dinners in their home. Always gracious Dr. Young expressed his appreciation earnestly: “I want to extend my heartfelt thanks to my colleagues at Carnegie Mellon especially Professors Robert Kraemer Bruce Sherwood Ruth Chabay Helmut Vogel and Brian Quinn for many stimulating discussions about physics pedagogy and for their support and encour- agement during the writing of several successive editions of this book. I am equally indebted to the many generations of Carnegie Mellon students who have helped me learn what good teaching and good writing are by showing me what works and what doesn’t. It is always a joy and a privilege to express my gratitude to my wife Alice and our children Gretchen and Rebecca for their love support and emotional suste- nance during the writing of several successive editions of this book. May all men and women be blessed with love such as theirs.” We at Pearson appreciated his profession- alism good nature and collaboration. He will be missed. About tHe AutHoRS A. Lewis Ford is Professor of Physics at Texas AM University. He received a B.A. from Rice University in 1968 and a Ph.D. in chemical physics from the University of Texas at Austin in 1972. After a one-year postdoc at Harvard University he joined the Texas AM physics faculty in 1973 and has been there ever since. Professor Ford has specialized in theoretical atomic physics—in particular atomic collisions. At Texas AM he has taught a variety of undergraduate and graduate courses but primarily introductory physics. Z07_YOUN3610_14_SE_EXTENDED_FM.indd 8 08/11/14 11:36 AM

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1 1 Tornadoes are spawned by severe thunderstorms so being able to predict the path of thunderstorms is essential. If a thunderstorm is moving at 15 km/h in a direction 37° north of east how far north does the thunderstorm move in 2.0 h i 30 km ii 24 km iii 18 km iv 12 km v 9 km. Units Physical QUantities an d Vectors Learning goaLs Looking forward at … 1.1 What a physical theory is. 1.2 The four steps you can use to solve any physics problem. 1.3 Three fundamental quantities of physics and the units physicists use to measure them. 1.4 How to work with units in your c a l cul a t i o n s . 1.5 How to keep track of significant figures in your calculations. 1.6 How to make rough order-of-magnitude estimates. 1.7 The difference between scalars and vectors and how to add and subtract ve c t o r s g r a ph i c a l l y . 1.8 What the components of a vector are and how to use them in calculations. 1.9 What unit vectors are and how to use them with components to describe vectors. 1.10 Two ways to multiply vectors: the scalar dot product and the vector cross pr o d uc t . P hysics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics including chemists who study the structure of molecules paleontologists who try to reconstruct how dinosaurs walked and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV a prosthetic leg or even a better mousetrap without first understanding the basic laws of physics. The study of physics is also an adventure. You will find it challenging some- times frustrating occasionally painful and often richly rewarding. If you’ve ever wondered why the sky is blue how radio waves can travel through empty space or how a satellite stays in orbit you can find the answers by using fundamental physics. You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves. In this opening chapter we’ll go over some important preliminaries that we’ll need throughout our study. We’ll discuss the nature of physical theory and the use of idealized models to represent physical systems. We’ll introduce the sys- tems of units used to describe physical quantities and discuss ways to describe the accuracy of a number. We’ll look at examples of problems for which we can’t or don’t want to find a precise answer but for which rough estimates can be useful and interesting. Finally we’ll study several aspects of vectors and vector algebra. We’ll need vectors throughout our study of physics to help us describe and analyze physical quantities such as velocity and force that have direction as well as magnitude. M01_YOUN3610_14_SE_C01_001-033.indd 1 9/11/14 10:40 AM

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2 Chapter 1 Units physical Quantities and Vectors 1.1 The NaTure of Physics Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena. These patterns are called physical theories or when they are very well established and widely used physi- cal laws or principles. cauTioN The meaning of “theory” A theory is not just a random thought or an unproven concept. Rather a theory is an explanation of natural phenomena based on observation and accepted fundamental principles. An example is the well-established theory of bio- logical evolution which is the result of extensive research and observation by generations of biologists. ❙ To develop a physical theory a physicist has to learn to ask appropriate ques- tions design experiments to try to answer the questions and draw appropriate conclusions from the results. Figure 1.1 shows two important facilities used for physics experiments. Legend has it that Galileo Galilei 1564–1642 dropped light and heavy ob- jects from the top of the Leaning Tower of Pisa Fig. 1.1a to find out whether their rates of fall were different. From examining the results of his experiments which were actually much more sophisticated than in the legend he made the inductive leap to the principle or theory that the acceleration of a falling object is independent of its weight. The development of physical theories such as Galileo’s often takes an indirect path with blind alleys wrong guesses and the discarding of unsuccessful theo- ries in favor of more promising ones. Physics is not simply a collection of facts and principles it is also the process by which we arrive at general principles that describe how the physical universe behaves. No theory is ever regarded as the final or ultimate truth. The possibility al- ways exists that new observations will require that a theory be revised or dis- carded. It is in the nature of physical theory that we can disprove a theory by finding behavior that is inconsistent with it but we can never prove that a theory is always correct. Getting back to Galileo suppose we drop a feather and a cannonball. They certainly do not fall at the same rate. This does not mean that Galileo was wrong it means that his theory was incomplete. If we drop the feather and the cannon- ball in a vacuum to eliminate the effects of the air then they do fall at the same rate. Galileo’s theory has a range of validity: It applies only to objects for which the force exerted by the air due to air resistance and buoyancy is much less than the weight. Objects like feathers or parachutes are clearly outside this range. 1.2 solviNg Physics Problems At some point in their studies almost all physics students find themselves thinking “I understand the concepts but I just can’t solve the problems.” But in physics truly understanding a concept means being able to apply it to a variety of problems. Learning how to solve problems is absolutely essential you don’t know physics unless you can do physics. How do you learn to solve physics problems In every chapter of this book you will find Problem-Solving Strategies that offer techniques for setting up and solving problems efficiently and accurately. Following each Problem-Solving Strategy are one or more worked Examples that show these techniques in action. The Problem-Solving Strategies will also steer you away from some incorrect techniques that you may be tempted to use. You’ll also find additional examples that aren’t associated with a particular Problem-Solving Strategy. In addition at the end of each chapter you’ll find a Bridging Problem that uses more than one of 1.1 Two research laboratories. University Physics 14e Young/Freedman Benjamin Cummings Pearson Education 9736101002 Fig 01_01 Pickup: 6754601003 Rolin Graphics lm 1/27/14 13p0 x 35p5 mc 3/14/14 bj 3/28/14 a According to legend Galileo investigated falling objects by dropping them from the Leaning Tower of Pisa Italy ... b The Planck spacecraft is designed to study the faint electromagnetic radiation left over from the Big Bang 13.8 billion years ago. ... and he studied pendulum motion by observing the swinging chandelier in the adjacent cathedral. These technicians are reected in the spacecraft’s light-gathering mirror during pre-launch testing. M01_YOUN3610_14_SE_C01_001-033.indd 2 15/06/15 2:02 PM

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1.2 Solving Physics Problems 3 the key ideas from the chapter. Study these strategies and problems carefully and work through each example for yourself on a piece of paper. Different techniques are useful for solving different kinds of physics prob- lems which is why this book offers dozens of Problem-Solving Strategies. No matter what kind of problem you’re dealing with however there are certain key steps that you’ll always follow. These same steps are equally useful for problems in math engineering chemistry and many other fields. In this book we’ve orga- nized these steps into four stages of solving a problem. All of the Problem-Solving Strategies and Examples in this book will follow these four steps. In some cases we will combine the first two or three steps. We encourage you to follow these same steps when you solve problems yourself. You may find it useful to remember the acronym I SEE—short for Identify Set up Execute and Evaluate. idenTify the relevant concepts: Use the physical conditions stated in the problem to help you decide which physics concepts are rel- evant. Identify the target variables of the problem—that is the quantities whose values you’re trying to find such as the speed at which a projectile hits the ground the intensity of a sound made by a siren or the size of an image made by a lens. Identify the known quantities as stated or implied in the problem. This step is essential whether the problem asks for an algebraic expression or a numerical answer. seT uP the problem: Given the concepts you have identified the known quantities and the target variables choose the equations that you’ll use to solve the problem and decide how you’ll use them. Make sure that the variables you have identified correlate exactly with those in the equations. If appropriate draw a sketch of the situation described in the problem. Graph paper ruler pro - tractor and compass will help you make clear useful sketches. As best you can estimate what your results will be and as ap - propriate predict what the physical behavior of a system will be. The worked examples in this book include tips on how to make these kinds of estimates and predictions. If this seems challeng - ing don’t worry—you’ll get better with practice execuTe the solution: This is where you “do the math.” Study the worked examples to see what’s involved in this step. evaLuaTe your answer: Compare your answer with your esti- mates and reconsider things if there’s a discrepancy. If your an- swer includes an algebraic expression assure yourself that it correctly represents what would happen if the variables in it had very large or very small values. For future reference make note of any answer that represents a quantity of particular significance. Ask yourself how you might answer a more general or more dif- ficult version of the problem you have just solved. Problem-Solving STraTegy 1.1 Solving PhySicS ProblemS idealized models In everyday conversation we use the word “model” to mean either a small-scale replica such as a model railroad or a person who displays articles of clothing or the absence thereof. In physics a model is a simplified version of a physical system that would be too complicated to analyze in full detail. For example suppose we want to analyze the motion of a thrown baseball Fig. 1.2a. How complicated is this problem The ball is not a perfect sphere it has raised seams and it spins as it moves through the air. Air resistance and wind influence its motion the ball’s weight varies a little as its altitude changes and so on. If we try to include all these things the analysis gets hopelessly com - plicated. Instead we invent a simplified version of the problem. We ignore the size and shape of the ball by representing it as a point object or particle. We ignore air resistance by making the ball move in a vacuum and we make the weight constant. Now we have a problem that is simple enough to deal with Fig. 1.2b. We will analyze this model in detail in Chapter 3. We have to overlook quite a few minor effects to make an idealized model but we must be careful not to neglect too much. If we ignore the effects of grav- ity completely then our model predicts that when we throw the ball up it will go in a straight line and disappear into space. A useful model simplifies a problem enough to make it manageable yet keeps its essential features. 1.2 To simplify the analysis of a a base- ball in flight we use b an idealized model. Direction of motion Direction of motion Treat the baseball as a point object particle. No air resistance. Baseball spins and has a complex shape. Air resistance and wind exert forces on the ball. Gravitational force on ball depends on altitude. Gravitational force on ball is constant. a A real baseball in ight b An idealized model of the baseball M01_YOUN3610_14_SE_C01_001-033.indd 3 16/05/14 3:29 PM

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4 ChaPter 1 Units Physical Quantities and Vectors The validity of the predictions we make using a model is limited by the va- lidity of the model. For example Galileo’s prediction about falling objects see Section 1.1 corresponds to an idealized model that does not include the effects of air resistance. This model works fairly well for a dropped cannonball but not so well for a feather. Idealized models play a crucial role throughout this book. Watch for them in discussions of physical theories and their applications to specific problems. 1.3 sTandards and uniTs As we learned in Section 1.1 physics is an experimental science. Experiments require measurements and we generally use numbers to describe the results of measurements. Any number that is used to describe a physical phenomenon quantitatively is called a physical quantity. For example two physical quanti - ties that describe you are your weight and your height. Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition. Two examples are measuring a distance by using a ruler and measuring a time interval by using a stopwatch. In other cases we define a physical quantity by describing how to calculate it from other quantities that we can measure. Thus we might define the average speed of a moving object as the distance traveled measured with a ruler divided by the time of travel measured with a stopwatch. When we measure a quantity we always compare it with some reference stan - dard. When we say that a Ferrari 458 Italia is 4.53 meters long we mean that it is 4.53 times as long as a meter stick which we define to be 1 meter long. Such a standard defines a unit of the quantity. The meter is a unit of distance and the second is a unit of time. When we use a number to describe a physical quantity we must always specify the unit that we are using to describe a distance as sim - ply “4.53” wouldn’t mean anything. To make accurate reliable measurements we need units of measurement that do not change and that can be duplicated by observers in various locations. The system of units used by scientists and engineers around the world is com- monly called “the metric system” but since 1960 it has been known officially as the International System or SI the abbreviation for its French name Système International. Appendix A gives a list of all SI units as well as definitions of the most fundamental units. Time From 1889 until 1967 the unit of time was defined as a certain fraction of the mean solar day the average time between successive arrivals of the sun at its highest point in the sky. The present standard adopted in 1967 is much more precise. It is based on an atomic clock which uses the energy difference between the two lowest energy states of the cesium atom 133 Cs. When bombarded by microwaves of precisely the proper frequency cesium atoms undergo a transition from one of these states to the other. One second abbreviated s is defined as the time required for 9192631770 cycles of this microwave radiation Fig. 1.3a. Length In 1960 an atomic standard for the meter was also established using the wavelength of the orange-red light emitted by excited atoms of krypton 1 86 Kr2. From this length standard the speed of light in vacuum was measured to be 299792458 ms. In November 1983 the length standard was changed again so that the speed of light in vacuum was defined to be precisely 299792458 ms. 1.3 The measurements used to determine a the duration of a second and b the length of a meter. These measurements are useful for setting standards because they give the same results no matter where they are made. Light source Cesium-133 atom Cesium-133 atom Microwave radiation with a frequency of exactly 9192631770 cycles per second ... ... causes the outermost electron of a cesium-133 atom to reverse its spin direction. An atomic clock uses this phenomenon to tune microwaves to this exact frequency. It then counts 1 second for each 9192631770 cycles. Light travels exactly 299792458 m in 1 s. a Measuring the second b Measuring the meter 0:00 s 0:01 s Outermost electron M01_YOUN3610_14_SE_C01_001-033.indd 4 16/05/14 3:29 PM

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1.3 Standards and Units 5 Hence the new definition of the meter abbreviated m is the distance that light travels in vacuum in 1299792458 second Fig. 1.3b. This modern definition provides a much more precise standard of length than the one based on a wave- length of light. Mass The standard of mass the kilogram abbreviated kg is defined to be the mass of a particular cylinder of platinum–iridium alloy kept at the International Bureau of Weights and Measures at Sèvres near Paris Fig. 1.4. An atomic standard of mass would be more fundamental but at present we cannot measure masses on an atomic scale with as much accuracy as on a macroscopic scale. The gram which is not a fundamental unit is 0.001 kilogram. Other derived units can be formed from the fundamental units. For example the units of speed are meters per second or ms these are the units of length m divided by the units of time s. Unit Prefixes Once we have defined the fundamental units it is easy to introduce larger and smaller units for the same physical quantities. In the metric system these other units are related to the fundamental units or in the case of mass to the gram by multiples of 10 or 1 10 Thus one kilometer 11 km2 is 1000 meters and one centi- meter 11 cm2 is 1 100 meter. We usually express multiples of 10 or 1 10 in exponential notation: 1000 10 3 1 1000 10 -3 and so on. With this notation 1 km 10 3 m and 1 cm 10 -2 m. The names of the additional units are derived by adding a prefix to the name of the fundamental unit. For example the prefix “kilo-” abbreviated k always means a unit larger by a factor of 1000 thus 1 kilometer 1 km 10 3 meters 10 3 m 1 kilogram 1 kg 10 3 grams 10 3 g 1 kilowatt 1 kW 10 3 watts 10 3 W A table in Appendix A lists the standard SI units with their meanings and abbreviations. Table 1.1 gives some examples of the use of multiples of 10 and their prefixes with the units of length mass and time. Figure 1.5 next page shows how these prefixes are used to describe both large and small distances. 1.4 The international standard kilogram is the metal object carefully enclosed within these nested glass containers. Table 1.1 Some Units of Length Mass and Time Length Mass Time 1 nanometer 1 nm 10 -9 m a few times the size of the largest atom 1 micrometer 1 mm 10 -6 m size of some bacteria and other cells 1 millimeter 1 mm 10 -3 m diameter of the point of a ballpoint pen 1 centimeter 1 cm 10 -2 m diameter of your little finger 1 kilometer 1 km 10 3 m distance in a 10-minute walk 1 microgram 1 mg 10 -6 g 10 -9 kg mass of a very small dust particle 1 milligram 1 mg 10 -3 g 10 -6 kg mass of a grain of salt 1 gram 1 g 10 -3 kg mass of a paper clip 1 nanosecond 1 ns 10 -9 s time for light to travel 0.3 m 1 microsecond 1 ms 10 -6 s time for space station to move 8 mm 1 millisecond 1 ms 10 -3 s time for a car moving at freeway speed to travel 3 cm         M01_YOUN3610_14_SE_C01_001-033.indd 5 05/06/14 2:14 PM

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Dust Stars 5 light-years Gas 1481 W hat are the most fundamental constituents of matter How did the universe begin And what is the fate of our universe In this chapter we will explore what physicists and astronomers have learned in their quest to answer these questions. The chapter title “Particle Physics and Cosmology” may seem strange. Fun - damental particles are the smallest things in the universe and cosmology deals with the biggest thing there is—the universe itself. Nonetheless we’ll see in this chapter that physics on the most microscopic scale plays an essential role in determining the nature of the universe on the largest scale. The development of high-energy accelerators and associated detectors has been crucial in our emerging understanding of particles. We can classify par - ticles and their interactions in several ways in terms of conservation laws and symmetries some of which are absolute and others of which are obeyed only in certain kinds of interactions. We’ll conclude by discussing our present under - standing of the nature and evolution of the universe as a whole. 44.1 Fundamental Particles—a History The idea that the world is made of fundamental particles has a long history. In about 400 b.c. the Greek philosophers Democritus and Leucippus suggested that matter is made of indivisible particles that they called atoms a word derived from a- not and tomos cut or divided. This idea lay dormant until about 1804 when the English scientist John Dalton 1766–1844 often called the father of modern chemistry discovered that many chemical phenomena could be explained if atoms of each element are the basic indivisible building blocks of matter. the electron and the Proton Toward the end of the 19th century it became clear that atoms are not indivisible. The characteristic spectra of elements suggested that atoms have internal structure This image shows a por- tion of the Eagle Nebula a region some 6500 light-years away where new stars are forming. The luminous stars glowing gas and opaque dust clouds are all made of “normal” matter—that is atoms and their constituents. What percentage of the mass and energy in the universe is com- posed of “normal” matter i 75 to 100 ii 50 to 75 iii 25 to 50 iv 5 to 25 v less than 5. learning goals Looking forward at … 44.1 The key varieties of fundamental subatomic particles and how they were discovered. 44.2 How physicists use accelerators and detectors to probe the properties of subatomic particles. 44.3 The four ways in which subatomic particles interact with each other. 44.4 How the structure of protons neutrons and other particles can be explained in terms of quarks. 44.5 The standard model of particles and interactions. 44.6 The evidence that the universe is expand- ing and that the expansion is speeding up. 44.7 The history of the first 380000 years after the Big Bang. Looking back at … 13.3 Escape speed. 27.4 Motion of charged particles in a magnetic field. 32.1 Radiation from accelerated charges. 38.1 38.3 38.4 Photons electron–positron annihilation uncertainty principle. 39.1 39.2 Electron waves discovery of the nucleus. 41.5 41.6 Electron spin exclusion principle. 42.6 Valence bands and holes. 43.1 43.3 Neutrons and protons b + decay. Particle Physics and cosmology 44 M44_YOUN3610_14_SE_C44_1481-1522.indd 1481 25/10/14 11:30 AM

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1482 Chapter 44 particle physics and Cosmology and J. J. Thomson’s discovery of the negatively charged electron in 1897 showed that atoms could be taken apart into charged particles. Rutherford’s experiments in 1910–11 see Section 39.2 revealed that an atom’s positive charge resides in a small dense nucleus. In 1919 Rutherford made an additional discovery: When alpha particles are fired into nitrogen one product is hydrogen gas. He reasoned that the hydrogen nucleus is a constituent of the nuclei of heavier atoms such as nitrogen and that a collision with a fast-moving alpha particle can dislodge one of those hydrogen nuclei. Thus the hydrogen nucleus is an elementary particle that Rutherford named the proton. The following decade saw the blossoming of quantum mechanics including the Schrödinger equation. Physicists were on their way to understanding the principles that underlie atomic structure. the Photon Einstein explained the photoelectric effect in 1905 by assuming that the energy of electromagnetic waves is quantized that is it comes in little bundles called photons with energy E hf. Atoms and nuclei can emit create and absorb destroy photons see Section 38.1. Considered as particles photons have zero charge and zero rest mass. Note that any discussions of a particle’s mass in this chapter will refer to its rest mass. In particle physics a photon is denoted by the symbol g the Greek letter gamma. the neutron In 1930 the German physicists Walther Bothe and Herbert Becker observed that when beryllium boron or lithium was bombarded by alpha particles the target material emitted a radiation that had much greater penetrating power than the original alpha particles. Experiments by the English physicist James Chadwick in 1932 showed that the emitted particles were electrically neutral with mass approximately equal to that of the proton. Chadwick christened these particles neutrons symbol n or 1 0 n. A typical reaction of the type studied by Bothe and Becker with a beryllium target is 2 4 He + 4 9 BeS 6 12 C + 0 1 n 44.1 Elementary particles are usually detected by their electromagnetic effects— for instance by the ionization that they cause when they pass through matter. This is the principle of the cloud chamber described below. Because neutrons have no charge they are difficult to detect directly they interact hardly at all with electrons and produce little ionization when they pass through matter. However neutrons can be slowed down by scattering from nuclei and they can penetrate a nucleus. Hence slow neutrons can be detected by means of a nuclear reaction in which a neutron is absorbed and an alpha particle is emitted. An example is 0 1 n + 5 10 BS 3 7 Li + 2 4 He 44.2 The ejected alpha particle is easy to detect because it is charged. Later experi - ments showed that neutrons and protons like electrons are spin 1 2 particles see Section 43.1. The discovery of the neutron cleared up a mystery about the composition of the nucleus. Before 1930 the mass of a nucleus was thought to be due only to protons but no one understood why the charge-to-mass ratio was not the same for all nuclides. It soon became clear that all nuclides except 1 1 H contain both protons and neutrons. Hence the proton the neutron and the electron are the building blocks of atoms. However that is not the end of the particle story these are not the only particles and particles can do more than build atoms. the Positron The positive electron or positron was discovered by the American physicist Carl D. Anderson in 1932 during an investigation of particles bombarding the earth M44_YOUN3610_14_SE_C44_1481-1522.indd 1482 15/10/14 10:38 AM

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44.1 Fundamental particles—a history 1483 44.1 Photograph of the cloud-chamber track made by the first positron ever identified. The photograph was made by Carl D. Anderson in 1932. Positron track Lead plate 6 mm thick The positron follows a curved path owing to the presence of a magnetic field. The track is more strongly curved above the lead plate showing that the positron was traveling upward and lost energy and speed as it passed through the plate. 44.2 a Energy states for a free electron predicted by the Dirac equation. b Raising an electron from an E 6 0 state to an E 7 0 state corresponds to electron–positron pair production. c An electron dropping from an E 7 0 state to a vacant E 6 0 state corresponds to electron–positron pair annihilation. from space. Figure 44.1 shows a historic photograph made with a cloud chamber an instrument used to visualize the tracks of charged particles. The chamber contained a supercooled vapor a charged particle passing through the vapor causes ionization and the ions trigger the condensation of liquid droplets from the vapor. The droplets make a visible track showing the charged particle’s path. The cloud chamber in Fig. 44.1 is in a magnetic field directed into the plane of the photograph. The particle has passed through a thin lead plate which extends from left to right in the figure that lies within the chamber. The track is more tightly curved above the plate than below it showing that the speed was less above the plate than below it. Therefore the particle had to be moving upward it could not have gained energy passing through the lead. The thickness and curva- ture of the track suggested that its mass and the magnitude of its charge equaled those of the electron. But the directions of the magnetic field and the velocity in the magnetic force equation F S qY S : B S showed that the particle had positive charge. Anderson christened this particle the positron. To theorists the appearance of the positron was a welcome development. In 1928 the English physicist Paul Dirac had developed a relativistic generalization of the Schrödinger equation for the electron. In Section 41.5 we discussed how Dirac’s ideas helped explain the spin magnetic moment of the electron. One of the puzzling features of the Dirac equation was that for a free electron it predicted not only a continuum of energy states greater than its rest energy m e c 2 as expected but also a continuum of negative energy states less than -m e c 2 Fig. 44.2a. That posed a problem. What was to prevent an electron from emit- ting a photon with energy 2m e c 2 or greater and hopping from a positive state to a negative state It wasn’t clear what these negative-energy states meant and there was no obvious way to get rid of them. Dirac’s ingenious interpretation was that all the negative-energy states were filled with electrons and that these electrons were for some reason unobservable. The exclusion principle see Section 41.6 would forbid a transition to a state that was already occupied. A vacancy in a negative-energy state would act like a positive charge just as a hole in the valence band of a semiconductor see Section 42.6 acts like a positive charge. Initially Dirac tried to argue that such vacancies were protons. But after Anderson’s discovery it became clear that the vacancies were observed physically as positrons. Furthermore the Dirac energy-state picture provides a mechanism for the creation of positrons. When an electron in a negative-energy state absorbs a photon with energy greater than 2m e c 2 it goes to a positive state Fig. 44.2b in which it becomes observable. The vacancy that it leaves behind is observed as a positron the result is the creation of an electron–positron pair. Similarly when an electron in a positive-energy state falls into a vacancy both the electron and the vacancy that is the positron disappear and photons are emitted Fig. 44.2c. Thus the Dirac theory leads naturally to the conclusion that like photons electrons can be created and destroyed. While photons can be created and destroyed singly electrons can be produced or destroyed only in electron–positron pairs or in association with other particles. Creating or destroying an electron alone would mean creating or destroying an amount of charge -e which would violate the conservation of electric charge. – + Continuum of positive-energy states m e c 2 -m e c 2 Continuum of negative-energy states 0 a b c Electron 72m e c 2 Positron Photon m e c 2 m e c 2 m e c 2 -m e c 2 Photon Photon M44_YOUN3610_14_SE_C44_1481-1522.indd 1483 15/10/14 10:38 AM

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1484 Chapter 44 particle physics and Cosmology In 1949 the American physicist Richard Feynman showed that a positron could be described mathematically as an electron traveling backward in time. His reformulation of the Dirac theory eliminated difficult calculations involving the infinite sea of negative-energy states and put electrons and positrons on the same footing. But the creation and destruction of electron–positron pairs remain. The Dirac theory provides the beginning of a theoretical framework for creation and destruction of all fundamental particles. Experiment and theory tell us that the masses of the positron and electron are identical and that their charges are equal in magnitude but opposite in sign. The positron’s spin angular momentum S S and magnetic moment M S are parallel they are opposite for the electron. However S S and M S have the same magnitude for both particles because they have the same spin. We use the term antiparticle for a particle that is related to another particle as the positron is to the electron. Each kind of particle has a corresponding antiparticle. For a few kinds of particles necessarily all neutral the particle and antiparticle are identical and we can say that they are their own antiparticles. The photon is an example there is no way to distinguish a photon from an antiphoton. We’ll use the standard symbols e - for the electron and e + for the positron. The generic term “electron” often includes both electrons and positrons. Other antiparticles may be denoted by a bar over the particle’s symbol for example an antiproton is p. We’ll see other examples of antiparticles later. Positrons do not occur in ordinary matter. Electron–positron pairs are produced during high-energy collisions of charged particles or g rays with matter. This process is called e + e - pair production Fig. 44.3. The minimum available energy required for electron–positron pair production equals the rest energy 2m e c 2 of the two particles: E min 2m e c 2 219.109 10 -31 kg212.998 10 8 ms2 2 1.637 10 -13 J 1.022 MeV The inverse process e + e - pair annihilation occurs when a positron and an elec- tron collide see Example 38.6 in Section 38.3. Both particles disappear and two or occasionally three photons can appear with total energy of at least 2m e c 2 1.022 MeV. Decay into a single photon is impossible: Such a process could not conserve both energy and momentum. Positrons also occur in the decay of some unstable nuclei in which they are called beta-plus particles 1b + 2. We discussed b + decay in Section 43.3. We’ll frequently represent particle masses in terms of the equivalent rest energy by using m Ec 2 . Then typical mass units are MeVc 2 for example m 0.511 MeVc 2 for an electron or positron. Particles as Force mediators In classical physics we describe the interaction of charged particles in terms of electric and magnetic forces. In quantum mechanics we can describe this in - teraction in terms of emission and absorption of photons. Two electrons repel each other as one emits a photon and the other absorbs it just as two skaters can push each other apart by tossing a heavy ball back and forth between them Fig. 44.4a. For an electron and a proton in which the charges are opposite and the force is attractive we imagine the skaters trying to grab the ball away from each other Fig. 44.4b. The electromagnetic interaction between two charged particles is mediated or transmitted by photons. If charged-particle interactions are mediated by photons where does the en - ergy to create the photons come from Recall from our discussion of the uncer - tainty principle see Sections 38.4 and 39.6 that a state that exists for a short time t has an uncertainty E in its energy such that E t Ú U 2 44.3 44.3 a Photograph of bubble-chamber tracks of electron–positron pairs that are produced when 300-MeV photons strike a lead sheet. A magnetic field directed out of the photograph made the electrons and positrons curve in opposite directions. b Diagram showing the pair-production process for two of the photons. B S Electron–positron pair a b g e - e + g e - e + BIO application Pair annihilation in medical diagnosis A technique called positron emission tomography PET can be used to identify the early stages of Alzheimer’s disease. A patient is administered a glucose-like compound called FDG in which one oxygen atom is replaced by radioactive 18 F. FDG accumulates in active areas of the brain where glucose metabolism is high. The 18 F undergoes b + decay positron emission with a half-life of 110 minutes and the emitted positron imme- diately annihilates with an atomic electron to produce two gamma-ray photons. A scanner detects both photons then calculates where the annihilation took place—the site of FDG accumulation. These PET images—which show areas of strongest emission and hence greatest glucose metabolism in red—reveal changes in the brains of patients. M44_YOUN3610_14_SE_C44_1481-1522.indd 1484 15/10/14 10:38 AM

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44.1 Fundamental particles—a history 1485 44.4 An analogy for how particles act as force mediators. a Two skaters exert repulsive forces on each other by tossing a ball back and forth. b Two skaters exert attractive forces on each other when one tries to grab the ball out of the other’s hands. F F F F This uncertainty permits the creation of a photon with energy E provided that it lives no longer than the time t given by Eq. 44.3. A photon that can exist for a short time because of this energy uncertainty is called a virtual photon. It’s as though there were an energy bank you can borrow energy provided that you pay it back within the time limit. According to Eq. 44.3 the more you borrow the sooner you have to pay it back. mesons Is there a particle that mediates the nuclear force By the mid-1930s the nuclear force between two nucleons neutrons or protons appeared to be described by a potential energy U1r2 with the general form U1r2 -f 2 a e -rr 0 r b nuclear potential energy 44.4 The constant f characterizes the strength of the interaction and r 0 describes its range. Figure 44.5 compares the absolute value of this function with the func- tion f 2 r which would be analogous to the electric interaction of two protons: U1r2 1 4pP 0 e 2 r electric potential energy 44.5 In 1935 the Japanese physicist Hideki Yukawa suggested that a hypothetical particle that he called a meson might mediate the nuclear force. He showed that the range of the force was related to the mass of the particle. Yukawa argued that the particle must live for a time t long enough to travel a distance compa- rable to the range r 0 of the nuclear force. This range was known from the sizes of nuclei and other information to be about 1.5 10 -15 m 1.5 fm. If we assume that an average particle’s speed is comparable to c and travels about half the range its lifetime t must be about t r 0 2c 1.5 10 -15 m 213.0 10 8 ms2 2.5 10 -24 s From Eq. 44.3 the minimum necessary uncertainty E in energy is E U 2t 1.05 10 -34 J s 212.5 10 -24 s2 2.1 10 -11 J 130 MeV The mass equivalent m of this energy is about 250 times the electron mass: m E c 2 2.1 10 -11 J 13.00 10 8 ms2 2 2.3 10 -28 kg 130 MeVc 2 Yukawa postulated that an as yet undiscovered particle with this mass serves as the messenger for the nuclear force. A year later Carl Anderson and his colleague Seth Neddermeyer discovered in cosmic radiation two new particles now called muons. The m - has charge equal to that of the electron and its antiparticle the m + has a positive charge with equal magnitude. The two particles have equal mass about 207 times the electron mass. But it soon became clear that muons were not Yukawa’s particles because they interacted with nuclei only very weakly. In 1947 a family of three particles called p mesons or pions were discovered. Their charges are +e -e and zero and their masses are about 270 times the electron mass. The pions interact strongly with nuclei and they are the particles predicted by Yukawa. Other heavier mesons the v and r evidently also act as shorter-range messengers of the nuclear force. The complexity of this explanation suggests that the nuclear force has simpler underpinnings these involve the quarks 44.5 Graph of the magnitude of the Yukawa potential-energy function for nuclear forces 0 U1r20 f 2 e -rr 0 r. The function U1r2 f 2 r proportional to the potential energy for Coulomb’s law is also shown. The two functions are similar at small r but the Yukawa potential energy drops off much more quickly at large r. f 2 r f 2 a e -rr 0 r b O 0Ur0 r 4f 2 r 0 Coulomb potential energy Yukawa potential energy 3f 2 r 0 2f 2 r 0 f 2 r 0 r 0 2r 0 3r 0 M44_YOUN3610_14_SE_C44_1481-1522.indd 1485 15/10/14 10:38 AM

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