SCIENCE 1209ATOMIC AND NUCLEAR PHYSICS

Author: Robert Hughson, M.S.Editor: Alan Christopherson, M.S.Illustrations: Jim Lahowetz

Alpha Omega Graphics

CONTENTS

I. QUANTUM THEORY . . . . . . . . . . . . . . . . . . . . 2ELECTROMAGNETIC RADIATION . . . . . . . . . . . . . . . . . . . . 2MATTER WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8ATOMIC MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11ATOMIC SPECTRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12BOHR MODEL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

II. NUCLEAR THEORY . . . . . . . . . . . . . . . . . . . . 22BUILDING BLOCKS OF THE NUCLEUS . . . . . . . . . . . . . . . 22PROPERTIES OF THE NUCLEUS . . . . . . . . . . . . . . . . . . . . 23

III. NUCLEAR REACTIONS . . . . . . . . . . . . . . . . . 30NUCLEAR FISSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30FUSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32NUCLEAR REACTION APPLICATIONS . . . . . . . . . . . . . . . . 33

GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39FORMULAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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The last page of this LIFEPAC contains formulas and constants that may be used forproblem-solving, both on activities and on tests.

ATOMIC AND NUCLEAR PHYSICSYou are about to begin the study of modern physics, the physics of very small objects. You will learn

more about how atoms and their subparts interact. The laws of physics that you have already learned willbe used, but you will notice that at times some new concepts will be considered.

OBJECTIVES

Read these objectives. The objectives tell you what you will be able to do when you havesuccessfully completed this LIFEPAC®.

When you have finished this LIFEPAC, you should be able to:1. Explain when wave theory is applicable and when quantum theory is applicable.2. Calculate the energy of photoelectrons and X rays.3. Explain de Broglie waves.4. State and apply the uncertainty principle.5. Define emission spectra and absorption spectra.6. Define line spectra and continuous spectra.7. Describe the Bohr model of the hydrogen atom.8. Define nucleon and isotopes.9. Explain mass defect in terms of mass-energy equivalent.

10. Explain how the binding energy curve shows that fission and fusion can release energy.11. Explain the concept of half-life.12. Explain how alpha and beta decay can stabilize a nucleus.13. Describe fission reaction and fusion reaction.14. Explain a chain reaction and nuclear energy.

Survey the LIFEPAC. Ask yourself some questions about this study. Write your questions here.

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SECTION OBJECTIVESReview these objectives. When you have completed this section, you should be able to:

1. Explain when wave theory is applicable and when quantum theory is applicable.2. Calculate the energy of photoelectrons and X rays.3. Explain de Broglie waves.4. State and apply the uncertainty principle.5. Define emission spectra and absorption spectra.6. Define line spectra and continuous spectra.7. Describe the Bohr model of the hydrogen atom.

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For many centuries, the primary concern ofphysics was to describe the behavior of largeobjects. Newtonian mechanics describes thebehavior of matter influenced by gravitationalfields or by electromagnetic interactions.Newtonian physics had been successful; sosuccessful, in fact, that most physicists believedthey were approaching the ultimate description ofnature. They thought that in just a matter of timethey would be able to work out the details of aperfect, ordered world. Many believed that thefuture work of physics would be essentially justmeasuring the last decimal place.

Problems with this neat and supposedlycomplete theoretical description began to ariseabout the end of the nineteenth century. Moreprecise experiments opened a whole new world to

the physicist who was beginning to investigate theproperties of very small particles. The behavior ofthese microscopic systems could not be explained interms of the classical physics and Newtonianmechanics, which had been the physicists’ stock andtrade up to this point.

In classical physics the physicist had explainedthe behavior of objects in terms of direct andcompelling deductions from a well defined set ofexperiments. Attempts to do the same from newobservations were not successful. The new physics, orquantum physics, was too abstract to make deductiveexplanations possible. The main reasons weretwofold: The basic constructs of this quantum theorywere removed from everyday experience, and themicroscopic particles could not be observed directly.

I. QUANTUM THEORY

Note: All vocabulary words in this LIFEPAC appear in boldface print the first time they are used. If you are unsure ofthe meaning when you are reading study the definitions given.

VOCABULARYStudy these words to enhance your learning success in this section.

absorption spectrum energy levels proton

alpha particle excited atom quanta

continuous spectrum ground state quantum number

de Broglie wave line spectrum radiation

electron volt photoelectric effect uncertainty principle

emission spectrum photon X ray

ELECTROMAGNETIC RADIATION

The wave theory of light was well recognized bythe end of the nineteenth century. Experimentalwork was being conducted in which both light raysand high speed electrons were allowed to strike ametal surface. The results of these experiments

could not be explained by existing theory. As aresult a new theory was developed, called thequantum theory. At the time, physicists did not fullyrealize what was happening; but modern physicshad been born.

Photoelectric effect. During the late 1800’sseveral experiments disclosed that electrons wereemitted when light fell on a metal plate. Thisphenomenon is the photoelectric effect. At first noone was surprised: Light waves were known to carryenergy; some of this energy, therefore, could somehowbe absorbed by electrons to give them enough kineticenergy to escape from the metal surface.

Soon some problems developed: First, theenergy of the photoelectrons was not related to theintensity of the light. When the light was madebrighter, more electrons were emitted; but they allhad the same average energy as those emitted bydim light. Second, the energy of the photoelectronswas related to the frequency of the light. If thefrequency was below a certain value, no electronswere emitted even if the light was intense.Conversely, if the frequency was above the value,electrons were emitted even in very dim light.

Photoelectrons emitted by any given frequencywere observed to have energy that ranged from zeroto some maximum value. If the frequency of thelight was increased, the maximum electron energyincreased. In other words, a faint blue lightproduced electrons with higher energy than did abright red light even though the bright red lightproduced more electrons. The relationship betweenKEmax, the maximum photoelectron energy, and thefrequency of the incident light can be stated:

maximum photoelectron energy= h (frequency - frequency0) KEmax = h (v - v0).

The symbol v (the Greek nu) represents thefrequency of incident light. The value of h was alwaysthe same value, but v0 changed for each metal.

An explanation of this phenomenon was givenin 1905 by Albert Einstein. He used a result ofearlier work by the German physicist Max Planck,who described the radiation emitted by a glowingobject. Planck could get his theory to work if heassumed that the light was emitted in little “lumps”of energy. He called these little bursts of energyquanta and showed that they had energy of

E = hv,

where v is the frequency and h is a constant knownas Planck’s constant. The value of Planck’s constanth is given as

h = 6.63 • 10-34 joule•sec.

Few physicists really believed in Planck’s quanta,but Einstein pointed out that the photoelectriceffect was experimental verification of Planck’sequation. He suggested that the photoelectricequation be rewritten:

hv = KEmax + hv0,

and be stated:

quantum (incident photon) energy = maximumelectron energy + energy required to eject anelectron from the metal surface.

A large portion of the photoelectron populationwill have less than maximum energy for thefollowing reasons:

1. The photon (the quantum of incident light)may have shared its energy with more thanone electron.

2. The electron may have lost part of its energybefore it got out of the metal.

The energy of photons is so small that the jouleis cumbersome. A unit of energy suited to theatomic scale is the electron volt. One electron voltis the energy change realized by an electron movingthrough a potential change of one volt. Numerically,

1 ev = 1.6 • 10-19 joules

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AMMETER

LIGHT

LlFEPACs 1204 and 1205 dealt with diffractionand interference. The observed phenomena could beexplained in terms of the wave theory of light. Nowyou have seen an argument that light behaves like aseries of packets of energy, called photons, or quanta,each photon small enough to interact with a singleelectron. The wave theory cannot explain thephotoelectric effect and the quantum theory cannotexplain interference and diffraction. Which is thecorrect theory? Many times before in physics, onetheory has been replaced by a new theory; but thisapparent conflict was the first time that two different

theories were needed to describe a phenomenon.Developing a model for light is a situation in whichscience must acknowledge that nature is not an “openbook” to man. These two theories are complementary:One is correct in some experiments, but the othertheory must be used in others.

Interestingly, light can exhibit either a wave ora particle nature, but never exhibits both in anysingle situation. Since we cannot reconcile the twodescriptive models, we have no choice but to acceptthem both.

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Answer these questions.

1.1 What is the photoelectric effect?

1.2 Why do photoelectrons have a maximum energy?

1.3 Why does faint light not appear as a series of flashes?

1.4 Why can the photoelectric effect not be explained without quantum theory?

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Complete these sentences.

1.5 The phenomenon that describes the emission of electrons from a metal surface when lightshines on it is the .

1.6 The maximum energy of photoelectrons a. with frequency and b.with increasing intensity of the light. (increases, decreases, remains constant)

1.7 Photon energy is proportional to .

1.8 Photons are also known as .

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Solve these problems.

1.9 A yellow lamp emits light with a wavelength of 6 • 10-7 m.

a. Write the common value for the speed of light, in meters per second.