Simple Nature - Light and Matter

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could never do that again in a million years.” But she tries again,and finds that she can’t help doing it even if she doesn’t want to.Luckily she has just learned about collisions in her physics course.Once she has written down the equations for conservation of energyand no loss of kinetic energy, she really doesn’t have to complete thealgebra. She knows that she has two equations in two unknowns,so there must be a well-defined solution. Once she has seen theresult of one such collision, she knows that the same thing musthappen every time. The same thing would happen with collidingmarbles or croquet balls. It doesn’t matter if the masses or velocitiesare different, because that just multiplies both equations by someconstant factor.The discovery of the neutronThis was the type of reasoning employed by James Chadwick inhis 1932 discovery of the neutron. At the time, the atom was imaginedto be made out of two types of fundamental particles, protonsand electrons. The protons were far more massive, and clusteredtogether in the atom’s core, or nucleus. Electrical attraction causedthe electrons to orbit the nucleus in circles, in much the same waythat gravity kept the planets from cruising out of the solar system.Experiments showed, for example, that twice as much energy wasrequired to strip the last electron off of a helium atom as was neededto remove the single electron from a hydrogen atom, and this wasexplained by saying that helium had two protons to hydrogen’s one.The trouble was that according to this model, helium would havetwo electrons and two protons, giving it precisely twice the mass ofa hydrogen atom with one of each. In fact, helium has about fourtimes the mass of hydrogen.Chadwick suspected that the helium nucleus possessed two additionalparticles of a new type, which did not participate in electricalinteractions at all, i.e., were electrically neutral. If these particleshad very nearly the same mass as protons, then the four-to-one massratio of helium and hydrogen could be explained. In 1930, a newtype of radiation was discovered that seemed to fit this description.It was electrically neutral, and seemed to be coming from the nucleiof light elements that had been exposed to other types of radiation.At this time, however, reports of new types of particles werea dime a dozen, and most of them turned out to be either clustersmade of previously known particles or else previously known particleswith higher energies. Many physicists believed that the “new”particle that had attracted Chadwick’s interest was really a previouslyknown particle called a gamma ray, which was electricallyneutral. Since gamma rays have no mass, Chadwick decided to tryto determine the new particle’s mass and see if it was nonzero andapproximately equal to the mass of a proton.Unfortunately a subatomic particle is not something you can138 Chapter 3 Conservation of Momentum
h / Chadwick’s subatomic pool table. A disk of the naturally occurringmetal polonium provides a source of radiation capable of kickingneutrons out of the beryllium nuclei. The type of radiation emitted bythe polonium is easily absorbed by a few mm of air, so the air has to bepumped out of the left-hand chamber. The neutrons, Chadwick’s mysteryparticles, penetrate matter far more readily, and fly out through the walland into the chamber on the right, which is filled with nitrogen or hydrogengas. When a neutron collides with a nitrogen or hydrogen nucleus, itkicks it out of its atom at high speed, and this recoiling nucleus then ripsapart thousands of other atoms of the gas. The result is an electricalpulse that can be detected in the wire on the right. Physicists had alreadycalibrated this type of apparatus so that they could translate the strengthof the electrical pulse into the velocity of the recoiling nucleus. Thewhole apparatus shown in the figure would fit in the palm of your hand, indramatic contrast to today’s giant particle accelerators.just put on a scale and weigh. Chadwick came up with an ingenioussolution. The masses of the nuclei of the various chemical elementswere already known, and techniques had already been developed formeasuring the speed of a rapidly moving nucleus. He therefore setout to bombard samples of selected elements with the mysteriousnew particles. When a direct, head-on collision occurred betweena mystery particle and the nucleus of one of the target atoms, thenucleus would be knocked out of the atom, and he would measureits velocity.Suppose, for instance, that we bombard a sample of hydrogenatoms with the mystery particles. Since the participants in thecollision are fundamental particles, there is no way for kinetic energyto be converted into heat or any other form of energy, and Chadwickthus had two equations in three unknowns:equation #1: conservation of momentumequation #2: no loss of kinetic energyunknown #1: mass of the mystery particleunknown #2: initial velocity of the mystery particleSection 3.1 Momentum In One Dimension 139
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Fullerton, Californiawww.lightandma
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Contents0 Introduction and Review0.
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5.5 More About Heat Engines . . . .
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669.11.3 Magnetic Fields by Ampère
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The Mars Climate Orbiter is prepare
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temperatures and with many combinat
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idence that quarks have smaller par
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give clearer explanations.Finally,
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It can also be handy to have a rela
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The prefix centi-, meaning 10 −2
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goes like this:V = 1 3 Ah[1]A = πr
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the notation 10 0 to stand for one,
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calculation, 5.04 cm, was really no
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0.2 Scaling and Order-of-Magnitude
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to many times your own height. The
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g / 1. This plank is as long as it
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the front panels of the three violi
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Correct solution #4: The area of a
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here?” The scientific Mr. Spock w
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1. Don’t even attempt more than o
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Problem 10.mean, however, is define
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(d) Find the person’s acceleratio
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Albert Einstein, and his moustache,
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54 Chapter 0 Introduction and Revie
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a / Portrait of Monsieur Lavoisiera
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1.1.1 Problem-solving techniquesHow
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∆m = 0, where m is the total mass
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different substances will have diff
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c / Left: In a frame of referenceth
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f / Discussion question B.(discusse
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Self-check D.since the derivative o
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ProblemsThe symbols √ , , etc. ar
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difficult? ⊲ Solution, p. 932Key
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Heat energy can be convertedto ligh
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a new form of invisible “mystery
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f / A realistic drawing of Joule’
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numbers. With a purely numerical ap
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of gravity doesn’t change much if
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field. If the plane can start from
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m / Discussion question C.n / A hyd
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Page 90 and 91: A car drives over a cliff.new frame
Page 92 and 93: How long does it take to move 1 met
Page 94 and 95: a / Approximations to thebrachistoc
Page 96 and 97: a / An ellipse is circle that hasbe
Page 98 and 99: to deduce the general equation for
Page 100 and 101: to the mass of the object that inte
Page 102 and 103: The minimum velocity required for t
Page 104 and 105: and since sin θ dθ occurs in the
Page 106 and 107: that is deeper than r. Under the as
Page 108 and 109: 2.3.6 ⋆ Evidence for repulsive gr
Page 110 and 111: a / A vivid demonstration thatheat
Page 112 and 113: ture. This is a very good question,
Page 114 and 115: Three functions with thesame curvat
Page 116 and 117: This looks like a cosine function,
Page 118 and 119: ProblemsThe symbols √ , , etc. ar
Page 120 and 121: Problem 16.13 Anya and Ivan lean ov
Page 122 and 123: Problem 27.then we’d have U/m =
Page 124 and 125: 37 Two springs with spring constant
Page 126 and 127: ExercisesExercise 2A: Reasoning wit
Page 128 and 129: 128 Chapter 2 Conservation of Energ
Page 130 and 131: 3.1 Momentum In One Dimensiona / Sy
Page 132 and 133: eing to the right. The initial mome
Page 134 and 135: 3.1.3 Momentum compared to kinetic
Page 136 and 137: 3.1.4 Collisions in one dimensiong
Page 140 and 141: i / The highjumper’s body passeso
Page 142 and 143: where x 1 is the mass of the first
Page 144 and 145: 3.1.6 The center of mass frame of r
Page 146 and 147: The airbag increases ∆tso as to r
Page 148 and 149: d / Two magnets exert forceson each
Page 150 and 151: x (m) t (s)10 1.8420 2.8630 3.8040
Page 152 and 153: 3.2.4 Forces between solidsConserva
Page 154 and 155: Maximum acceleration of a car examp
Page 156 and 157: Discussion QuestionA Criticize the
Page 158 and 159: C A pool ball is rebounding from th
Page 160 and 161: forces, as if the hand were a pair
Page 162 and 163: This may not sound like an impressi
Page 164 and 165: stroke are both executed in straigh
Page 166 and 167: Accelerating a cart example 35If yo
Page 168 and 169: w / A wedge.x / Archimedes’ screw
Page 170 and 171: As in the preceding example, we hav
Page 172 and 173: that have the same frequency is a s
Page 174 and 175: around until I got this result, sin
Page 176 and 177: quality factor, Q, is defined as Q
Page 178 and 179: ight direction to add energy to the
Page 180 and 181: i / Example 45: a viola withouta mu
Page 182 and 183: Collapse of the Nimitz Freeway exam
Page 184 and 185: end up canceling out, however:Q =
Page 186 and 187: 186 Chapter 3 Conservation of Momen
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c / Bullets are dropped and shot at
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the asteroid’s energy and boostin
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coordinate axes. Even though ∆x,
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of the three components,∆p x = 0
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A useless vector operation example
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Solving for the unknowns gives∆x
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o / Example 64.p / Adding vectors g
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How to generalize one-dimensional e
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needed to support the object in fig
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The easiest method is the one demon
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Incorrect solution #4:(same notatio
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The magnitude of the acceleration i
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dropped out like a trap door, showi
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af / Breaking trail, by WalterE. Bo
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know how to integrate with respect
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Problem 16.Problem 19.resistance.)1
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of gravity on Mars.(a) Find the tim
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partner force. (a) A swimmer speeds
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Problem 45the 0.4-gram masses would
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53 If you walk 35 km at an angle 25
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(b) Interpret this equation in the
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Problem 71.232 Chapter 3 Conservati
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77 A car accelerates from rest. At
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Problem 81.81 Complete example 71 o
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ExercisesExercise 3A: Force and Mot
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Exercise 3C: Worksheet on Resonance
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Exercise 3D: Vectors and MotionEach
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244 Chapter 3 Conservation of Momen
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An overhead view of apiece of putty
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inward toward the hinge will have n
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special case, we can choose to visu
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j / Two asteroids collide.k / Every
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Note that although the factors of 2
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Relationship between force and torq
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is straight down, which is perpendi
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⊲ All three objects in the figure
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aa / Example 10.to either side of e
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momentum tells us that L = mrv sin
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In the absence of any torque, a rig
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Radial acceleration at the surface
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The parallel axis theorem example 1
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differential. The result isarea ===
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of inertia as if the object was smo
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h / Moments of inertia of somegeome
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4.3 Angular Momentum In Three Dimen
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14 deg, and it points along an axis
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manner like this, then the definiti
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k / Example 27.torque to the left w
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We can also generalize the plane-ro
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Problem 1.Problem 6.Problem 8.Probl
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14 (a) The bar of mass m is attache
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Problem 22.22 The sun turns on its
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35 The nucleus 168 Er (erbium-168)
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ExercisesExercise 4A: TorqueEquipme
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pesky set of constraints on heat en
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mit more air into the cavity behind
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Pressure of lava underneath a volca
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h / A simplified version of anideal
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for us to construct a simple connec
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For the first time we have an inter
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a / 1. The temperature differencebe
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Carnot engines operating between a
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from A to B, he lets it by, but whe
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B When we run the Carnot engine in
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f / A phase space for a singleatom
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time, the energy sharing is very un
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will the the one that maximizes the
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If the gas is monoatomic, then we k
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5.4.4 The arrow of time, or “this
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5.4.6 Summary of the laws of thermo
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may be in the form of microscopic d
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significant amount of heat to flow
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while the smaller area under the bo
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7 (a) Determine the ratio between t
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338 Chapter 5 Thermodynamics
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end of this book, we’ll even see
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c / As the wave pattern passes the
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the wave move ahead faster and get
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k / Hitting a key on a pianocauses
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Our final result for the speed of t
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care, because the delay is the same
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An easy way to visualize this is in
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can be constructed as a superpositi
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⊲ Looking up the speed of light i
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scientists, to speak of the Big Ban
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6.2 Bounded WavesSpeech is what sep
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d / An uninverted reflection. There
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our intuitive expectation of strong
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valid solutions. In the following s
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j / In the mirror image, theareas o
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m / A pulse bounces backand forth.i
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q / Graphs of loudness versusfreque
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s / Standing waves on a rope. (PSSC
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“cavity” and “neck” parts o
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Problem 5.Problem 8.5 The figure sh
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Problem 16.16 A Fabry-Perot interfe
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c / Newton’s laws do not distingu
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f / The correspondence principlereq
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d / A Galilean version of therelati
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g / Three types of transformations
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system, velocities are always unitl
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p / Apparatus used for the testof r
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sumption, the assumption that it ma
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at rest relative to the water. But
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7.2.4 No action at a distanceThe Ne
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so that Alice can complete her moti
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time into different regions accordi
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position relative to the sun at exa
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7.2.7 ⋆ Four-vectors and the inne
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would depend on the relative veloci
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7.3 DynamicsSo far we have said not
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In this frame, as expected, the sma
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But this whole argument was based o
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meters per second, so converting to
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Expressing γ as ( 1 − v 2 /c 2)
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7.3.4 ⋆ ProofsThis optional secti
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these lines. For example, a car sit
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An Einstein’s ring. Thedistant ob
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two-dimensional universe as if it w
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h / 1. A ray of light is emittedupw
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object that that isn’t influenced
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it impossible for any observer to b
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a variant on the Penrose singularit
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in it. Instead, it is currently spe
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2 Astronauts in three different spa
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(d) Simplify your answer to part c
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Problem 25b. Redrawn fromVan Baak,
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ExercisesExercise 7A: The Michelson
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Exercise 7B: Sports in Slowlightlan
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448 Chapter 7 Relativity
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Exercise 7D: Misconceptions about R
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452 Chapter 7 Relativity
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sun, moon, stars, and planets were
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Two types of chargeWe can easily co
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the other acquires an equal amount
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to get the beam up to speed in the
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telling us that we know about matte
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the muddle. The row-and-column sche
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the force of air friction canceled
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ectly evaluate the implications of
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that they were indeed electrically
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C Thomson found that the m/q of an
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the object with a net positive char
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thickness of material the radioacti
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It was already known that although
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particle. It turned out that it was
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For example they could easily strip
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cording to Mosely, the atomic numbe
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that fly off to see what was inside
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solution was found by measuring the
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o / A nuclear power plant at Catten
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neutrons. In a nuclear fission bomb
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We can now list all four of the kno
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1. Our sun’s source of energy is
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a / The known nuclei, represented o
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killed, because the DNA becomes una
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e / Wild Przewalski’s horsesprosp
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Problem 1. Top: A realisticpicture
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12 The subatomic particles called m
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ExercisesExercise 8A: Nuclear decay
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saxophone, every technological tool
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Example 1Ions moving across a cell
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ut the original meaning was to trav
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Force depends only on position. Sin
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Here are a few questions and answer
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flow through it.For many substances
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superconductivity in metals that wo
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j / Example 9. In 1 and 2,charges t
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look like the usual resistor. The f
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9.1.5 Current-conducting properties
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attery acid becomes depleted of hyd
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9.2 Parallel and Series CircuitsIn
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to each resistance, resulting inI t
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where “...” means that the sum
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the two resistors in figure h/3.We
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Choice of high voltage for power li
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A complicated circuit example 20⊲
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Problem 2.ProblemsThe symbols √ ,
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Problem 16.only count that as one u
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knob turned all the way clockwise,
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A printed circuit board, likethe ki
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ExercisesExercise 9A: Voltage and C
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Exercise 9C: Reasoning About Circui
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556 Chapter 9 Circuits
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a / A bar magnet’s atoms are(part
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defined. The ship’s captain can m
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Reduction in gravity on Io due to J
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j / Example 3.self-check AFind an e
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a dipole moment — they are define
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10.2.1 One dimensionVoltage is elec
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The interpretation is that if you b
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Figure c shows some examples of way
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For large values of d, this express
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where Q is the total charge of the
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g / Example 12: variation of the fi
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corners to the disk and transform i
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10.4 Energy In Fieldsa / Two opposi
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self-check DWe can think of the qua
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of the inward field contributed by
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space, 2 while charge doesn’t, we
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a / The symbol for a capacitor.b /
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ounding each capacitor will be half
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in time:x ↔ qv ↔ Iself-check GH
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due to its own momentum. It perform
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or|V | =∣ LdIdt ∣ ,which in man
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the inductor resists such a sudden
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Example 26.Death by solenoid; spark
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ordering.( 1 √2+√ i ) 2 = √ 1
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x / The complex number e iφlies on
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Figure aa shows a useful way to vis
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Inductors tend to be big, heavy, ex
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The reason for using the trig ident
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a purely inductive or capacitive lo
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Resonance with damping example 33
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orE outward, on side 1 A + E outwar
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|E| = kq totalr 2 ,where r is the r
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y considering its point charges ind
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Discussion Questionsg / Discussion
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with charge, change the Coulomb con
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The symmetry between the two sides
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where dv is the volume of the cube.
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The three terms in the divergence a
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Problem 19.Problem 20.proton, for e
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the lightning strike.(b) Based on y
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units.(b) Verify that RC has units
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lating freely (without any driving
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ExercisesExercise 10A: Field Vector
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5. Now hook up the two solenoids in
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A large current is createdby shorti
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time I used it implicitly was in fi
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f / A standard dipole madefrom a sq
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and substituting q = λh and v = m/
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o / Magnetic forces cause abeam of
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electric field, a magnetic one, can
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u / In this scene from SwanLake, th
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so the total field in the z directi
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For the y component, we havee / A s
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We can pin down the result even mor
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i / The field of a dipole.where r i
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circulates around the y axis, so at
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to be, not where it is now. Coulomb
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We have found one specific example
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to a flagpole, we can cancel out a
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11.4 Ampère’s Law In Differentia
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y evaluating the field at the midpo
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i.e.,F = axˆx + byˆx + cˆx + dx
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k / A summary of the derivative, gr
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c / Detail from Ascending andDescen
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the magnet. Are these atomic curren
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field in her region of space has be
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A changing magnetic flux makes a cu
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nearly zero. By Faraday’s law, th
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c / An Ampèrian surface superimpos
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and Maxwell’s equations becomeΦ
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k / Red and blue light travelat the
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second, the zero-point is located a
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is the magnitude of the momentum ve
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Discussion question A.Discussion qu
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only penetrates to a very small dep
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elationship D = ɛE would actually
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esulting in cancellation.The opposi
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a low permeability, while the other
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n / A fluxgate compass.is externall
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6 Two parallel wires of length L ca
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an instant at the upper right, but
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Problem 25.20 Four long wires are a
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Problem 35.Problem 37.32 Verify Amp
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Problem 42.beam of light usually co
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(c) Discuss the relationship betwee
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(f) Use conservation of energy to r
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5. Now position yourself with your
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12.1.1 The nature of lightThe cause
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An image of Jupiter andits moon Io
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d / Two self-portraits of theauthor
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ultimate truth about light, but the
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• There is a tendency to conceptu
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self-check AEach of these diagrams
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m / Discussion question B.Discussio
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12.2 Images by ReflectionInfants ar
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Discussion QuestionA The figure sho
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down magnification is AB/DE. A repe
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i / A Newtonian telescopebeing used
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B Locate the images formed by two p
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12.3 Images, QuantitativelyIt sound
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⊲ The object and image angles are
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12.3.2 Other cases with curved mirr
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signs also have to be memorized for
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h / A diverging mirror in the shape
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j / Spherical mirrors are thecheape
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general type of eye that we share w
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shown on this graph and then attemp
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the mechanical model would predict
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that your calculator will flash an
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D Classify the examples shown in fi
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12.4.6 ⋆ Microscopic description
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12.5 Wave OpticsElectron microscope
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of a crystal? Sound waves are used
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j / Thomas Youngk / Double-slit dif
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object that diffracts it, so the tr
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Although the equation λ/d = sin θ
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things we’ve learned about diffra
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apidly changing distances; on reuni
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6 The figure on the next page shows
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14 Here’s a game my kids like to
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27 Suppose a converging lens is con
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same depth, but not quite. [Check:
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Problem 42.42 Panel 1 of the figure
Page 806 and 807:
46 The figure below shows two diffr
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53 The beam of a laser passes throu
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Problem 59.the ancient problem of i
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3. Now imagine the following new si
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Exercise 12B: Object and Image Dist
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Exercise 12D: Double-Source Interfe
Page 818 and 819:
Exercise 12E: Single-slit diffracti
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Exercise 12F: Diffraction of LightE
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energy, instead of being spread out
Page 824 and 825:
correlated. If they have been playi
Page 826 and 827:
small.The statement that the rule f
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But the y axis can no longer be a u
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for a long time once it gets there,
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j / Calibration of the 14 C dating
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given by(probability of a ≤ x ≤
Page 836 and 837:
k / In recent decades, a huge hole
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A wave is partially absorbed.c / A
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f / The hamster in her hamsterball
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How would you extract h from the gr
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F Does E = hf imply that a photon c
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of approaching this issue.)j / Bull
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We assume v is small enough so that
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the probability distribution will b
Page 852 and 853:
trons that we have already used for
Page 854 and 855:
equations of general validity are t
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wave carries high probability and w
Page 858 and 859:
An infinite sine wave can only tell
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momentum implies a definite kinetic
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of snapshots would amount to a desc
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close are the electrons to the limi
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dimensional particle in a box, and
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Applying this to conservation of en
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the probability of making it throug
Page 872 and 873:
Three dimensionsFor simplicity, we
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1. Oscillations can go backand fort
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C The figure shows a skateboarder t
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a / Eight wavelengths fit aroundthi
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As shown by these examples, the unc
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e / The three states of the hydroge
Page 884 and 885:
f / The energy levels of a particle
Page 886 and 887:
∂r/∂x = x/r comes in handy. Com
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50% of its time in each atom. It’
Page 890 and 891:
tus to the z axis) and more memorab
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ut why does that have anything to d
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the data are only inaccurate due to
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14 The photoelectric effect can occ
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Problem 25.(b) Sketch a graph showi
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conservation of energy and momentum
Page 902 and 903:
Problem 43.43 On pp. 884-885 of sub
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ExercisesExercise 13A: Quantum Vers
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⊲ First we convert the equation i
Page 908 and 909:
Programming With PythonThe purpose
Page 910 and 911:
Appendix 2: MiscellanyUnphysical
Page 912 and 913:
18 bestt = t19 c1 = bestc120 c2 = b
Page 914 and 915:
p i + ∑ iThe spin theoremTheorem:
Page 916 and 917:
Appendix 3: Photo CreditsExcept as
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Appendix 4: Hints and SolutionsHint
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Hints for Chapter 6Page 377, proble
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Answers to Self-Checks for Chapter
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Page 301: (1) Not valid. The equati
Page 926 and 927:
Page 584:N −1 m −2 C 2 V 2 m
Page 928 and 929:
the dashed ray.Page 748: You should
Page 930 and 931:
direction it was initially going (i
Page 932 and 933:
Page 52, problem 38: The cone of mi
Page 934 and 935:
Page 224, problem 37: (a) Spring co
Page 936 and 937:
object, we have static friction, wh
Page 938 and 939:
Page 549, problem 29:(a) Conservati
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Page 798, problem 19: (a) The objec
Page 942 and 943:
.0.8 Notation and unitsquantity uni
Page 944 and 945:
surfaces. For comparison, a typical
Page 946 and 947:
elations:a = ∆v∆tx = 1 2 at2 +
Page 948 and 949:
we are moving along with the projec
Page 950 and 951:
the number of oscillations required
Page 952 and 953:
In general, the cross product of ve
Page 954 and 955:
Sound waves consist of increases an
Page 956 and 957:
signs for charge is that with this
Page 958 and 959:
know that there is a delay in time
Page 960 and 961:
is related byΦ = 4πkq into the ch
Page 962 and 963:
to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
Page 966 and 967:
oth position and momentum, the Heis
Page 968 and 969:
Schrödinger’s, 864cathode rays,
Page 970 and 971:
unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
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Einstein’s early theory, 838energ
Page 976 and 977:
Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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