WAVE-PARTICAL DUALITY

Teacher's Guide

Wave-Particle Duality Teacher's Guide The Series ContentsThis Teacher's Guide is designed for use with theWave-Particle Duality series of programs produced byTVOntario and available on videotape to educationali nstitutions and nonprofit organizations. The programsare broadcast by TVOntario, the television service ofThe Ontario Educational Communications Authority.For broadcast dates, consult the appropriate1VOntario schedule. Ordering information for video-tapes and this publication appears on page 20.

Canadian Cataloguing in Publication Data

Konrad, William, 1942-Wave-particle duality teacher's guide

To be used with the television program, Wave-particle duality.

Bibliography: p.

I SBN 0-88944-048-4

1. Wave-particle duality (Television program)2. Wave-particle duality. 1. TV Ontario. It. Title.

QC403.K61984 535'.13 84-093011-9

© Copyright 1984 by The Ontario EducationalCommunications Authority.All rights reserved.

Printed in Canada 1212/84

Producer/ Director: David ChamberlainWriter Alan RitchieAnimation: Norlhey Productions Ltd./

Groupe Imagination Inc. ,Narrator: James MoriartyConsultant: William Konrad

The Guide

Project Leader: David ChamberlainWriter. William KonradEditor Elizabeth MacLeanDesigner. Tom PilsworthConsultant: George Laundry

Note to Teachers

This series consists of six ten-minute programs thattrace the development of the wave-particle model forelectromagnetic radiation and matter over a span ofabout three centuries. The series shows very clearlyhow scientists have been forced to revise their modelfor light as new evidence becomes available. It alsoshows how occasionally ideas derived empirically givedirection to further experimentation in the laboratoryand result in new discoveries.

This guide contains a detailed description of eachprogram. It also includes additional backgroundinformation, which the teacher may wish to use duringclass discussion to improve students' insight into therole played by various discoveries in the model-building process.

I n addition to these materials, there are questionsand suggested activities that the teacher may finduseful in incorporating a particular program into alesson sequence.

Program 1 The Particle Model............. 1Program 2 The Wave Model ............... 4Program 3 The Electromagnetic Model ...... 7Program 4 The Quantum Idea............. 11Program s Photons .................... 15Program 6 Matter Waves ................ 17For Further Reading ...................... 20

Ordering Information ..................... 20

PROGRAM 1 /The Particle ModelObjectivesAfter viewing the program students should beable to:

1. Describe one model for light suggested by theancient Greeks.

2. Explain why it is difficult to demonstrate thatlight takes time to travel from one point toanother.

3. Explain how Roemer's observations showedthat light does take time to travel from onepoint to another.

4. Recognize that the particle model isassociated with Isaac Newton.

5. Explain why Newton assumed that particles oflight are very small.

6. Explain why Newton assumed that particles oflight travel very fast. .

7. Show how the particle model of light can ac-count for reflection, refraction, and dispersion.

8. Explain why Newton predicted that lightparticles would speed up if they bent towardthe normal as they entered a new medium.

Program Description

The program starts with these fundamentalquestions: What is light? How does it differ fromdarkness? It then proceeds to a brief illustrationof one view of light proposed by the ancientGreeks - namely, the idea that light is a kind ofstreamer emitted from the eye.

The program next shows that it is difficult toillustrate that light actually takes time to travel

from one point to another because whenever alight is turned on, it seems to appear everywhereat once. It wasn't until. Olaus Roemer observedthe moons of Jupiter late in the seventeenthcentury that it was seen that light took about 16minutes to travel across earth's orbit.

The rest of the program deals with Newton'sparticle model, developing the two assumptionsthat are basic to this model. The first is that theintersection of two streams of particles willresult in collisions between particles that willcause them to deviate from their original path.Two intersecting light beams do not show thisbehavior. This variance can be explained in termsof particles, only if the particles are assumed tobe incredibly small.

The second assumption is that particles oflight should be attracted by the earth'sgravitational field and should therefore move in acurved path. The program shows that the faster aparticle moves, the less curvature there is in itstrajectory. If light is assumed to be moving veryfast, the fact that its path is a straight line can beaccounted for.

The program then proceeds to examineseveral behaviors of light and explains them interms of particles. First it shows that when aparticle (like a bullet) strikes a reflecting surface,the angle of incidence is equal to the angle ofreflection. Light is shown to behave in a similarmanner.

Next it shows that when an object isimmersed in water, its position appears to beshifted, and considers the behavior of anindividual particle of light going from air to water.

The uneven pull on the particle of light when itis at the air-water interface can account for theabrupt bending as it enters the water. Thenarrator points out that in Newton's time it wasnot possible to check out his theory byexperiment.

Finally, the program shows how the dispersionof light by a triangular prism can be explained bythe assumption that particles of light causingthe different colors are different sizes.

The program concludes with the explanationthat, in spite of other theories, Newton's nameand reputation were enough to "sell" his versionof the nature of light. But we see the "waveworm" attacking the "particle apple," suggestingthat there is more to come.

Additional Background

The very first scientists to suggest that lightconsisted of a stream of particles were theancient Greeks. Pythagoras (about 500 B.C.) andDemocritus (about 450 B.C.) felt that vision wascaused by particles being projected from theobject into the pupil of'the eye. Empedocles (490B.C.) and Euclid (300 B.C.) felt that the eye sendsout ocular beams that cause sight as soon asthey meet something else that is emanated byan object. Aristotle (350 B.C.) rejected both thesetheories of light, and proposed that vision wasthe result of some kind of action occurring in atransparent medium between the eye and theobject.

Isaac Newton is identified as one of the mainproponents of the particle theory. Newton, it

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appears, first became interested in light when heset out to construct an astronomical telescope.One of the problems he ran into was a coloredborder (now called "chromatic aberration") thatsurrounded the image. This problem led toNewton's extensive study of light and color. Theresults were published in 1672, in his firstscientific paper, Philosophical Transactions.Criticism from some of his contemporaries ledto more careful research on the nature andbehavior of light. In 1704, Newton finallypublished his celebrated treatise, Opticks, i nwhich he compiled nearly all of his work on light.Reading through this collection, one becomesaware of Newton's systematic study of light'sbehavior and his gradual tendency to view lightas consisting of particles, or "corpuscles."

It is interesting to note that Newton alsocontributed a great deal to the theory of soundand water waves. His main objection to thetheory that light might be a wave was that wavetheory could not explain why light travels in astraight line in any medium. Newton felt that iflight were a wave it should show considerablebending.

This program does not deal exhaustively withall the predictions implicit in the particle model.Teachers may wish to include the followingproperties of light as they consider the suitabilityof the particle model.1. Propagation through a vacuum: The particle

theory can readily explain how light from thesun and stars reaches us through the vacuumof space.

2. Absorption and heating: Dark surfaces, whichabsorb particles, heat up more rapidly thanlight surfaces, which reflect particles.

3. Intensity of illumination: If a point source oflight is emitting particles in all directions, itfollows that these particles will spread out

more and more as they get farther away fromthe source. It can be shown that I a 1 , where

d2I is the illumination and d is the distance fromthe source.

4. Light Pressure: A stream of particles strikingan object should exert pressure on that object.This pressure, though small, can be shown toexist.

5. Partial reflection and transmission: It isdifficult to explain why some particles of lightreflect from an interface between two mediawhile others enter the new medium andrefract. Newton tried to explain this by statingthat the particle experienced "fits of easyreflection" and "fits of easy refraction," butthe proportion of reflected light increases asthe angle of incidence increases.

Before ViewingI. Before viewing the program, it is essential to

discuss the role of the model in science.Students will find. the criteria listed belowhelpful in assessing the various models theywill encounter. To enable them to understandthese criteria more easily, you can use ascientific model with which they are familiar toillustrate each criterion listed. In the followingmaterial, the heliocentric model of the solarsystem is used. It is a model with which moststudents are familiar and yet students willrealize that it isn't obvious to an observer whohas not heard of it before.

To approach the subject of modelling, theteacher could supplement a discussion withtwo additional TVOntario videotapes. "Modelsin the Mind" (BPN 112610) in the Dimensions inScience series and "Modelling" (BPN 7)in search for Solutions show how models are

used to test hypotheses, predict effects, andsuggest precautions.

Characteristics of a Useful ScientificModel

1. A theory or model helps us interpret or explainthe unknown in terms of the known.

We can explain the motion of objects in theheavens by visualizing spheres moving in aspecific manner.

2. A theory or model correlates many separatefacts into a more easily grasped structure ofthought.

If we consider the earth, rotating on its tiltedaxis and moving around the sun along with theother planets, we can explain a large numberof observations. We can explain day and night,as well as the seasons. We know why the starsappear to move along an arc in the eveningsky, and we can explain why the motion of theplanets appears different from that of thestars.

3. A theory or model often makes predictionsabout phenomena that have not yet beenobserved.

I n the mid-nineteenth century, astronomersobserved irregularities in the orbit of Uranus. Iftheir model of the solar system was correct,then these irregularities could be explained bythe assumption that another planet beyondUranus was also orbiting the sun. Whenastronomers looked carefully at the heavensbeyond Uranus, they discovered Neptune.

4. A successful theory or model usually has asmall number of plausible basic assumptions,or hypotheses.

In the solar-system model, one suchassumption is that the force of gravitationalattraction between the various bodies in thesystem can account for the observed motion.

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5. A successful theory is flexible enough toundergo modification where necessary. Themechanics Newton used to explain the solarsystem are today regarded as a special case ofEinstein's all-encompassing, relativisticmechanics.

11. Students sometimes view a scientific modelas the absolute truth. The following poemillustrates the models that each of six blindmen formulated for an elephant, based ontheir own observations. It is followed by amodern version that can be used as apuzzle.

The Blind Men andthe Elephant

It was six men of IndostanTo learning much inclined,

Who went to see the Elephant(Though all of them were blind),

That each by observationMight satisfy his mind.

The First approached the Elephant,And happening to fall

Against his broad and sturdy side,At once began to bawl:

"God bless me! but the ElephantI s very like a wall!"

The Second, feeling of the tusk,Cried, "Ho! what have we here

So very round and smooth and sharp?To me 'tis mighty clear

This wonder of an ElephantI s very like a spear!"

The Third approached the animal,And happening to take

The squirming trunk with his hands,Thus boldly up and snake:

"I see," quote he, "the ElephantI s very like a snake!"

The Fourth reached out an eager hand,And felt about the knee.

"What most this wondrous beast is likeIs mighty plain," quoth he;

"Tis clear enough the ElephantIs very like a tree!"

The Fifth who chanced to touch the ear,Said: "E'en the blindest man

Can tell what this resembles most;Deny the fact who can,

This marvel of an ElephantIs very like a fan!"

The Sixth no sooner had begunAbout the beast to grope.

Than seizing on the swinging tailThat fell within his scope,

"I see," quoth he, "the ElephantI s very like a rope!"

And so these men of IndostanDisputed loud and long,

Each in his own opinionExceeding stiff and strong.

Though each was partly in the rightAnd all were in the wrong!

John Godfrey SaxeAmerican poet, 1816 -1887

A more modern version of the six blind men andthe elephant is suggested by the followingproblem. A printed capital letter of the Englishalphabet is scanned photoelectrically and theresultant signal is converted into digital form andread into a digital computer. Seven subroutinesin the digital computer inspect it. The first statesthat the letter is like a U because it has at leastone pocket to hold rain coming from above; thesecond shows that is is like a K because it hasat least one pocket to hold rain from below; thethird and fourth find that it is like an A because ithas no pockets on tight or left; the fifth shows

that it is like a V because it has two ends; thesixth shows that it is like an S because it has nojunctions; the seventh shows that it is like a Dbecause it has two corners. Combining theseseven models of the letter, determine what it is.`

`From Engineering Concepts Curriculum Project. Man Made World,Part 1, E.E. David, Jr., and J.G. Truxal, editors, McGraw-Hill, New York,1969. Reprinted by permission.

While ViewingHave students consider the following questionswhile they watch the program.1. How does the early Greek view of light differ

from Newton's model?2. What two assumptions did Newton make

about particles of light?3. How is the way light reflects explained in

terms of particles?4. How are the refraction and dispersion of light

explained in terms of particles?5. Why did Newton feel that light particles speed

up when they bend toward the normal uponentering a new medium?

After Viewing1. Have the students assess the particle model

in terms of the criteria for a useful scientificmodel. This discussion may be reopenedperiodically as additional behaviors of light areconsidered from the perspective of the particlemodel of light.

2. Ask a student or students to find out howAlbert Michelson was able to make a veryaccurate measurement of the speed of light in1905, and to report on the results of theinvestigation to the rest of the class.

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PROGRAM 2/The Wave Model

Objectives

After viewing the program, students should beable to:

1. Define the term "wave."2. Recognize that Christian Huygens is credited

with being one of the first scientists tosuggest that the behavior of light can beexplained if it is assumed to be a wave.

3. Show how the assumption that light is awave can account for its behavior as itpasses through a narrow slit.

4. Show how the reflection of light can beexplained in terms of waves.

5. Sketch the pattern that results when planewaves in deep water enter a section ofshallow water at an angle of incidence otherthan 0°.

6. State what happens to the speed of a waterwave as it bends toward the normal andexplain the significance of this behavior interms of the behavior of light when it bendstowards the normal.

7. Recognize that the particle and wave modelsmake contradictory predictions for the speedof light in various media.

8. Suggest why Huygens' wave model wasrejected by most scientists for more than acentury.

9. Explain why Thomas Young's double-slitexperiment improved the standing of thewave model for light.

10. Explain how a barrier with two slits placed infront of a light source produces an inter-

ference pattern of dark and bright lines.11. Explain the significance of Jean Foucault's

determination of the speed of light in wateron the credibility of the wave and particlemodels.

Program Description

Continuing where "The Particle Model" left off,this program develops the "wave model forlight:" The definition that is developed for a wave(namely, that it is a travelling disturbance thattransmits energy from one place to another) iscompatible with both classic and modem viewsof the wave because the term "medium" is notused. The concept that all waves require amedium (prevalent from the seventeentb throughthe nineteenth centuries) is then introduced, andthe suggestion of that era (namely, the existenceof an all-pervasive but invisible "ether" throughwhich light waves propagate) is also made.

The program then introduces the idea thatlight is a wave by examining the behavior of lightwhen it passes through a narrow slit and compar-ing this to the behavior of water waves as theypass through a narrow opening.

The program continues to show how wavescan explain additional properties of light. Thereflection of plane waves from a barrier iscompared to the reflection of tight from a mirror.The bending of waves passing from deep toshallow water is shown to be similar to thebehavior of light as it passes from air into water.At this point the viewer's attention is drawn tothe difference in the predictions made by the

particle and wave models about the speed oflight in water.

The narrator recounts that Huygens' theory,while it convincingly explained many propertiesof light, was neglected for more than a century.Newton's theory prevailed, largely because ofthe weight of his reputation.

The fact that two intersecting light sources donot produce a visible interference pattern wasl ong considered a weakness of the wave modelof light. Thomas Young's classic 1802 experi-ment proving that interference occurred whenlight was shone through two pinholes isdeveloped next in the program.

The animation shows how waves diffractingthrough each of the two slits interfere with eachother. The animated three-dimensional wavepattern between the slits and the screen,showing how the "light waves" interfere witheach other, is a particularly effective demonstra-tion of how the pattern of light and dark bars isproduced.

The program concludes with a discussion ofthe discovery of 1850 by Jean Foucault, that lighttravelled slower in water than in air. This settlesthe controversy about the speed of light raisedearlier in the program.

Additional Background

The discovery of the diffraction of light isactually credited to Francesco Grimaldi, aprofessor of mathematics at the University ofBologna. His description of this phenomenonand of a number of other experiments was

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published in 1665 shortly after his death. Newtonwas aware of Grimaldi's work but felt that whatwas occurring was some kind of refractioneffect.

In 1678 Huygens developed a theorysuggesting that light was a wave that movedthrough the "ether" that pervaded everything.Huygens pictured light as consisting of longitu-dinal waves. Using this theory, he could accountfor diffraction, reflection, refraction, and partialreflection and transmission, as well as explainwhy light rays could pass through each other.Huygens proposed his wave model at about thesame time that Newton proposed his particlemodel. For about a century, however, mostscientists favored Newton's particle model. Thereasons for this appear to be:

1. Huygens did not try to account for the color oflight in terms of waves.

2. Most scientists felt that if light really is a waveit should diffract more. What appeared to be aslight amount of diffraction when light passedthrough a small opening was, they felt,probably just a refraction effect.

3. Waves interfere when they pass through eachother. When two light rays intersect, no inter-ference is visible.

4. Newton had made many outstanding contribu-tions to science in the field of mechanics, andweak spots in his theory were overlooked. Hismere suggestion that light consisted of par-ticles gave the idea considerable credibility.

Thomas Young's work in 1802 illustratinginterference of light did a lot to enhance thecredibility of the wave model. Young was anexpert in many fields of science and, amongother experiments, he repeated all of Newton'swork with light. In spite of his impressive work,his ideas were received with hostility by many

British scientists who were extremely reluctantto abandon Newton's theory In 1818 AugustinFresnel, a French engineer, correctly pointed out

' that diffraction becomes more apparent as theratio of the wavelength to slit width increases.Independently he also discovered the opticalphenomena that Young had been studying.Fresnel was able to coordinate all of this in amathematical theory of wave motion.

Both Young and Fresnel discovered that lightcan be polarized. They realized that thisi ndicated that light was not a longitudinal wave,as Huygens had suggested, but a transversewave. This generated a new problem: liquids andgases will transmit only longitudinal waves.(Although waves on the surface of the water areapproximately transverse, waves propagatedthrough water are longitudinal.) Only solids withthe property of elasticity can propagate atransverse wave. In addition, the speed of atransverse wave is given by the relationship

Before ViewingOnly the key developments in the wave modelare examined in this program. The program, how-ever, gives a historical perspective that may notbe given in class. It may be preferable, then, toshow this program after students have studiedinterference of light in class. The program will

then explain how evidence for the wave nature oflight gradually eroded the particle model of light.

While ViewingProvide students with the following list beforethey view the program, so that they can focustheir attention on the program content essentialto completing the activities and answering thequestions.

1. What is a wave?2. Which scientist is associated with the wave

model for light?3. Draw a sketch that shows how the diffraction

of light may be explained in terms of waves.4. A straight wave approaches a barrier so that

the angle between the barrier and the waves is40°. Draw a diagram showing the wave ap-proaching the barrier and a second diagramshowing what happens after the wave strikesthe barrier.

5. Straight waves generated in the deep sectionof a ripple tank approach the shallow sectionso that the angle between the waves and thedeep-shallow interface is 50°. Draw a diagramshowing the waves in both deep and shallowsections of the tank. On your diagram label thefollowing: incident waves, refracted waves,direction of motion of incident waves,direction of motion of refracted waves, angleof incidence, angle of refraction. Indicate alsowhich waves are travelling the fastest.

6. Why is it that Newton's particle model wasfavored over Huygens' wave model eventhough both models could explain a number ofaspects of light's behavior?

7. Explain why Young's double-slit experimentimproved the status of the wave model forlight.

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the elasticity of the medium, and d is the densiof the medium. For a wave that travelled as fasas light, the medium would have to be like asolid with a very high elasticity and a very lowdensity. At the same time, planets would have 1

be able to travel through the ether unimpeded.medium with such contradictory properties wahard to visualize.

where v is the speed of the wave, e is

8. What was the significance of Foucault'sdetermination of the speed of light in water onthe credibility of the wave and particlemodels?

After Viewing1. Construct the following chart and fill it in

during a class discussion. Complete thecolumns.

Use of this chart will help students to assessthe status of each of the two models. Thechart should be kept, and extended andrevised after the class has viewed programs 3,4, and 5.

2. Have the students evaluate the wave modelusing the criteria listed under "Characteristicsof a Useful Scientific Model" in the section forprogram 1, "The Particle Model."

3. Newton, justifiably celebrated as a brilliantscientist, was also warden of the mint,president of the Royal Society, and a memberof Parliament. Have a student research andreport on some of the lesser-known aspects ofthis character's fascinating career.

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Phenomenon Light Particle Wave

Reflection

Refraction

Speed of light in various media

Partial reflection and refraction

Propagation through a vacuum

Diffraction

Interference

Intensity of light

Light pressure

Absorption and heating

PROGRAM 3/The Electromagnetic ModelObjectives

After viewing the program, students should beable to:

1. Describe the shape of the magnetic fieldaround (a) a wire through which an electriccurrent is flowing, and (b) a charged particlemoving in a straight line.

2. State the condition under which a magneticfield will induce a flow of current through aconductor.

3. Describe the relationship between the size ofthe current and the strength of the magneticfield created by the flow of charge.

4. Recognize that a changing magnetic fieldi nduces an electric field and that a changingelectric field induces a magnetic field.

5. Recognize that Maxwell's model wasdeveloped from theory and. not by experi-mentation.

6. Sketch the electric field produced by apositive charge oscillating back and forth.

7. Sketch the magnetic field produced by apositive charge oscillating back and forth.

8. Show, by means of a diagram, therelationship between the electric andmagnetic fields produced by an oscillatingpositive charge.

9. Recognize that an oscillating charge emitselectromagnetic radiation in all directions.

10. Describe the significance of the predictionmade by Maxwell that electromagnetic radiation does not require a medium.

11. Recognize that Maxwell predicted that

whenever an electric charge is accelerated,electromagnetic waves are produced.

12. Describe the experiment conducted byHeinrich Hertz.

13. List in order, from long wavelength to shortwavelength, the types of electromagneticwaves produced by accelerated charges.

Program DescriptionThis program is designed to give the student aqualitative understanding of the prediction madeby James Maxwell (1831-79) that acceleratedcharges produce electromagnetic waves. This isdone without getting into the rigorous mathe-matics involved in Maxwell's work.

The development proceeds as follows. Thefact that electric charge flowing through a wireproduces a magnetic field is reviewed. Then, thefact that a changing magnetic field can induceelectric charge to flow through a conductor isalso shown. Next, it is suggested that a singlecharged particle moving through space wouldproduce a magnetic field that is strongest in thevicinity of the charge. The effect of a change invelocity on the strength of the field is alsoillustrated.

These concepts are then combined to illus-trate Maxwell's prediction that a charged particleoscillating back and forth in simple harmonicmotion creates a changing electric field which,in turn, produces a changing magnetic field,which produces a changing electric field, and soon. The phase relationship between the twofields and the positive particle is also shown.

Further, Maxwell's prediction that this electro-magnetic disturbance doesn't need a medium isalso stressed and the speed (3 x 10 8 m/s) hepredicted for these waves is also indicated.

The narrator then raises the logical question:I s light a form of electromagnetic radiation? Theefforts of Heinrich Hertz to detect electromag-netic waves are then described.

The program ends with an examination of thevarious radiations that make up the electromag-netic spectrum.

Additional Background

Maxwell was a brilliant theoretical physicist who_built on the work of Michael Faraday (1791-1867).Faraday had discovered that an electric chargeand a magnetic pole can exert a force on eachother if they are in motion relative to each other.He is also credited with introducing the conceptof a field and describing the field aroundelectrically charged objects and around amagnet.

It is important to note a major differencebetween Faraday and Maxwell. Faraday was abrilliant researcher and experimenter. Maxwell,on the other hand, derived his equations fromtheoretical considerations and the work ofFaraday.

Maxwell's equations involve mathematicsbeyond that of highschool level so they will notbe stated here. It is, however, important to listthe predictions that these theories made.

1. Accelerated charges produce electromagneticwaves.

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Maxwell's work raised several questions:

1. Do electromagnetic waves really exist?2. If the answer to that question is yes, is light an

electromagnetic wave?3. Do invisible electromagnetic waves exist?

Maxwell's theory failed to attract muchattention for about two decades, probablybecause it seemed difficult to test in thel aboratory and it was radically new.

I n 1887-88 Heinrich Hertz deliberately set outto determine whether Maxwell's main hypothesis(namely, that accelerated charges produceelectromagnatic waves) was correct.

Hertz was not only able to prove that thishypothesis was correct but was also sosuccessful in confirming all of Maxwell'spredictions that the scientific communitybecame convinced that light itself is anelectromagnetic wave.

c)

Before ViewingUnlike the first two programs of the series,which cover material taught over an extendedperiod of time, this program lends itself for useas a very valuable aid for a single lesson.

Before showing the program, you may wish tohave the students complete these questions,which review concepts taken previously inphysics.

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2. These waves do not require a medium. (Inspite of this prediction, Maxwell, like hiscontemporaries, still thought in terms of theall-pervading ether)

3. These waves travel atalready measured for light).

(the speed

1. Sketch the electric field around each of thefollowing charged objects.

a) b)

2. Sketch the magnetic field around each of the b) c)following:a)

(arrow shows direction of electronflow through wire)

3. Show the direction of the induced current in b) c)each of the following cases:

a)

r

Show the direction of (1) switch S1 is closed.electron flow in both (2) switch S1 is keptcoil 1 and coil 2 when closed.

(3) switch S1 is opened.

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1 0

While Viewing the ProgramProvide students with the following list beforethey view the program so that they can focustheir attention on the program content essentialto completing the activites and answering thequestions. Perhaps you may wish to show theprogram a second time, or repeat varioussegments to enable students to answer all thequestions.

1. What change occurs in the magnetic fieldaround a wire carrying an electric current ifthe current increases? Illustrate your answerby means of a sketch.

2. How can a magnetic field be used to causeelectric charge to flow through a conductor?

3. Sketch the magnetic field found around acharged particle moving with constantvelocity. What happens to this field as theparticle speeds up?

4. By means of a diagram, show the electricfield produced by a positively chargedparticle that is oscillating back and forthalong a straight line.

5. In the diagram drawn for 4, show themagnetic field produced by the oscillatingcharged particle.

6. Does the electromagnetic wave drawn forquestions 4 and 5 require a medium?

7. What features of Maxwell's electromagneticwave theory suggested that light might be anelectromagnetic wave? .

8. Draw a diagram of the apparatus Hertz usedto test for the existence of electromagneticwaves.

9. What led Hertz to realize that he had in factdetected electromagnetic waves?

10. What type of electromagnetic waves didHertz produce and detect?

11. List in order, from low frequency (longwavelength) to high frequency (short wave-l ength), the types of electromagnetic radia-tion found in the electromagnetic spectrum.

12. Why did the electromagnetic wave modelseem to be the final explanation for thebehavior of light?

After ViewingAfter the program has been viewed and thequestions relating to it have been discussed, thefollowing assignment could be given.

By referring to a suitable reference book,construct a chart showing the various types ofelectromagnetic radiation listed in order ofincreasing frequency. For each type of radiation,state (a) the frequency range, (b) the wavelengthrange, (c) the way the radiation is produced; and(d) describe how the radiation is used or where itcould be found.

PROGRAM 4/The Quantum IdeaObjectivesAfter viewing the program, students should beable to:

1. List two failures of the electromagnetic wavemodel for light as developed by Maxwell.

2. Describe the assumption made by Planckabout the way in which atoms radiated energy.

3. Explain the meaning of the term "quantum"4. State the relationship between the energy of a

quantum and its frequency in the form of (a) astatement of proportion, and (b) an equation.

5. Explain the meaning of the term "photoelec-tric effect."

6. Complete the following table:

7. State Einstein's explanation for photoelectricemission, including situations for which (a) thephoton energy is less than the energy requiredfor emission, (b) the photon energy is equal tothe energy required for emission, (c) thephoton energy is greater than the energyrequired for emission, and (d) the intensity oflight is increased.

Program DescriptionThe program again raises the question "What islight?" and briefly reviews the electromagneticwave model developed in the previous program.It then moves directly to the concept of thequantum.

The student is introduced to the phenomenon,studied by Max Planck, of "black body radiation."(The term is not used in the program but theteacher may wish to introduce it in the follow-updiscussion.) By means of animation, radiation isshown being emitted and absorbed inside aclosed box. The narrator makes the point thatPlanck found a way to mathematically predictthe actual observations of energy distributions.To come up with a physical model correspondingto his mathematical predictions, he had toassume that energy is emitted in discretebundles that he called "quanta" (singular"quantum") instead of being emitted contin-uously, as was thought previously. Theproportional relationship between quantum

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Situation Electromagnetic Wave Model Prediction Experimental Observation _

a) Electromagnetic radiationbeing used to illuminatea metal electrodedoes not causephotoemission.What change should bemade to cause emissionfrom the electrode?

b) A particularfrequency of electro-magnetic radiation iscausing emission. Theintensity of theradiation is thenincreased. What changeis observed?

1 2

energy and frequency is then developed, (i.e.,Eaf or E = hf).

The program next shows how Albert Einsteinused the quantum idea to explain the "photo-electric effect." Two metal plates sealed in anevacuated tube and connected to a powersupply are shown. When the negatively chargedplate is covered with potassium and thenilluminated with blue light, electrons are seenbeing emitted from the negative plate, movingacross the space to the positive electrode, andflowing through the circuit. The programanimation then shows how the predictions madeby the electromagnetic wave theory differ fromactual observation, specifically in the effect ofi ncreasing the intensity and changing the color

Additional Background

or frequency of radiation. Because potassium isthe metal from which electrons are beingemitted, it is possible to use frequencies in thevisible region of the electromagnetic spectrumthroughout this unit since the threshold fre-quency for potassium is blue light. The programthen shows how making the assumption thatEinstein made (namely, that light is absorbed inquanta by the atoms of potassium) enables us toexplain all the observations made when a metalis illuminated with light of various frequencies.

The program ends with the introduction of theterm "photon" and the pointing out that aphoton has particle as well as wave character-istics.

The device shown at the left approaches thebehavior of a perfect radiator or absorber ofenergy. Electromagnetic radiation entering thecavity through the opening will be absorbedinside with very little escaping by internalreflections. Conversely, if the device is heated inan oven, the radiation escaping from the holewill have the properties of a perfect radiatorsometimes referred to as a "black body" or"black surface."

Electromagnetic theory had been successfuli n correctly predicting that the total energy (J)emitted per unit time per unit area wasproportional to the absolute temperature (7)raised to the fourth power Ja T4 (Stefan-Boltzmann Law). The theory had also correctlypredicted that the wavelength of the mostprominent radiation given off could be given by

distributions at a specific temperature could notbe derived solely from theoretical considera-tions, in spite of efforts by outstanding theorists.The curve for a specific temperature could, ofcourse, be determined by observation andlooked like this:

Planck was successful in empirically derivingan equation that could successfully predict thecorrect energy distribution curve at anywavelength. This equation is

where C, and C2 are constants, and e is the baseof the natural logarithms.

After correctly developing his empiricalequation, Planck wondered about the mecha-nism at the atomic level that would-support it oreven explain it. At first, he felt that tinysubmicroscopic charged particles in constantoscillation radiated electromagnetic waveswhich had the same frequency as the frequencyof oscillation. As a particle oscillator absorbedenergy, it was thought that its amplitude ofvibration increased. Similarly, as it emittedenergy, its amplitude would decrease.

(Wiens' Displacement Law) where

is the wavelength of the most prominentradiation. The shape of the curve for energy

Planck finally came to the realization that tocome up with a mechanism that agreed with hisempirical equation, he had to depart drasticallyfrom this view. He found he had to make thefollowing assumptions: .

1. Each submicroscopic oscillator can only havecertain energies. The energies possible aregiven by the formula E = nhf where n can be0,1,2,3..., h is Planck's Constant, and f isfrequency. This means that any change inenergy is abrupt rather than gradual.

2. The submicroscopic oscillator radiates electro-magnetic energy only when it changes fromone allowable energy level to another. Thismeans that the energy is given off in bundles,or quanta, of energy hf.

Planck announced his discovery on December14,1900, and this date is now considered to markthe birth of quantum physics. It is interesting tonote that Planck was deeply disturbed by theassumptions he had to make,' but found thatthey were the only way he could explain thesuccess of his empirical equation.

In 1905 Albert Einstein applied Planck'shypothesis to the photoelectric effect. Accordingto Einstein, a quantum of energy hf given off byan atom did not spread out to become a wavebut instead remained intact as a quantum ofelectromagnetic radiation. It would then con-tinue in this form until it interacted as a quantumor photon with individual particles of matter.Einstein realized that some photons lackedsufficient energy to cause emission and that thefollowing relationship applied when a photonsuccessfully emitted an electron:

Ek=hf-B

Ek is the maximum kinetic energy of the emitted

electron, hf is photon energy, and B is the workfunction (the energy required to release theelectron from the metal).

It is worthy of note that Planck was reluctantto accept Einstein's explanation of thephotoelectric effect. Einstein won the NobelPrize in physics in 1921 for his work on thephotoelectric effect.

'The reasons for Planck's concerns are well explained in Foundationso1 Modern Physics by Gerald Holton and Duane Roller (see "ForFurther Reading" on page 20). Although this book is out of print, it isan excellent text, and well worth the effort to find.

Before ViewingI. Review the status of the wave and particle

models of light. If students completed thechart comparing particles, waves, and light forprogram 2, they should review it at this time.

It. Demonstrate the photoelectric effect asfollows:

1. Place a zinc plate (freshly cleaned withsandpaper or steel wool) on the knob of asensitive metal-leaf electroscope.

2. Charge the electroscope negatively.3. Shine an ultraviolet light source on the

electroscope, and note the behavior of themetal leaf. ,

4. Recharge the electroscope negatively. Thistime, place a clear glass plate between theultraviolet light source and the chargedelectroscope. Note the behavior of theelectroscope.

You can repeat this demonstration with a heliumneon laser and compare results with thoseachieved using ultraviolet light.

Stress to students the importance of makingcareful observations. You can also ask them tohypothesize about the mechanism by which theelectroscope becomes discharged. Rather thanexplain the procedure in detail at the start, viewthe program first.

While ViewingProvide students with the following list ofquestions before they view the program so thatthey can focus their attention on the informationthey need to answer them. You may wish toshow the program a second time to enablestudents to answer all the questions.

1. What phenomenon was Planck studying whenhe made his dramatic discovery?

2. What basic assumption did Planck makeabout the way in which atoms radiatedenergy?

3. What is the relationship between the energy ofa quantum and its frequency? State this

1 3

relationship first as a statement of proportion,and then as an equation.

4. What is meant by the term "photoelectriceffect"?

5. Complete the chart below, referring to thisapparatus.

1 4

6. Explain the experimental observations in thischart in terms of quantum theory.

7. If a quantum has more energy than is requiredto emit an electron, what happens to the extraenergy?

8. A photon or quantum of light is both wave-likeand particle-like. List all of the photonproperties that make it appear wave-like and allthat make it appear particle-like.

After ViewingAsk students to explain the observations madein the "Before Viewing" activity.

1. Why did the metal leaf on the electroscopecollapse when ultraviolet light was shone onthe zinc plate?

2. Why did the electroscope not respond when aglass plate was inserted between the electro-scope and the ultraviolet light source?

3. Which types of electromagnetic radiation otherthan ultraviolet would cause the electroscopeto discharge?

4. When the zinc plate is replaced with a copperplate, the ultraviolet light has no effect on thecharged electroscope. Suggest why this is so.What type or types of electromagnetic radiation could you use to try to discharge theelectroscope when there is a copper plate onthe knob?

Situation Electromagnetic Wave Model Prediction Experimental Observation

Red light does notcause emission ofelectrons. Whatchange will resultin emission?

Dim violet lightcauses emission ofelectrons. Whatwill happen if itis made more .intense?

PROGRAM 5/PhotonsObjectives

After viewing the program students should beable to:

1. State how the momentum of an object maybe calculated.

2. Construct the momentum vector for anobject, given its mass and velocity.

3. Explain what is meant by the term"conservation of momentum."

4. Describe a head-on collision in whichmomentum is conserved.

5. Draw a momentum vector diagram for aglancing collision in which momentum isconserved.

6. Describe the experiment, conducted byArthur Compton, that led him to concludethat photons have momentum.

7. State which specific observations made inthe Compton experiment support thehypothesis that photons have momentum.

8. Describe one other aspect of light's behaviorthat can readily be explained in terms ofphoton momentum.

9. Explain why a comet's tail points away fromthe sun.

10. Describe Taylor's experiment and explain itssignificance in terms of the wave and particlemodels of light.

11. Cite evidence demonstrating that the wavenature of electromagnetic radiation of longwavelength and low frequency is moreprominent than its particle nature.

12. Cite evidence demonstrating that the particle

nature of electromagnetic radiation of shortwavelength and high frequency is moreprominent than its wave nature.

Program Description

This program continues from program 4, inwhich the concept of the quantum was intro-duced. It begins with a brief review of thestruggle between the particle and the wavemodels to account for light's behavior, and areview of the concept of a quantum of electro-magnetic radiation, the photon.

The concept of momentum is introduced, andhead-on and glancing collisions between bodiesof equal mass are considered. A momentumvector for each of the moving masses is shown,and the conservation of momentum in eachcollision is demonstrated by arranging themomentum vectors in the appropriate order.

Arthur Compton's 1923 experiment demon-strating photon momentum is then illustrated.X-rays of known photon energy are fired into acloud chamber. Occasionally, the track of anelectron is produced. When this occurs, it resultsin a photon of lower energy travelling in adirection different from that of the originalphoton. The similarity between this interactionand a two-body glancing collision is thendemonstrated. This again reinforces the particlenature of light. The program briefly shows howlight pressure affects a comet as it movesaround the sun. (There is a second reason, notmentioned in the program, for the direction of

the comet's tail. It is solar wind.)The question, "Can scientists use the photon

particle to explain all behaviors of light?" is thenraised, and leads into an examination of thephenomenon of interference. Sir GeoffreyTaylor's 1909 experiment, in which the intensitywas gradually reduced until on the average onlyone photon at a time was moving through the'slits, is examined. We see that the wave natureof electromagnetic radiation is still required toaccount for its behavior.

The last section of the program shows thatthe wave nature and particle nature of aparticular photon are not equally prominent forall photons, and that the predominant naturedepends on the region of the electromagneticspectrum to which the photon belongs. Radiowaves, for example, have a long wavelengthwhich easily demonstrates interference, but forwhich the photon energy is so low that it isalmost impossible to detect a single radiophoton. Gamma rays, on the other hand, have awavelength so short that it is virtually impossibleto produce a set of slits close enough togetherto demonstrate interference. However, a singlegamma photon is relatively easy to detectbecause it has so much energy.

The program ends, concluding that bothparticle and wave models are required tounderstand the behavior of electromagneticradiation.

1 5

1 6

Additional BackgroundIt is interesting to note one major differencebetween a photon involved in the photoelectriceffect and a photon involved in the "Comptoneffect" A photon that causes the emission of anelectron from a metal is completely absorbed.Any energy in excess of that required to causeemission appears as kinetic energy of theemitted electron. In order to interact with anelectron in a manner described as the Comptoneffect, a photon must be a high-energy photon.I n this case, it loses some of its energy as itinteracts with the electron, but continues toexist after the interaction as a lower-frequencyand lower-energy photon. The momentum of aphoton is given by the equation p = hA.

Before ViewingIt is highly likely that you will wish to showprogram 5 shortly after program 4. If theconcepts established in the minds of thestudents by program 4 are still fairly fresh, noadditional preparation is required.

While ViewingProvide students with the following list ofquestions so that they can focus their attentionon the relevant information during the program.To enable students to answer most of thequestions, you may wish to show the programtwice.

1. Newton's particle model and Huygens' wavemodel were introduced at about the sametime. Newton's particle model was thepreferred model for over a century. Recountthe developments that resulted in a gradual

replacement of the particle model by thewave model by the early nineteenth century.

2. How did the work of Maxwell and Hertzi mprove the wave model?

3. How did the work of Planck and Einstein givenew life to the particle model?

4. Construct a momentum vector for a 2000 kgcar travelling north at 20 m/s.

5. A curling rock travelling at 2 m/s )N) collideshead on with another rock which is at rest.Describe the motion of each of the rocksafter the collision.

6. A curling rock travelling at 2 m/s ]N] collidesin a glancing collision with another rock,which is at rest. If the first rock is movingnortheast at 2 m/s after the collision, what isthe velocity of the other rock after thecollision?

7. With the aid of a diagram, describe theexperiment conducted by Arthur Compton.

8. Which observations made by Comptonsupport the hypothesis that photons havemomentum?

9. Describe Taylor's experiments with the aid ofa diagram.

10. What was the fundamental question Taylorwas trying to answer with his experiment?What was the answer?

11. Explain why wave theory is still required toexplain interference of light.

12. Explain why the wave nature of electromag-netic radiation in the radio frequency range ismore apparent than its particle nature.

13. Explain why the particle nature of electro-magnetic radiation in the gamma frequencyrange is more apparent than its wave nature.

After ViewingExplain to students that photon momentum canbe calculated using the formula p = hA. Workout several examples in which the momentum ofa photon is calculated and assign additionalquestions from their text book.

PROGRAM 6/Matter WavesObjectivesAfter viewing the program students should beable to:

1. Demonstrate how both wave and particletheories are required to give a completeexplanation for the behavior of light and otherforms of electromagnetic radiation.

2. Explain the role played by the wavelength indetermining the behavior of a photon as itapproaches a double slit.

3. State the prediction made by Louis de Broglie.4. Explain why the suggestion that particles

might demonstrate a wave nature appearedridiculous.

5. Calculate the de Broglie wavelength of anobject, given its mass and speed.

6. Explain why objects that we see in oureveryday experience do not demonstratevisible wave characteristics.

7. State under what conditions the wave natureof matter becomes apparent.

8. State two ways in which an electron and aphoton of the same wavelength differ.

Program Description

The program begins with a review showing thatelectromagnetic radiation has both particle andwave characteristics, then focuses on interfer-ence in particular, and develops the idea that thewavelength associated with a photon is useful inpredicting the photon's probable path. Althoughthe exact path can never be predicted, the

wavelength enables one to calculate theprobability that the photon has of striking aparticular spot.

The narrator then turns to Louis de Broglie'sprediction that a particle can behave like a wave.As a specific example, it deals with the characterCasey and his famous strikeout in the poem,"Casey at the Bat." The question is raised:"Would it be possible for the ball and bat to passthrough each other like waves?"

The program then shows that diffractionbecomes significant when the value of thewavelength approaches the value of theobstacle's size. A calculation of the de Brogliewavelength for a moving baseball shows thatdiffraction around a bat is not possible. Theprogram then goes on to show that a very smallobject like an electron would have a long enoughwavelength to display diffraction effects.

Actually, an electron travelling at 3.6 x 106 m/swould have a wavelength equivalent to an x-ray.The diffraction by a salt crystal of first an x-rayand then an electron beam is demonstrated. Toshow that an electron and an x-ray havesignificant differences, even though they mayhave the same wavelength, the speed and restmass for each is calculated. The programconcludes with the reminder that the particleand wave models are namely that - models.

Additional Background

Louis de Broglie's prediction that matter mighthave a wave nature was part of his Ph.D. thesisin 1924. It is interesting to note that he had no

experimental basis for this prediction. At first hisexaminers found the thesis unacceptable, butwhen Albert Einstein was shown the prediction,he felt that it might well be true. Within threeyears, Davisson and Germer of the United Stateswere able to demonstrate electron diffraction.Shortly thereafter, G.P. Thomson of England alsowas able to demonstrate the diffraction ofelectrons.

As shown in the program, the wavelength of aparticle is given by the equation X - hlmv. Thefrequency of the wave is given by t - mczlh.The wave speed, which is the product of thewavelength and the frequency, comes out to&lv, where c is the speed of light and v is thespeed of the particle. This may raise thequestion, "If the matter wave travels faster thana particle, why does it not leave the particlebehind?" The answer is that the waverepresenting any individual particle such as anelectron is not a continuous wave of constantamplitude but a wave group as shown below.

Such a wave group is the resultant wave ofmany continuous waves associated with theparticle, and it travels at the speed of the

1 7

1 8

particle. At all other points the waves interferedestructively, meaning that the probability offinding the particles at those points is 0.

From de Broglie's theoretical suggestions,other physicists in the 1920s, such as Austria'sSchrodinger and Germany's Heisenberg, wereable to develop a complete mathematical theoryof the wave nature of matter.

Finally, it should be noted that particles suchas neutrons and protons have also demonstratedwave characteristics. Interference patterns areproduced not only by passing these particlesthrough crystals, but also by reflecting themfrom crystals. Several of the sources listed under"For Further Reading," which follows this unit,contain a variety of photographs showing theinterference pattern produced by variousparticles, as well as the patterns produced byelectromagnetic radiation of comparable wave-length.

Before Viewing

The pattern of bright spots projected on thescreen, as shown above, will be seen.

2. Rotate the diffraction grating so that the slitsin the grating are horizontal. The pattern willnow rotate so that it is vertical.

3. Now place two gratings in front of the laser.The slits on one should be vertical and on theother they should be horizontal. The patternshown below will be observed.

It is likely that this program will be shown fairlysoon after program 5 ("Photons") has beenviewed. If the concepts established in program 5are clear in the minds of the students, littleadditional preparation is required.

Students may find it easier to understand thei nterference pattern produced by the salt crystalin the program if the following demonstrationusing a helium neon laser is done. (Cautionstudents never to look into the laser.)

1. Direct a laser beam at a diffraction grating sothat the slits in the grating are vertical.

While ViewingProvide the students with the following list ofquestions to be answered while viewing theprogram or in the time period right after theprogram. You may wish to allow the students toview the program a second time so that all thequestions can be answered.

1. Explain the role played by the wavelengthassociated with a photon in determining itsbehavior as it approaches a double slit.

2. What prediction did Louis de Broglie makeabout matter?

3. Explain why de Broglie's prediction seemed

ridiculous.4. Calculate the de Broglie wavelength of a 60g

rock thrown at 20 m/s.5. The rock in question 4 is heading directly for a

telephone pole 30 cm in diameter. Is the rocklikely to behave like a particle or like a waveduring its interaction with the pole? Why?

6. Explain why objects that we see in ourday-to-day experiences do not demonstratevisible wave characteristics.

7. What particles other than electrons could beexpected to demonstrate wave character-istics?

8. State two ways in which an electron and aphoton of the same wavelength differ.

After ViewingThe program showed two ways in which anelectron and a photon of the same wavelengthdiffered. There are other differences. To enablestudents to get a clearer understanding of thedifference between an electron and a photon,have them complete the following question.

How does an electron with a de Broglie wave-length of 8.5 x 10- '° m differ from a photon of thesame wavelength? To answer the question, com-plete the chart below.

19

Electron Photon

Wavelength 8.5 x 10'°m 8.5 x 10-'°m

Speed

Rest Mass

Momentum

Energy

Frequency

20

For Further Reading

The following books and periodicals providesupplementary material on the nature of light.Although several of them are out of print, theycan likely be found in school and school boardli braries.

OrderingInformation

Adler, Mortimer J., ed. Great Books of theWestern World, No. 34, "Newton/ Huygens."Chicago: Encyclopaedia Britannica,1952.

Atkins, Kenneth R. Physics. New York: JohnWiley and Sons, 1972.

Boulind, H.F. Waves or Particles. London:Longman Group Ltd., 1972.

Brown, Thomas B. Foundations of ModernPhysics. New York: John Wiley and Sons,1960.

Chaundry, David. Waves. London: LongmanGroup, 1972.

Giancoli, Douglas C. Physics. Englewood Cliffs,N.J.: Prentice-Hall, 1980.

Haber-Schaim, Uri, et al. PSSC Physics. 5th ed.Lexington, Mass.: D.C. Heath, 1981.

Holton, Gerald, and Duane H.D. Roller. Founda-tions of Modern Physical Science. Reading,Mass.: Addison-Wesley, 1965.

Scientific American. Vol. 219, September 1968.Entire issue is devoted to light.

Scientific American. Lasers and Light, Readingsfrom Scientific American. Introductions byArthur Schawlow. San Francisco: W.H.Freeman, 1969.

Stollberg, Robert, and Faith Fitch Hill. Physics:Fundamentals and Frontiers. Rev ed. Boston:Houghton Mifflin, 1975.

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