Prepared by Tilahun TESFAYE African Virtual university Université Virtuelle Africaine Universidade Virtual Africana

Prepared by Tilahun TESFAYE

African Virtual universityUniversité Virtuelle AfricaineUniversidade Virtual Africana

Nuclear Physics Nuclear Physics

African Virtual University �

Notice

This document is published under the conditions of the Creative Commons http://en.wikipedia.org/wiki/Creative_Commons Attribution http://creativecommons.org/licenses/by/2.5/ License (abbreviated “cc-by”), Version 2.5.


I. NuclearPhysics ___________________________________________ 5

II. PrerequisiteCourseorKnowledge_____________________________ 5

III. Time____________________________________________________ 5

IV. Materials_________________________________________________ 5

V. ModuleRationale __________________________________________ 5

VI. Content__________________________________________________ 7

6.1 Overview___________________________________________ 7 6.2 Outline_____________________________________________ 7 6.3 GraphicOrganizer____________________________________ 7

VII. GeneralObjective(s)________________________________________ 9

VIII. SpecificLearningObjectives_________________________________ 10

IX. Pre-assessment __________________________________________ 11

X. TeachingandLearningActivities______________________________ 23

XI. GlossaryofKeyConcepts___________________________________ 85

XII. ListofCompulsoryReadings________________________________ 87

XIII. CompiledListof(Optional)MultimediaResources________________ 88

XIV. CompiledListofUsefulLinks________________________________ 89

XV. SynthesisoftheModule____________________________________ 90

XVI. SummativeEvaluation______________________________________ 91

XVII.References _____________________________________________ 109

XVIII.MainAuthoroftheModule________________________________ 110

XIX.FileStructure ___________________________________________ 111

Table of ConTenTs


Notice

Foreword

This module has four major sections.

The first one is the INTRODUCTORY section that consists of five parts vis:

TITLE:- The title of the module is clearly described

PRE-REQUISITE KNOWLEDGE: In this section you are provided with informa-tion regarding the specific pre-requisite knowledge and skills you require to start the module. Carefully look into the requirements as this will help you to decide whether you require some revision work or not.

TIME REQUIRED: It gives you the total time (in hours) you require to complete the module. All self tests, activities and evaluations are to be finished in this specified time.

MATERIALS REQUIRED: Here you will find the list of materials you require to complete the module. Some of the materials are parts of the course package you will receive in a CD-Rom or access through the internet. Materials recommended to conduct some experiments may be obtained from your host institution (Partner institution of the AVU) or you may acquire or borrow by some other means.

MODULE RATIONALE: In this section you will get the answer to questions like “Why should I study this module as pre-service teacher trainee? What is its relevance to my career?”

The second is the CONTENT section that consists of three parts

OVERVIEW: The content of the module is briefly presented. In this section you will fined a video file (QuickTime, movie) where the author of this module is interviewed about this module. The paragraph overview of the module is followed by an outline of the content including the approximate time required to complete each section. A graphic organization of the whole content is presented next to the outline. All these three will assist you to picture how content is organized in the module.

GENERAL OBJECTIVE(S): Clear informative, concise and understandable objec-tives are provided to give you what knowledge skills and attitudes you are expected to attain after studying the module.

SPECIFIC LEARNING OBJECTIVES (INSTRUCTIONAL OBJECTIVES): Each of the specific objectives, stated in this section, are at the heart of a teaching learning activity. Units, elements and themes of the module are meant to achieve the specific objectives and any kind of assessment is based on the objectives intended to


be achieved. You are urged to pay maximum attention to the specific objectives as they are vital to organize your effort in the study of the module.

The third section is the bulk of the module. It is the section where you will spend more time and is referred to as the TEACHING LEARNING ACTIVITIES. The gist of the nine components is listed below:

PRE-ASSESSMENT: A set of questions, that will quantitatively evaluate your level of preparedness to the specific objectives of this module, are presented in this section. The pre-assessment questions help you to identify what you know and what you need to know, so that your level of concern will be raised and you can judge your level of mastery. Answer key is provided for the set of questions and some pedagogical comments are provided at the end.

TEACHING AND LEARNING ACTIVITIES: This is the heart of the module. You need to follow the learning guidance in this section. Various types of activities are provided. Go through each activity. At times you my not necessarily follow the order in which the activities are presented. It is very important to note:

• formative and summative evaluations are carried out thoroughly• all compulsory readings and resources are done• as many as possible useful links are visited • feedback is given to the author and communication is done

COMPILED LIST OF ALL KEY CONCEPTS (GLOSSARY): This section contains short, concise definitions of terms used in the module. It helps you with terms which you might not be familiar with in the module.

COMPILED LIST OF COMPULSORY READINGS: A minimum of three com-pulsory reading materials are provided. It is mandatory to read the documents.

COMPILED LIST OF (OPTIONAL) MULTIMEDIA RESOURCES: Total list of copyright free multimedia resources referenced in, and required for completion of, the learning activities is presented.

COMPILED LIST OF USEFUL LINKS: a list of at least 10 relevant web sites that help you understand the topics covered in the module are presented. For each link, complete reference (Title of the site, URL),a screen capture of each link as well as a 50 word description are provided.

SYNTHESIS OF THE MODULE: Summary of the module is presented.

SUMMATIVE EVALUATION:

Enjoy your work on this module.


I. nuclear PhysicsBy Tilahun Tesfaye Addis Ababa University Ethiopia

II. Prerequisite Course or KnowledgeIn order to study this module you need to complete the QUANTUM MECHANICS of the AVU Teachers’ Training Module.

III. TimeThis module can be completed in 120hrs.

IV. MaterialsThe following list identifies and describes the equipment necessary for all of the activities in this module. The quantities listed are required for each group.

1. Computer: - A personal computer with word processing and spreadsheet software

2. PCNudat (Free software): - Nuclear database.

V. Module RationaleWe need to study nuclear physics because it is fundamental to understanding our lives and the physical world around us. We are all made from the products of exploding stars. Processes like the creation of chemical elements production of energy in stars and on Earth are understood in nuclear studies.

Building matter with quarks and leptons, neutrons, protons, deuterons, Nuclei and decay of matter as in emission of alpha, beta, gamma particles and fission are all nuclear phenomena.

Nuclear processes are used all around us and there are key applications in many aspects of our lives:

• Radioactivity in medicine, industry and research -Nuclear Magnetic Resonance (cancer), -Security (e.g. mine detection), -Fundamental studies such as neutrino properties (double beta decay)


• Medical applications -Cancer therapy using radiation -Historic use to kill cells - e.g. radium -Modern use with ion beams (e.g. GSI)• Medical imaging -MRI (Nuclear magnetic imaging) -Positron Emission Tomography -X-ray imaging etc• The environment -Carbon dating 12C/14C ratio -Argon gas dating -Rb/Sr dating of rocks• Biology -Archaeology (dating by isotope ratios) -Use of radioactivity to trace fluids in organs -Forensic• Security and industry -Oil well logging -Detection of bomb material etc

Study of atomic nucleus is the basis to harness the tremendous amount of energy locked by nature inside the nucleus and to use radiations emitted by the atomic nu-cleus. Concepts studied in Atomic physics module are extended to the nucleus of an atom in this module.

This module aims to

• study the general properties of nuclei, • examine the characteristics of the nuclear force,• introduce the principal models of the nucleus, • discuss the spontaneous decay of nuclei including those far from the region

of stability, • study nuclear reactions, in particular fission and fusion • introduce detectors• discuss the practical applications of nuclear physics• develop problem solving skills in the above areas

Further the energy level concepts and emission spectrum concepts of atomic physics are also used to explain some observables in the atomic nucleus. As most of the in-formation available about the atomic nucleus is obtained from its emission spectrum and the interaction of the radiation with matter, it is essential to study the atomic nucleus starting from its properties.


VI. Content

6.1 Overwiew

This module (Nuclear Physics) introduces the basic properties of the atomic nucleus nuclear constituents; the binding energy; isotopes; and nuclear models are concepts dealt in the first activity.

Most atoms found in nature are stable and do not emit particles or energy that change form over time. Heavy elements, such as uranium or thorium, and their decay chain elements do not have stable nuclei. They emit radiation in their naturally occurring state. The second activity of the module dwells on radioactivity and related appli-cations.

The third activity is on the interaction of nuclear radiation. The study of interaction of radiation with matter is the basis for radiation detection and measurement. Most appli-cations of radiation require the knowledge of interaction of radiation with matter.

One needs to know elementary particles and their interaction to gain a more unified understanding of nuclear forces and to achieve greater predictive power. Activity four is a survey of elementary particles and theories that explain nuclear interaction in terms of elementary particles.

6.2 Outline

1 Basic Properties of the Atomic Nucleus (30 hours)

&Basic Propertiesof the atomic nucleus, Nuclear constituents, Iosotopes,&Nuclear Binding Energy.&Nuclear Stability,&Mass and Isotopic Abundance;&Nuclear Models.

2 Radioactivity (35 hours)

&Radioactivity, discovery, alpha, bet and gamma radiation, Laws of Radioactive Distegration.

&Natural Radioactivity (Series and non Series), radioactive equilibrium,&Applications of Radioactivity.

3 Interaction of Radiation With Matter (35 hours)

&Interaction of heavy and light Charged Particles with matter,&Interaction of photons with matter,&Interaction cross-sections and interaction coefficients.&Nuclear Radiation Detectors.


4 Nuclear Forces and Elementary Particles (20 hours)

&Fundamental Interaction in nature. &Survey of elementary particles. &Yukawa’s theory of nuclear forces.

6.3 Graphic Organizer

NUCLEARPhysics

A . B asi c P ro pe rt ieso f the At om i c N uc leus

B . R adi o ac tiv ity

C. In te ra ct io n of R adia tio n W it h Matt er

D. Nuc lear Fo rces a ndElem en ta ry Par tic les

Basi c proper ti es of th e atom i c nu cl eu s.Nuc lear const itu ents. I sot opes,

Nuc lear bin ding energ y,

Nuc lear stabili ty ,

Mass an d iso topi c abun dance,

Nu clear m odels

Rad ioact iv it y. I t s d isc over y, alp ha,beta and gamm a radi at ion,Laws of radi oac ti ve d isi ntegration .

Natural radi oacti vi ty (seri es and n on s er ies)radi oacti ve equili b riu m,

App li cati ons of radi oacti v ity .

Interac ti on of h eavy and li ghtc harged part icl es w ith m atter .

Interacti on of phot ons w ith m atter .

Int eract ion cross- secti onsan d i nterac ti on coeff ici ents.

Nuc lear radi ation detect ors.

Fundam ental int eract ions in n ature.

Y ukawa’s th eory of nuc lear forc e.

Survey of elem entar y parti cl es.

NUCLEARPhysics


VII. General objective(s)

After completing the module you should be able to

• Understand the basic properties of nuclei and the atomic nucleus• Describe radioactivity and related phenomena• Explain the various interactions of nuclear radiation with matter• Understand nuclear interactions and elementary particles involved in the

interactions

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VIII. specific learning objectives (Instructional objectives)

Content Learning objectives After Completing this section you should be able to:

1. Basic Properties of the Atomic Nucleus (30 hours)

&Basic Propertiesof the atomic nucleus, Nuclear constituents, Iosotopes,

&Nuclear Binding Energy.&Nuclear Stability,&Mass and Isotopic Abundance;&Nuclear Models.

2. Radioactivity: (35 hours)

&Radioactivity, discovery, alpha, bet and gamma radiation, Laws of Radioactive Distegration.

&Natural Radioactivity (Series and non Series), radioactive equilibrium,

&Applications of Radioactivity.

3. Interaction of Radiation With Matter (35 hours)

&Interaction of heavy and light Charged Particles with matter,

&Interaction of photons with matter,&Interaction cross-sections and

interaction coefficients.&Nuclear Radiation Detectors.

4. Nuclear Forces and Elementary Particles (20 hours)

&Fundamental Interaction in nature. &Survey of elementary particles&Yukawa’s theory of nuclear forces.

• Identify constituents of the atomic nucleus and their collective proper-ties.

• Describe mass defect• Relate neutron: proton ratio to sta-

bility• Describe the shell and liquid drop

models of the nucleus

• Describe radiations from the nucleus• Use radioactivity disintegration

laws to solve problems• Identify and decide the type of equi-

librium for a given series decay• Apply the radioactivity law (half

life) in carbon dating

• Describe interaction of light char-ged particles and heavy charged particles with matter

• Identify and describe the four major interactions of photons with matter

• Use cross sections and coefficients of interaction to solve problems

• Describe gas filled, scintillation and semiconductor detectors (construc-tion, principle and use)

• Identify fundamental interactions in nature

• Identify elementary particles and describe their role in the process of interaction

• Explain Yukawa’s theory of nuclear force

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IX. Pre-assessment are You Ready for nuclear Physics?

Dear Learner

In this section, you will find self-evaluation questions that will help you test your preparedness to complete this module. You should judge yourself sincerely and do the recommended action after completion of the self-test. We encourage you to take time and answer the questions.

Dear Instructor

The Pre-assessment questions placed here guide learners to decide whether they are prepared to take the content presented in this module. It is strongly suggested to abide by the recommendations made on the basis of the mark obtained by the learner. As their instructor you should encourage learners to evaluate themselves by answering all the questions provided below. Education research shows that this will help learners be more prepared and help them articulate previous knowledge.

9.1 Self Evaluation Associated With Nuclear Physics

Evaluate your preparedness to take the module on thermal physics. If you score greater than or equal to 60 out of 75, you are ready to use this module. If you score something between 40 and 60 you may need to revise your school physics on topics of heat. A score less than 40 out of 75 indicates you need to physics.

Try the following questions and evaluate whether you have the necessary background to take on topics related to Nuclear Physics.

1 Which statement best describes the structure of an atom?

(a) A positive core surrounded by electrons packed tightly around it.(b) A particle comprised of a mixture of protons, electrons and neutrons.(c) A tiny nucleus of protons and neutrons with electrons orbiting around it.(d) A large core of protons and electrons surrounded by neutrons.

2 Of the following, when an atom emits an alpha particle its mass number is

(a) decreased by 4 and its atomic number is increased by 2(b) increased by 4 and its atomic number is decreased by 2(c) increased by 4 and its atomic number is increased by 2(d) decreased by 4 and its atomic number is decreased by 2


3 An electron moves with a speed equal to 4/5 that of light, Which one of the following is the ratio the electron’s mass to its rest mass.

(a) 5/4(b) 5/3(c) 25/9(d) 25/16

4 Of the following the one which can penetrate through 20cm thick steel plate is

(a) positive rays(b) α -rays

(c) β -rays

(d) γ -rays

5 The half life period of radioactive nuclide is 3 hours, its activity will be reduced by a factor of

(a)

1

8

(b)

1

6

(c)

1

27

(d)

1

9

6 Which of the following radioactive decay emits α -particle

(a) 82pb214 →

93Bi 214 + ...

(b) 91Th234 →

91pa234 + ...

(c) 92U 238 →

90Th234 + ...

(d) 91pa234 →

92U 234 + ...

7 A simple contains 16g of radioactive material, the half life of which is 2 days. After 32 days the amount of radioactive material left in the sample is

(a) 1g(b) 0.5g(c) 0.25g(d) <1 mg


8 A nuclide A (with mass number m and atomic number n) disintegrates emitting an α -particle. The resulting nuclide B has mass number and atomic number respectively equal to

(a) m-2 and n(b) m-4 and n-2(c) m-4 and n-1(d) m+4 and n+1

9 As a result of radioactive decay a 92

238 U nucleus is changed to 91

234 Pa nucleus. During this decay the particles emitted are

(a) two β -particles and one proton

(b) two β -particles and one neutron

(c) one α -particle and one β -particle(d) one proton and two neutrons

10 The relation between half life T1/ 2

of a radioactive sample and its mean life τ is

(a) τ = 2.718T

1/ 2

(b) τ = T

1/ 2

(c) τ = 0.693T

1/ 2

(d) T1/ 2

= 0.693τ

11 The decay constant λ of a radioactive sample

(a) is independent of the age (b) depends on the nature of activity(c) increases as the age of atoms increases(d) decreases as the age of atoms increases

12 Of the three isotopes of hydrogen 1 H 1 ,1

H 2 and 1H 3

(a) two are stable (b) all are stable

(c) 1 H 3 decays to, 1 H 2

(d) 1 H 3 decays to 2 He3


13 A certain radioactive substance has a half-life of 5 years. Thus for a nucleus in a sample of the element, probability of decay in 10 years is

(a) 100%(b) 75%(c) 60%(d) 50%

14 A gamma ray photon creates an electron positron pair. If the rest mass of electron is 0.5 MeV and the total kinetic energy of the electron positron pair is 0.78 MeV, the energy of gamma ray photon must be

(a) 0.28 MeV(b) 1.28 MeV(c) 1.78 MeV(d) 0.78 MeV

15 If the mass of proton is completely converted into energy, it will be about

(a) 3.1MeV(b) 931 MeV(c) 10078 MeV(d) 9310 MeV

16 A π0 meson at rest decays into two gamma rays π

0 →γ + γ then which of the following is correct

(a) the twoγ ’s move in the directions opposite to each other

(b) the twoγ ’s have unequal energies

(c) both theγ ’s move in the same direction

(d) theγ ’s will be periodically approaching and receding from each other

17 If the half life of a radioactive metal is 2 years

(a) The metal will completely disintegrate in 2 years(b) 1/4th of it will remain after 8 years(c) the metal will completely disintegrated in to 4 years(d) it will never disintegrate completely

18 When aluminium is bombarded with α -particles, radioactive phosphorus is

formed i.e. 13Al 27 +

2He4 →

15P 30 one more particle formed in this reaction

is

(a) an electron(b) a neutron (c) negatively charged helium atom(d) a negatively charged hydrogen atom


19 If 5 B10 is bombarded with neutrons and α -particle is emitted. The residual nucleus is

(a) 0 n1

(b) 1 D 2

(c) 1 H 3

(d) 13Li7

20 What is X in the following relation 13Li7 +

1H 1 →

2He4 + X

(a) 1 H 3

(b) 0 D1

(c) 1 D 2

(d) 2 He4

21 If α ,β and γ -rays have ionising powers Iα

, Iβ and I

γ respectively then

(a) Iα

,> Iβ >I

γ

(b) . Iα

,< Iβ <I

γ

(c) Iα= I

β =I

γ

(d) none of these

22 Which of the following is a correct statement

(a) β -radioactivity is the process in which an electron is emitted from an unstable atom whose atomic number Z remains unchanged

(b) γ -radioactivity is the process in which the daughter nucleus has atomic number 1 unit more than that of the parent nucleus

(c) α -radioactivity is the process in which an unstable atom emits the nucleus of a helium atom

(d) α γ -radioactivity is the process in which a heavy atom emits electromagnetic radiations of very high frequency


23 The counting rate observed from a radioactive source at t=0s was 1600 counts per second and at t=8s it was 100 counts per second. The counting rate observed as counts per second at t=6 seconds will be

(a) 400(b) 300(c) 200(d) 150

24 Consider a radioactive material of half life 1.0 minute. If one of the nuclei decays now, the next one will decay

(a) after 1 minute

(b) after 1/ loge 2 minutes

(c) after 1.N minute, where N is the number of nuclei present at that moment(d) after any time

25 What is the binding energy of 6 C 12 ? (Given mass of proton = 1.00078 a.m.u. mass of neutron = 1.0087 a.m.u. =931 MeV)

(a) 9.2 MeV (b) 92 MeV(c) 920 MeV(d) 0.92 Mev

26 The binding energy per nucleus were to split into two eequal size nuclei, about how much energy would be released in the process.

(a) 238MeV(b) 23.8MeV(c) 2.38MeV(d) 119MeV

27 Most suitable element for nuclear fission is the element with atomic number near

(a) 92(b) 52(c) 21(d) 11


28 In order to carryout the nuclear reaction

1H 1 +1

H 1 +1

H 2 =1

He4 +1

e0 + energy

(a) Very high temperature and low pressure would be necessary(b) Vary high temperature and relatively high pressure would be necessary(c) Moderates temperature and very high pressure will be necessary(d) Very high temperature will only be necessary

29 When a microgram of matter is converted to energy, the amount of energy re-leased will be

(a) 3×104 J

(b) 9 ×107 J

(c) 9 ×1010 J

(d) 9 ×1014 J

30 A radioactive nucleus undergoes a series of decay according to the scheme.

Aα⎯ →⎯ A

1

β⎯ →⎯ A2

α⎯ →⎯ A3

λ⎯ →⎯ A4

If the mass number and atomic

number of A are 180 and 72 respectively, what are these numbers for A

4

(a) 172,69(b) 170,69(c) 174,71(d) 180,70

31 The material used for absorbing the extra neutrons in a nuclear reactor is

(a) zinc (b) uranium (c) radium(d) cadmium

32 Thermal neutrons have energy around

(a) 100eV(b) 10eV(c) 1eV

(d) 92U 238 →

82pb206


33 On an average how many neutrons are released per fission

(a) 2(b) 1(c) 3(d) 2.5

34 Moderators are used in the nuclear reactors to

(a) accelerate the neutrons(b) slow down the neutrons(c) to slow down neutrons(d) produce neutrons

35 Cadmium rods are used in a nuclear reactor to

(a) generate neutrons(b) absorb neutrons(c) slow down neutrons(d) produce neutorns

36 How many radioactive disintegrations per second are defined as Becquerel

(a) 106

(b) 3.7 ×1010

(c) 1(d) none of the above

37 In the nuclear reactor at Trombay which of the following is used as moderator

(a) ordinary water(b) cadmium(c) copper(7) heavy water

38 Which of the following particles is used to cause fission in an atomic reactor?

(a) proton(b) α -particle

(c) β -particle(d) neutron

39 Which of the following is the best nuclear fuel?

(a) Neptunium 293(b) plutonium 239(c) Uranium 236(d) Thorium 236


40 The moderator in a reactor

(a) absorbs thermal energy(b) slows down neutron(c) accelerate neutron(d) absorbs neutrons

41 For an atomic reactor being critical the ratio of the average number of neutrons produced and used in chain reaction

(a) depends on the mass of fissionable material (b) is greater than one(c) is equal to one(d) is less than one

42 An element A decays into element C by a two step process

A→ B +2

He4 , B → C + 2e− . Then

(a) A and C are isobars(b) A and B are isotopes(c) A and C are isotopes(d) A and B are isobars

43 A radioactive sample with a half-life of 1 month has the label: ``Activity =2 mi-crocuries on 1.8.1991’’. What was its activity two moths later in microcuries?

(a) 1.0(b) 0.5(c) 4(d) 8

44 Isotopes are atoms having

(a) Same number of protons but different number of neutrons (b) Same number of protons but different number of protons(c) Same number of protons and neutrons(d) None of the above

45 Which one of the following nuclear reactions is a source of energy in the sun?

(a) 4 Be9 +2

He4 →6

C 12 +0

n−1

(b) 92U 238 →

82pb206

(c) 56Ba144 +

56K r 92 →

92U 235 +

0n−1

(d) 26F e56 +

48Ca112 →

74W 167 +

0n1


46 Transuranium elements are those whose atomic number is

(a) always more then 92(b) less than 92(c) always more than 103(d) none of the above

47 Radio isotopes are used as tracers in many problems on account of the fact that

(a) Their chemical properties are different(b) They can be detected accurately in small quantities(c) They can not be distinguished from normal atoms easily(d) They can not be distinguished from normal atoms easily

48 The element not occurring in nature is

(a) 92U 233

(b) 92U 235

(c) 92U 238

(d) 90Th232

49 Which of the following statements are true regarding radioactivity?

(a) All radioactive elements decay exponentially with time(b) Half life time of a radioactive element is time required for one half of the

radioactive atoms to disintegrate(c) Age of earth can be determined with the help of radioactive dating(d) Half life time of a radioactive element is fifty percent of its average life pe-

riod

50 Heavy water is used as moderator in a nuclear reactor. The function of the mo-derator is

(a) to control the energy released in the reactor(b) to absorb neutrons and stop chain reaction (c) to cool the reactor(d) to slow down the neutrons to thermal energies


9.2 Answer Key

1. C

2. D

3. B

4. D

5. A

6. C

7. D

8. B

9. C

10. D

11. A

12. D

13. B

14. C

15. B

16. A

17. D

18. B

19. D

20. D

21. A

22. C

23. C

24. D

25. B

26. A

27. A

28. A

29. B

30. A

31. D

32. A

33. D

34. B

35. B

36. C

37. D

38. D

39. B

40. C

41. C

42. B

43. A

44. A

45. B

46. A

47. B

48. A

49. C

50. D


9.3 Pedagogical Comment For The Learner

Nuclear physics can be seen, historically, as the child of chemistry and atomic phy-sics and in turn as the parent of particle physics and one of the parents of medical physics.

When hearing the word ’nuclear’ most people will think of two things: nuclear bombs and nuclear reactors. Both are not exactly popular these days. Thanks to bombs and reactors nuclear physics was probably the part of science with the biggest impact on politics in the 20th century. Just think of the entire cold war. The Manhattan project was probably the most high-profile science project of the 20th century, with a large number of future Nobel-prize winners involved. In cultural relevance it is possibly rivalled by the moon-landing -another technological spin-off of World-War II, and in every-day-relevance by electronics.

In this module basic concepts of nuclear physics with emphasis on nuclear structure and radiation interactions with matter. Nuclear forces; shell structure of the nucleus; alpha, beta, and gamma radioactive decays; interactions of nuclear radiations (charged particles, gammas, and neutrons) with matter; nuclear reactions; fission and fusion.

The module is divided into five activities. Each activity has examples and reading assignments. You are required to complete all the learning activities and complete the compulsory reading material. This material is an extensive lecture notes and study guide with exercises. These lecture notes are developed by the author of this module from 2004 to 2007 in the University of Addis Ababa, Ethiopia.

Research in recent years has shown that the students who do best in physics (and other subjects) are those who involve themselves actively in the learning process. This involvement can take many forms: writing lots of questions in the margins of the module; asking questions by email; discussing physics in the AVU discussion forums etc. So you are strongly advised to exhaust all possiblities given to you by the AVU.

A Final Word

Physics, in general, is not so much a collection of facts as a way of looking at the world. The author of this module hopes that your first course in nuclear physics will be a big plus to your appreciation of nature and will contribute to improve your skills in careful thinking, problem solving, and precise communication. In this course you will gain lots of experience with qualitative explanations, rough numerical estima-tes, and careful quantitative problem solving. When you understand a phenomenon on all of these levels, and can describe it clearly to others, you are «thinking like a physicist» (as we like to say). Even if you eventually forget every fact learned in this course, these skills will serve you well for the rest of your life.


X. Teaching and learning activities

Activity 1: Basic Properties of the Atomic Nucleus

You will require 40 hours to complete this activity. In this activity you are guided with a series of readings, Multimedia clips, worked examples and self assessment questions and problems. You are strongly advised to go through the activities and consult all the compulsory materials and as many as possible among useful links and references.

Specific Teaching and Learning Objectives

• Identify constituents of the atomic nucleus and their collective properties.• Describe mass defect• Relate neutron: proton ratio to stability• Describe the shell and liquid drop models of the nucleus

Summary of the Learning Activity

The atomic nucleus is now known to be composed of protons and neutrons known as nucleon. The number of protons and neutrons in the nucleus is its mass number

A( ) and the number of protons is its atomic number

Z( ) . A nucleus, of chemical

symbol X is uniquely designated by:

Z

A X

The atomic nuclei has some properties of interest:

• Nuclear Size: In general atomic nuclei have spherical shape with radius roughly given by:

R = Ro

AA/3 where Ro=1.2 ± 0.2fm

• Charge: - The elelctric charge distribution within the nucleus is the same as thenuclear mass distribution Experimental results suggest that the ‘elelctrical radius of the nucleus’ and ‘nuclear matter radius’ are nearly the same.

• Nuclear Spin: For each nucleon orbital angular momentum

l .. and spin s com-

bine to the total angular momentum j The total angular momentum of a nu-cleus I is therefore the vector sum of the angular momenta of the nucleons

j=l+s I= j

ii=1

A

∑ odd-A: half-integer I, even-A: integer I


• Angular momentum: The angular momentum I has all of the usual properties of quantum mechanical angular momentum vectors:

I 2 = h

2 I ( I +1)

Iz= mh m= - I , - I +1, L , I

• The total angular momentum I is usually referred to as nuclear spin and the corresponding spin quantum number I is used to describe nuclear states.

Nuclear stability is related to the number of nucleons constituting the nucleus. Stable nuclei only occur in a very narrow band in the Z-N plane. All other nuclei are unstable and decay spontaneously in various ways.

There are three models of the atomic nucleus. the liquid drop model, the Fermi-gas model and the shell model. Each model explain certain observations of nuclear property. No single model explain all observations.

List of Required Readings

Copyright free readings should also be given in electronic form (to be provided on a CD with the module)

Reading 1: CHAPTER ONE.

Complete reference: PHYSICS 481 Lecture Notes and Study Guide From Department of Physics Addis Ababa University, by Tilahun Tesfaye(PhD) . Abstract: This Reading is structured in terms early atomic hypothesis; properties of the nucleus; theories of nuclear composition; binding energy; nuclear force and nuclear structure models. Each section is ended with a set of questions and pro-blems. Rationale: This chapter tallies well with the first activity of this module.

List of Relevant MM Resources (for the Learning Activity).

Software, Interactive online exercises Videos, animations etc

Resource #1

Title: The Rutherford Experiment URL: http://micro.magnet.fsu.edu/electromag/java/rutherford/ Date Consulted: August 2007 Description: This classic diffraction experiment was conducted in 1911 by Hans Geiger and Ernest Marsden at the suggestion of Ernest Rutherford. Details about the experiment and how to operate the tutorial are provided beneath the applet window.


List of Relevant Useful Links (for the Learning Activity).

List of links, providing an alternative perspective on the curriculum material, each with “screen capture”

Useful Link #1 ABC’s of Nuclear Science

Title: Nuclear Structure URL: http://www.lbl.gov/abc/Basic.html Screen Capture:

Description: Topics like Nuclear Structure, Radioactivity, Alpha Decay, Beta Decay, Gamma Decay, Half-Life, Reactions, Fusion, Fission, Cosmic Rays and Antimatter are discussed in this site. Further there are links to other sources for further reading.

Rationale: This site has comprehensive coverage of most of the nuclear physics topics dealt in this module. The learner can consult the links to see other lectures..

Date Consulted: January 2008


Detailed Description of the Activity (Main Theoretical Elements)

Introduction

In Atomic Physics Module, you have learnt the experiments that led to the formulation of the theory by which the nuclear atom was accepted. In this module we shall dwell on the structure of the atomic nucleus and examine some of the nuclear radiations and their interactions with matter.

All matter is composed of atoms. The atom is the smallest amount of matter that retains the chemical properties of an element. The English chemist John Dalton, in 1803,. stated that each chemical element possesses a particular kind of atom, and any quantity of the element is made up of identical atoms of this kind. What distinguishes one element from another element is the kind of atom of which it consists, and the basic physical difference between kinds of atoms is their weight.

For almost 100 years after Dalton established the atomic nature of atoms,. all the results of chemical experiments, indicated that the atom was indivisible. Eventually, experimentation into electricity and radioactivity indicated that particles of matter smaller than the atom did indeed exist. but these smaller particles no longer have the same properties as the overall element.

In 1906, J. J. Thompson won the Nobel Prize in physics for establishing the existence of electrons. Soon after the discovery of electrons, protons were discovered. Protons are relatively large particles and a positive charge equal in magnitude (but opposite in sign) to that of the electron. The third subatomic particle to be discovered, the neutron, was not found until 1932. The neutron has almost the same mass as the proton, but it is electrically neutral.

It is now well known that an atom

1.1 Basic Properties of the Atomic nucleus,

Charge and Mass of the Nucleus

The most important characteristics of a nucleus are its charge Z and its mass M . The charge on the atomic nucleus is determined by the number of positive charges

it contains. The carrier of an elementary charge, e = 1.6021×10−19 C , on the nu-cleus is proton. Since an atom as a whole is electrically neutral, the nuclear charge simultaneously determines the number of electrons around the nucleus. In other words, chemical elements are identified by their nuclear charge or, by their atomic numbers.

The mass of an atomic nucleus is practically the same as that of the entire atom be-cause the mass of the electrons in an atom is negligible. The mass of an electron is

1/1836th that of a proton. It is customary to measure the mass of an atom in atomic


mass units, abbreviated amu. The atomic mass unit is equal to one-twelfth of the

mass of the neutral 6

12 C atom.

1u = 1.6603×10−27 kg

Spin And Magnetic Moment of The Nucleus

In atomic physics module you have seen that the spin of an electron results in the fine structure of atomic spectrum. For atoms having one valence electron the relative orientation of the orbital and spin moments of the electron leads to the splitting of all energy levels (except the s-level) and as a result, to the splitting of spectral lines. With further improvement of spectroscopic instruments, investigators were able to investigate such lines. It was found that each of the two D-lines of sodium was in turn a doublet, that is , consisting of two very closely spaced spectral lines.

Fig. D-lines of Na

Pauli suggested that the hyperfine structure might be due to an occurrence of angular momentum in the atomic nucleus. The total angular momentum, or nuclear spin, along with nuclear charge and nuclear mass, is the most important characteristic of the nucleus.

The nucleus is made up of protons and neutrons each of which has spin h 2 . The nuclear spin is the vector sum of the spin angular momenta of all the component particles. A ucleus made up of an even number of nucleons has integral spin (in units of

h ) or zero spin. In addition to nuclear spin, the nucleus has a magnetic moment. Thus, all atomic particles (the nucleus and electrons) have a magnetic moment.

The magnetic moment of a nucleus is determined by those of its component particles. By analogy with the Bohr magneton, the magnetic moments of nuclei are expressed in terms of the so-called nuclear magneton defined as

μN=eh/2m

p

where μN is the nuclear gyromagnetic ratio.


Nuclear constituents

The nuclear model of the atom brought more questions than it answered when it was forwarded. What is the composition of the nucleus? How can a nuclear atom become stable? Answers to these questions could only be given after the discovery of various properties of the nucleus, notably nuclear charge Z, nuclear mass, and nuclear spin.

The nuclear charge was found to be defined by the sum of the positive charges it contains. Since an elementary positive charge is associated with the proton, the presence of protons in the nucleus appeared to be beyond any doubt from the outset Two more facts were also established, namely:

a. The masses of the isotopes (except ordinary hydrogen), expressed in proton mass units, were found to be numerically greater than their nuclear charges expressed in elementary charge units, this difference growing with increases in Z . For the elements in the middle of the periodic Table the isotopic masses (in amu) are about twice as great as the nuclear charge. The ratio is still greater for the heavier nuclei. Hence one was forced to think that the protons were not the only particles that make up the nucleus.

b. The masses of the isotopic nuclei of all chemical elements suggested two pos-sibilities, either the particles making up the nucleus had about the same mass, or the nucleus contained particles differing in mass to a point where the mass of some was negligible in comparison with that of the others, theta is, their mass did not contribute to the isotopic mass to any considerable degree.

The latter possibility appeared especially attractive because it fitted nicely with the proton-electron model of the nucleus. That the nucleus might contain electrons seemed to follow from the fact that natural beta-decay is accompanied by the emission of electrons. The proton-electron model also explained the fact why the isotopic atomic weights were nearly integers. According to this model, the mass of the nucleolus should be partially equal to the masses of the protons that make it up, because the electronic mass is about 1/2000th that of the proton. The number of electrons in the nucleus must be such that the total charge due to the positive protons and the negative electrons is the true positive charge of the nucleus.

For all its simplicity and logic, the proton-electron model was refuted by advances in nuclear physics. In fact, it ran counter to the most important properties of the nucleus.

If the nucleus contained electrons, the nuclear magnetic moment would be of the same order of magnitude as the electronic Bohr magneton Notice that the nuclear magnetic moment is defined by the nuclear magneton which is about 1/2000th the electronic magneton.

Data on nuclear spin also witnessed against the proton-electron model. For example,

according to this model the beryllium nucleus, 49 Be , would contain nine protons and

five electrons so that the total charge would be equal to four elementary positive charges. The proton and the electron have each a half-integral spin, h/2. The total


spin of the nucleus made up of 14 particles (nine protons and five electrons) would

have to be integral. Actually, the beryllium nucleus, 49 Be , has half-integral spin of

magnitude 3h/2. Many more examples might be cited.

Last but not least, the proton-electron model conflicted with the Heisenberg uncer-tainty principle. If the nucleus contained electrons, then the uncertainty in the electron

position, Δx, would be comparable with the linear dimensions of the nucleus, that is,

10−14 or 10−15 m. Let us choose the greater value, Δx = 10−14 From the Heisenberg uncertainty relation for the electron momentum we have

nP>>h/nx>>10-14 =10-19 kg m/s

The momentum P is directly related to its uncertainty, that is ΔP : P ≈ ΔP Once the momentum of the electro is known, one can readily find its energy. Since in the above

example P>>m

ec = 10−30 kg × 3×108m/s , one should use the relativistic relation

for energy and momentum

E2 =c2 p2 +m

e

2c4

Then we get

E = c p2 + mec2 = 3×108 10−38 + (10−30 × 3×108 )2

≈ 2 ×108 eV = 200 MeV This figure is greatly in excess of that (7-8MeV)found for the total binding energy by experiment and is many times the energy of electrons emitted in beta-decay. If, on the other hand, the electrons in the nucleus were assumed to have the energy comparable with that associated with the particles emitted in beta-decay (usually a few MeV), then the region where the electrons must be localized, that is, the size of the nucleus as found from the uncertainty relations would be much greater than that found by observation.

A way out was found when in 1932 Chadwick discovered a new fundamental particle. From an analysis of the paths followed by the particles produced in some nuclear reactions and applying the law of conservation of energy and momentum, Chadwick concluded that these paths could only be followed by a particle with a mass slightly greater than that of the proton and with a charge of zero. Accordingly, the new particle was called the neutron.

According to the present views, a nucleus consists of nucleons: protons and neutrons. As the mass of a nucleon is about 2000 times the mass of an electron the nucleus carries practically all the mass of an atom


A nuclid is a specific combination of a number of protons and neutrons. The complete symbol for a nuclide is written as:

Z

A X

where X is the chemical symbol of the element, Z is the atomic number, giving the number of protons in the nucleus. A is the totla number of nucleons in the nuclues.

It is also known as the mass number. N = A − Z is the number of neutrons.

In nucleus physics it is said that the proton and the neutron are two charge states of the same particle, the nucleon. The proton is the protonic state of the nucleon with a charge +e, and the neutron is its neutronic state with zero charge. According to the latest data, the rest mass of a proton and of a neutron respectively is

mp=1.0075975±0.000001 amu=(1836.09±0.01)m

e

mn=1.008982±0.000003 amu=(1838.63±0.01)m

e

The proton and the neutron have the same mass number equal to unity. In the nu-cleus, the nucleons are in states substantially differing from their free states. This is because in all nuclei, except that of ordinary hydrogen, there are at least two nucleons between which a special nuclear interaction or coupling exists.

The proton-neutron model of the nucleus accounts for both the observed values of isotopic masses and, the magnetic moments of the nuclei. For, since the magnetic moments of the proton and the neutron are of the same order of magnitude as the nuclear magneton, it follows that a nucleus built up of nucleons should have a ma-gnetic moment of the same order as the nuclear magneton. Therefore, with protons and neutrons as the building blocks of nuclei, the magnetic moment should be of the same order of magnitude. Observations have confirmed this.

1 fm (femto meter = fermi) = 10−10 m is the typical length scale of nuclear phy-sics.

Also with protons and neutrons as the constituents of nuclei, the uncertainty principle leads to reasonable value of energy for these particles in a nucleus, in full agreement with the observed energies per particle

Finally, with the assumption that nuclei are composed of neutrons and protons, the difficulty arising from nuclear spin has likewise been resolved. For if a nucleus contains an even number of nucleons, it has integral spin (in units of

h ). With an odd number of nucleons, its spin will be half-integral (in units of

h ).


1.2 Nuclear Binding Energy

Atomic nuclei containing positively charged protons and uncharged neutrons make up stable systems despite the fact that the protons experience Coulomb repulsion. The stability of nuclei is an indication that there must be some kind of binding force between the nucleons. The binding force can be investigated on the energy basis alone, without invoking any considerations concerning the nature and properties of nuclear forces.

An idea about the strength of a system can be gleaned from the effort required to break it up i.e. to do work against the binding. This approach leads to several important facts about the forces that hold the nucleons in a nucleus.

The energy required to remove any nucleon from the nucleus is called the binding (or separation) energy of that nucleon in the nucleus. It is equal to the work that must be done in order to remove the nucleon from the nucleus without imparting it any kinetic energy. The total binding energy of a nucleus is defined as the amount of work that must be done in order to break up the nucleus into its constituent nucleons. From the law of conservation of energy it follows that in forming a nucleus, the same amount of energy must be released as is put in to break it up.

The magnitude of the binding energy of nuclei may be estimated from the following considerations. The rest mass of any permanently stable nucleus has been found to be less than the sum of the rest masses of the nucleons that it contains. It appears as if in “packing up’’ to form a nucleus the protons and neutrons lose some of their masses.

An explanation of this phenomenon is given by the special theory of relativity. This fact is accounted for by the conversion of part of the mass energy of the particles into

binding energy. The rest energy of a body, E 0, is related to its rest mass m0

by:

o E0=m

0c2

where c is the velocity of light in a vacuum. Designating the energy given upon the

formation of a nucleus as ΔEb, then the mass equivalent of the total binding energy

o Δm

o

= ΔEb

/ c2

is the decrease in the rest mass as the nucleons combine to make up the nucleus. The

quantity Δm

o is also known as mass defect or mass decreament. If a nucleus of

mass M is composed of a number Z of protons with a mass m

p and of a number A-Z

of neutrons with a mass mn, the quantity Δm

0 is given by

Δm

o

= Zmp+ ( A− Z )m

n− M


The quantity Δm0

gives a measure of the binding energy:,

ΔE

b= Δm

o

c2 = [Zmp+ ( A− Z )m

n− M ]c2

In nuclear physics, energies are expressed in atomic energy units (aeu) corresponding to atomic mass units:

1aeu = c2 ×1amu = 9 ×1016m2 /s2( ) ×1.660kg

= 1.491×10-10J

= 931.1MeV

Thus, in order to find the binding energy in MeV, one should use the equation

ΔE

b= [Zm

p+ ( A− Z )m

n− M ]× 931.1MeV

Where the masses of the nucleons and the mass of the nucleus are expressed in atomic mass units. On the average, the binding energy per nucleon is about 8MeV, which is a fairly large amount.

Fig: A plot of the binding energy per nucleon as a function of mass number A


As is seen from the plot, the strength of binding varies with the mass number of the nuclei. The binding is at its strongest in the middle of the periodic Table, in the range

28<A<138, that is, from 14

28 Si to 56

138 Ba. In these nuclei, the binding energy is very close to 8.7 MeV. With further increases in the number of nucleons in the nucleus, the binding energy per nucleon decreases. For the nuclei at the end of the periodic

Table (for example, uranium), Δεbis about 7.6 MeV.

In the region of small mass numbers, the binding energy per nucleon shows characteris-tic maximua and minima. Minima in the binding energy per nucleon are shown by nu-

clei containing an odd number of protons and neutrons, such as 36 Li,

5

10 B and 7

14 N

Maxima in the binding energy per nucleon are associated with nuclei having an even

number of protons and neutrons, such as 24 He,

6

12 C and 8

16 O.

The general course of the curve gives a clue to the mechanisms by which nuclear energy is released. We find that nuclear energy can be released either by the fission of heavy nuclei and the fusion of light nuclei from still lighter ones. It is clear from general considerations that energy will be released in nuclear reactions for which the binding energy per nucleon in the end products exceeds the binding energy per nucleon in the original nuclei.


1.3 Nuclear Stability

Not all nuclei are stable. Unstable nuclei undergo radioactive decay into different nuclei. Stable nuclei have approximately equal numbers of neutrons and protons

N = Z for small A < 20 and a small excess of neutrons for large A as shown in the diagram.

The Pauli exclusion principle helps to understand the fact that nuclei with equal N and Z are stable. Imagine filling a 1-deminsional box with protons and neutrons.

We want the minimum energy configuration for a given value of A , say 5. Since both neutrons and protons have spin ½ they are fermions (like electrons) and so obey the Pauli exclusion principle. This principle restricts the number of protons and neutrons to 2 of each at each energy level. Recall that the energy of the nth energy in a 1-di-


mensional box is given by En= n2 E

1, where E1

is the energy of the round level.

If all 5 nucleons were neutrons, the total energy of the nucleus would be

9 + 2 × 4( ) + 2 ×1( )⎡⎣ ⎤⎦ E

1= 19E

1 as shown in diagram A . In contrast, if 3 were neu-

trons and 2 were protons (as shown in B), the energy would be

4 + 4 ×1( )⎡⎣ ⎤⎦ E1= 8E

1

which is far less. This simple picture shows that it is more favourable energetically to have

N : Z

If we include the Coulomb repulsion between the protons, the energy levels of the protons become higher than the energy levels of the neutrons. As A increases, it becomes more favourable to have a small excess of neutrons.

Some elements have more stable isotopes than others. The elements with the most number of stable isotopes have Z values of 2, 8, 20, 28, 50, 82 and 126. These are called magic numbers, as the reason for stability was not understood at the time they

were discovered. For example, calcium

Z = 20( ) has 6 stable isotopes whereas

potassium

Z = 19( ) and scandium

Z = 21( ) have only 2 stable isotopes each. Similarly, nuclei with N equal to a magic number have a larger than average number of isotones (an isotone has the same N value but a different Z value).

Nuclei with A : 60 are more tightly bound together and so they are at lower energy

compared to the rest. (Binding energy is analogous to the energy required to lift a bucket of water from a well. A large binding energy means the water is low in the well, i.e. the water is at a low energy). If two light nuclei with A << 60 are brought together they create a new nuclei at lower rest energy (this is called fusion). Also a heavy with A >> 60 can split into two nuclei of lower rest energy (this is called fission).


1.4 Mass and Isotopic Abundance

Properties of the atomic nucleus, discussed in the prevous sections, binding ener-gies; decay rates, etc are the basic quantities determining the elemental and isotopic abundances in nature.

The relative abundance of an isotope in nature compared to other isotopes of the same element is relatively constant. The Chart of the Nuclides presents the relative abundance of the naturally occurring isotopes of an element in units of atom percent. Atom percent is the percentage of the atoms of an element that are of a particular isotope. Atom percent is abbreviated as a/o. For example, if a cup of water contains

8.23 × 1024 atoms of oxygen, and the isotopic abundance of oxygen-18 is 0.20%,

then there are 1.65 × 1022 atoms of oxygen-18 in the cup.

The atomic weight for an element is defined as the average atomic weight of the isotopes of the element. The atomic weight for an element can be calculated by summing the products of the isotopic abundance of the isotope with the atomic mass of the isotope.

Example

Calculate the atomic weight for the element lithium. Lithium-6 has an atom percent abundance of 7.5% and an atomic mass of 6.015122 amu. Lithium-7 has an atomic abundance of 92.5% and an atomic mass of 7.016003 amu.

Solution:

Atomic Mass Lithium = 0.75( ) 6.015122amu( ) + 0.925( ) 7.016003( )amu

=6.9409 amu The other common measurement of isotopic abundance is weight percent (w/o). Weight percent is the percent weight of an element that is a particular isotope. For example, if a sample of material contained 100 kg of uranium that was 28 w/o ura-nium-235, then 28 kg of uranium-235 was present in the sample.


1.5 Nuclear Models

There are two basic types of simple nuclear model

Collective body with no individual particle states. An example is the Liquid Drop Model which is the basis of the semi-empirical mass formula.

Individual particle model with nucleons in discrete energy states for example the Fermi Gas Model or the Shell Model.

The Liquid Drop Model

This model is based on the fact that the density of the nucleus is roughly constant. It

predicts the total binding energy of the number from values of atomic number(Z);

neutron number (N) and and mass number (A) .

E

b= C

1A− C

2A2 / 3 − C

3

Z(Z −1)

A1/ 3− C

4

N − Z( )2

A

This is called the semi-empirical binding energy equation. The constants and the origin of the terms is as follows:

1. C1= 15.7MeV The constant density of the nucleus implies that the distance

between nucleons and the number of nearest neighbours (i.e. those within 3 fm) is also constant. Thus the binding energy of each nucleon should also be constant. Hence, the total binding energy should be proportional to the number A of nucleons. This is called the volume effect.

2. C 2= 17.8MeV The first term is an overestimate because it ignores the

fact that the nucleons near the surface of the nucleus have fewer neighbours compared to a nucleon inside. We have to subtract a term proportional to the

surface area, 4πR 2 . Using R = R

o

A1/ 3 , the surface area becomes 4πR

o

2 A2 / 3

which is proportional to A2 / 3 . This the surface effect.

3. C 3= 0.71MeV The repulsive force between protons reduces the binding

energy. There are

Z Z −1( )2

pairs of protons, each with a Coulomb poten-

tial of

kee2

R, where

R = A1/ 3 Ro

. Thus we subtract a term proportional to

Z Z −1( )A1/ 3

This is the Coulomb effect


4. C 4= 23.6MeV We found in the simple 1-dimensional box model that a

departure from N = Z increases the energy of the nucleus and thus lowers

the binding energy, hence we subtract a term proportional to

N = Z( )2

An

excess of neutrons is tolerated for a large A and so the term involves 1 / A This is the excess neutron effect.

Shell model

This model very much builds on the success of the atomic shell model which explains the periodic properties of atoms in terms of the filling of electron energy levels. When the group of levels associated with a shell are all occupied we have particularly stable (chemically inert) atoms - the rare gases. In the nuclear case we will first summarise the evidence that there are particular values of Z and N (so called magic numbers) which are significant with regard to the structure of nuclei.

There are a large number of isotopes, isotones at these particular values of Z,N. This is also supported by the natural abundances of elements shown in the figure below.


Formative Evaluation 1

1 A beam of fast moving α -particles were directed towards thin film of gold.

The path A ' , B ' , and C ' of the transmitted beams corresponding to incident parts A,B and C of the beam are shown in the figure below The number of α-particles in

(a) C ' will be minimum and in B’ maximum

(b) A ' will be minimum and C’ maximum

(c) A ' will be maximum and B’ minimum

(d) B ' will be minimum and in C’ will be maximum.

2 An α -particle of energy 6MeV is projected toward a nucleus of atomic number 50. The distance of nearest approach is

(a) 2.4 ×10−10 m

(b) 2.4 ×10−12 m

(c) 2.4 ×10−14 m

(d) 90,2.4 ×10−20 m

3 The nucleus radius is of the order of

(a) 10−14 m

(b) 10−15 m

(c) 10−6 m

(d) 10−10 m

4 The difference between 92U 235 and

92U 238 atoms is that

(a) U238 contains 3 more neutrons

(b) U238 contains 3 more neutrons nd three more electrons

(c) U238 contains 3 more protons and 3 more electrons

(d) U238 contains 3 more protons

5 Which of the following statements is true for nuclear forces

(a) They are equal in strength to the electromagnetic forces(b) They are short range forces(c) They obey the inverse third power law of distance (d) They obey the inverse square law of distance


6 Of the three basic forces gravitational, electrostatic and nuclear which two are able to provide an attractive force between two neutrons

(a) gravitation and electrostatic(b) electrostatic and nuclear(c) gravitational and nuclear(d) some other forces like van der Waals

7 In a nucleus the total mass of protons and neutrons is less than the sum of their individual masses. This suggests that

(a) The mass defect accounts for the enrgy of the electrons surrounding the nu-cleus

(b) The mass defect accounts for the binding energy hoding he particles together in the nucleus

(c) The mass defect is due to electrons surrounding the nucleus (d) None of the above

8 The phenomenon of nuclear fission is used in the construction of

(a) an atom bomb(b) hydrogen bomb(c) an ordinary bomb (d) none of the above

9 Oxygen of atomic number 8 is known to have three stable isotopes of mass numbers 16,17 and 18. Which of the following statement is not correct?

(a) All atoms of different mass numbers have different chemical properties (b) Some atoms have 10 neutrons, some have 9 neutrons and some have only 8

neutrons(c) Each atom has 8 protons in the nucleus and 8 electrons outside the nucleus

10 The binding energies per nucleon for deuteron 1

H 2( ) and helium α ,β and γ are 1.1 MeV and 7.0 MeV respectively. The energy released when two neutrons

form a helium nucleus 2

He4( ) is

(a) 11.8MeV (b) 32.4MeV(c) 23.6MeV(d) 28MeV


11 which of the following does not obey inverse square law force

(a) electrostatic force (b) magnetic force between two poles(c) gravitational force (d) nuclear force

12 The mass density of a nucleus varies with mass number A as

(a) A2

(b) A(c) constant(d) 1/A

13 According to Yukawa the nuclear force arises though the exchange between nucleons of

(a) proton(b) photon(c) positron(d) meson

14 A neutron when disintegrates, gives

(a) a proton and an electron with a neutrino (b) a positron and an electron with a neutrin9o(c) a proton and a positron with a neutrino

(d) a proton and λ -radiation with a neutrino

15 In the disintegration chain 92U 238 → X →

ZZ A , the values of Z and A will be

(a) Z = 90, A = 234

(b) Z = 88, A = 232

(c) Z = 91, A = 234

(d) Z = 92, A = 236

16 If the binding energy of the deuterium is 2.23 Mev, the mass defect given in amu is (1 a.m.u =931 MeV)-

(a) 0.0024(b) -0.0012(c) 0.0012(d) 0.0024


17 K40 , Ar 40 and Ca40 are

(a) isotopes(b) isobars (c) isotones(d) isoganals

18 In a graph between binding energy per nucleon and mass numbers small peaks indicate that the corresponding elements are

(a) radioactive (b) less stable(c) comparably more stable(d) more abundant

19 Which of the following pairs is an isobar?

(a) 1 H 1 and 1H 2

(b) 1 H 2 and 1H 3

(c) 6 C 12 and 6C 13

(d) 15P 30 and

14Si30

20 Consider the following forces in nature I Gravitation II Strong III Electrostatic IV Weak. If the forces are arranged in decreasing magnitude the correct combi-nation is

(a) III, II,IV,I(b) II, III, IV,I(c) II,IV,III,I(d) I,II,IV,III

21 If 1 g of 92U 235 contains about 1019 atoms, the total amount of energy released

by it in fission is n×108 J where n is equal to

(a) 0.2(b) 1.2(c) 2.2(d) 3.2


22 The mass defect of an atom of mass M, atomic number Z and mass number A is given by

(a) a. M/A(b) M/ZA

(c) ( A− Z ) MP

(d) [ZM

p+ ( A− Z ) M

n− M ]

23 The order of magnitude of the density of nuclear matter is

(a) 104 kg/m2

(b) 1017 kg/m3

(c) 10−15 kg/m3

(d) 1034 kg/m3

24 Atomic weight of Boron is 10.81 and it has two isotopes 10B 5 and

5B11 . Then

the radio of 10B10 and

5B11 isotopes in nature would be

(a) 19:81(b) 10:11(c) 15:16(d) 81:19

Teaching the Content in Secondary School 1

The topic on atomic nucleus and the historical development of the theory is a typical example of how scientific theories are developed. Observation > formulation of theory to explain the observation > prediction by the theory > new observations and re-testing of existing theories > and modify, update, revise etc the existing theories.

The content may be delivered from the perspective of development. of theories in science.


Activity 2: Radioactivity

You will require 35 hours to complete this activity. In this activity you are guided with a series of readings, Multimedia clips, worked examples and self assessment questions and problems. You are strongly advised to go through the activities and consult all the compulsory materials and use as many as possible useful links and references.


• Describe radiations from the nucleus• Use radioactivity disintegration laws to solve problems• Identify and decide the type of equilibrium for a given series decay• Apply the radioactivity law (half life) in carbon dating


The phenomena of spontaneous disintegration of the nucleus of an atom with the emission of some radiations is called radioactivity. Radioactivity transforms unstable nuclei by giving rise toα , β or γ radiations.

The fundamental law of radioactive decay states the rate of transformation of a ra-dioactive nuclei is proportional to the number of atoms of the nuclei.

N = N

o

e− λ t

This is the basic law equation for radiactivity.

The intensity measurement of radioactivity is done in two units which are:

• Curie: Defined as the that quantity of radioactive material which gives

3.7 ×1010 disintegration per second .• Rutherford (Rd): It is defined as that amount of radioactive substance which

gives 106 disintegrations/sec. In nature there are radioactive elements that exhibit successive transforma-tion, i.e one element decays into a radioactive substance that is also radioac-tive. In successive radioactive transformation, if the number of nuclides of


any member of the chain is constant and not changing with time, it is called in radioactive equilibrium. The condition for equilibrium is are, therefore,

NP= −λ

PN

P= 0

dND

dt= −λ

DN

D= 0

or λP

NP= λ

DN

D

λP

NP= λ

GN

Getc.

where subscripts P, D and G stand for parent, daugheter and granddaughter respectively.

Study of radioactivty and radioisotopes has several applications in science and tech-nology. Some of them are:

1. Radioactive dating: 2. Trace element analysis:3. Medical application as diagnostic and treatment etc.


Reading 2: CHAPTER TWO

Complete reference: PHYSICS 481 Lecture Notes and Study Guide From Department of Physics Addis Ababa University, by Tilahun Tesfaye(PhD) .

Abstract: In this reference Bbasic relations of radioactivity;α , β and γ decays are explained. There are a number of solved numerical problems in each section and a set of problems provided at the end. of each section of the cahpter. Rationale: This chapter in the unit tallies with the content of this activity.



Resource #2: Nuclear Decay Simulator.

URL:- http://www.eserc.stonybrook.edu/ProjectJava/Radiation/index.html Complete Reference:- This applet offers an interactive representation of radioactive decay series. The four series represented are Th232, Pu241, U238, and U235. Use the radio buttons to select the series that you would like to study.


The Sequence Info button displays a chart that depicts the path of the series with atomic number indicated on the vertical axis on the left, and number of neutrons shown along the bottom. Colored arrows represent alpha and beta decays. To return to the main user interface, click the Dismiss button.

Initially, a selected series contains all parent material, and the amount is represented by a colored bar on a vertical logarithmic scale. Each line represents a factor of ten. In order to step forward through the sequence by a specified number of years, you may type the appropriate number into the Time Step field and hit Enter. By hitting Enter repeatedly, you can view the series at successive intervals. A negative time step will backtack through the sequence.

Click the Animate button to automate the progress through the series. You can either choose a time step before you animate, or leave it at zero. If the time step is left at zero, the system will choose time steps to optimize viewing performance.

The scrollable Activity Log on the right keeps a record of the amounts of the parent and all daughter products for each time increment.

Resource #3: Nuclear Decay Simulator.

U R L : - h t t p : / / m i c h e l e . u s c . e d u / j a v a / f i s s i o n / n u c l e a r . h t m l Complete Reference:- A Java simulator. Allows the user to set up a square box full of two different types of particles. Each can have distinct values for spontaneous decay rate, neutrons generated/fission and neutron capture rate. There is also an external neutron source which can be set to inject a varying number of neutrons

This applet is designed to mimic a sample of a radioactive material. When the applet starts up, you should get three windows: the simulator itself, the control panel and the graph window.

Inside the simulator window you will see a number of unmoving blue (and possibly green) spheres. These mimic atoms in a solid, which may fission when hit by a neutron, or might fission spontaneously. The blue and green atoms may behave differently from each other- the settings are in the control panel. There are also moving red balls- these are neutrons. When a neutron passes close to an atom, it may be absorbed by that atom. This may cause the atom to fission, releasing more neutrons and making the atom disappear. It’s also possible that an atom may just fission on it’s own, releasing neutrons. Once a neutron has left the simulator, it disappears.




Useful Link #2 ABC’s of Nuclear Science

Title: Radioactive decay URL: http://en.wikipedia.org/wiki/Radioactive_decay Screen Capture:

Description: Topics like Nuclear Structure, Radioactivity, Alpha Decay, Beta Decay, Gamma Decay, Half-Life, Reactions, Fusion, Fission, Cosmic Rays and Antimatter are discussed in this site. Further there are links to other sources for further reading.

Rationale: This site has comprehensive coverage of most of the nuclear physics topics dealt in this module. The learner can consult the links to see other lectures..



Introduction

The term `natural radioactivity’ applies to the spontaneous transformation of one nuclear species into anther with the emission of some particles (such as alpha, beta, antineutrinos, and neutrinos) another with the emission of particles or electromagnetic radiations (gamma-rays). Natural radioactivity is displayed by the heavy nuclei at the end of the periodic Table, beyond lead. There are also naturally radioactive light

nuclei, such as the potassium isotope 19

40 K , and the carbon isotope 614 C , to name but

a few.

2.1 Radioactivity, Discovery and Laws:

Pierre and Marie Curie found that the radiation from pitchblende was four times as strong as from uranium. This led to an intensive search for the source of this stronger radiation. Finally, in 1898, the curies succeeded in discovering two new substances

which they named polonium, 84

210 Po , and radium, 88

226 Ra

The substances emitting the newly discovered radiation were called radioactive, and the newly discovered property was named radioactivity by Mme M. Curie.

It was soon found that the rays from these radioactive substances were of three kinds, called alpha-rays, beta rays and gamma rays.

Alpha rays are positive; , beta-rays are negative, and gamma rays are uncharged.


Further investigations showed that alpha-rays were helium nuclei. A glass vial hol-

ding a sample of radon, a radioactive gas 86

222 Rn( ) was placed in a glass vessel from which practically all air had been evacuated. The alpha-particles emitted by the radon sample were absorbed by the walls of the vessel, each captured two electrons, and turned to helium atoms. These were driven from the walls of the vessel by heating.

The spectrum of the gas in the vessel was found to be identical with the emission spec-trum of helium, and this confirmed that the alpha-particles emitted by the radon sample turned to helium. Applying the methods of magnetic and electrostatic deflection.

Rutherford determined the specific charge,

qm

α

, of alpha particles (where m

α

is the mass of an alpha-particle) and found that their charge was 2e and the mass the

same as that of the nucleus of the helium isotope, 24 He .

Beta-rays are streams of very fast electrons whose velocity exceeds that of ordinary cathode (electron) rays and approaches that of light in a vacuum. Their energy is 10 MeV. The character of betarays has been confirmed by measuring their specific

charge, q / m

β, where

m

β is the mass of a beta-particle.

Gamma-rays are a hard electromagnetic radiation much more penetrating of all radioactive rays. The properties of gamma-rays mostly from their absorption and scattering by substances. It has been found that they cause a weak ionization in the material they traverse. Since they have higher frequencies (that is, shorter wavelengths) than X-rays, their quantum-mechanical properties stand out with special clarity.

Experiments have shown that all radioactive radiations casue:

• chemical effects, • blacken photographic plates, • ionize gases and, some solids and liquids to fluoresce.

These properties are at the basis of experimental techniques for the detection and investigation of radioactive rays

Laws Of Radioactive Disintegration

In his experiments on the identification of alpha-particles, Ruther ford found that the amount of radioactive radon decreased with time exponentially as exp(-bt) where b is the decay constant independent of the environments and the concentration of ra-

dioactive atoms. The disintegration of radium in RaC12 and RaBr

2 has been found

to be dependent solely on the number of radium atoms in the compounds, that is, the rate of the disintegration is independent of whether the sample is a pure element or


a compound. These facts have led to the conclusion that radioactive transformations are the property of nuclei which can undergo these transformations spontaneously.

The nuclear transformations accompanied by the emission of alpha- and beta-particles are called alpha- and beta-decay, respectively. Gamma-decay is non-existent. The nucleus that undergoes a decay is called the parent, the intermediate products are called daughters, and the final stable element is called the end product.

Experimental studies into radioactive disintegrations have led to the formulation of transition rules:

For alpha decay: z

A Xα decay

⎯ →⎯⎯Z-2

A-4Y +2

4 He

For beta decay: z

A Xβ decay

⎯ →⎯⎯Z+1

AY +−1

0β

Where X is the chemical symbol of the parent nucleus, Y is that of a daughter nucleus,

24 He is the helium nucleus (the end product), and −1

0 e is the electron of charge -1 (in units of elementary charge e) and of mass number zero, since the electronic mass is 1/1836 the protonic mass.

The transition rules are based on the conservation of charge and of mass number: the sum of charges (and of mass numbers) of the daughter nuclei and end products is equal to the charge (mass number) of the parent nucleus. This is exemplified by the decay scheme of radium with the emission of radon and an alpha-particle:

88

226 Raα

⎯ →⎯86

222 Rn +2

4 He

Thus, the alpha-transformation removes four units of mass and two units of charge, producing an element two steps down in the periodic Table. The beta-disintegration removes one negative charge and essentially no mass, producing an element one step higher in the periodic Table.

The daughter nucleus produced by radioactive decay is, as a rule, capable of further decay, and so is the next daughter produced by the decay of the first. Thus we have a radioactive series or chain. Each member of a radioactive series is a radioactive isotope (radioisotope) of the element occupying the respective square in the periodic Table.

The naturally radioactive nuclei form three radioactive series, namely:

• the Uranium series, (starts from 92

238 U and terminates in a stable 82

206 Pb )

• the Thorium series (starts from 90

232 Th and terminates in a stable 82

208 Pb ) and

• the Actinium series, (starts from 92

238 U and terminates in a stable 82

207 Pb )


thus called after the respective parents, 92

238 U,90

232 Th, and 89

235 AC There is one more

radioactive series produced artificially and starting with neptunium, 93

237 Np , a transu-ranic element. In each radioactive series, each nuclide transforms into the next through a chain of alpha- and beta disintegrations, each chain terminating in a stable isotopic

nucleus. The neptunium series terminates in the 83Bi 209 (bismuth) nucleus.

Even though we might not know which member of a given series undergoes radioactive decay by the emission of alpha or beta and beta-transitions should take place before the parent turns into a specified product nucleus. As an example, we shall take up the transformation of the uranium nucleus into the lead nucleus:

92

238 U →L→L→82

206 Pb.

The number nα of alpha transitions can be found at once by dividing the difference

in mass number between the parent and the end product by four, because each alpha

transition removes four units of mass. In our example, nα

= ( A1− A

2) / 4 = 8.

To find the number of beta transitions, we first determine the decrease in charge number: 92-82=10 units. However, it should be recalled that each alpha transition removes two units of charge, while each beta transition adds one unit of charge. Thus, the number of beta-transitions is given by the equation:

Z1− Z

2= 2n

α− nβ

2nα− n

β= 10

From the value of nα, we find that

nβ= 6 . Thus, the uranium nucleus undergoes eight

alpha transitions and six beta transitions before it transforms to the lead nucleus.

With time, the number of parent nuclei decreases because of radioactive decay. This decrease obeys a certain law which we seek to find. Let at the initial instant of time, t = 0 there be Δt nuclei of the same element that will remain untransformed by an arbitrary time t. Since we are dealing with spontaneous transformations, it is natural to assume that a greater number of nuclei will decay over a longer interval of time. Furthermore, the number of nuclei under going decay per unit of time (say, a minute) will be greater with a law of radioactive decay. If we have N untransformed nuclei present at time t, and N − ΔN untransformed nuclei existing at time t + Δt then change in the number of untransformed nuclei that is the number of nuclei decaying in time Δt will be proportional to N, that is:

ΔN : NΔt; or ΔN = -λNΔt


where λ is a positive proportionality factor called the decay constant; it has a de-finite value for each nuclear species. The minus sign on the right-hand side of the above equation indicates that ΔN decreases with time. Thus it follows that the decay constant is the fractional decreases in the number of nuclei decaying per unit time:

λ =

−ΔN N( )Δt

In other words, the decay constant represents the proportion of nuclei decaying per unit time, or the decay rate. The decay constant is independent of ambient conditions and is solely determined by the internal properties of the nucleus. It has dimensions

of λ = T −1.

In order to find the time dependence for radioactive decay. we can show that the number of atoms of the original kind remaining after time t is

N = N0exp(−λt)

where N0 is the initial number of radioactive nuclei existing at t=0 and N is the

number of radioactive nuclei present at t. A plot of in (N / N0) as a function of

time shows the decrease is exponential. The decay constant λ can be found from the slope of the curve.

In practice the stability of radioactive nuclei against decay and the decay rate are most

often estimated in terms of the half life, t1/ 2

, rather than the decay constantλ .

The half-life is defined as the time at which half of the original nuclei have decayed. Stated somewhat differently, the half-life is the time after which one half the original number of nuclei remains untransformed. Thus,

t = t

1/ 2, if N (t

1/ 2) =

N0

2

By this definition and on the basis of the exponential decay law, t1/ 2

and λ are re-lated as

N0

2= N

0 exp (-λt

1/ 2)


Cancelling N0 and taking a logarithm, we obtain

t1/ 2

=ln 2

λ=

0.693

λor

1

λ=

T0.693

= 1.44T

The half-lives of naturally radioactive elements range between wide limits. For ura-nium it is 4 500 million years, for radium 1590 years, for protactinium 32 000 years,

for radon 3.825 days, and for radium-C (an isotope of polonium) it is 1.5×10−4 s . For some induced radioactive elements the half-life is a few millionths or even hundred-millionths of a second.

The constancy of t1/ 2

(or λ) for a given radioactive element implies that these quantities represent huge numbers of atomic nuclei. Thus, radioactive decay is a statistical process.

The above definition of the half-life is sometimes incorrectly construed as implying

that the total number of nuclei in a sample will decay in a time equal to 2t

1/ 2. This is

not so because if the number of nuclei remaining after the time t1/ 2

is N0/ 2 , then

after the time 2t

1/ 2 this number will be falf the number N0

/2, or one-quarter of N0,

and in the time 3t

1/ 2 this number will be half of N0

/4 that is, N0/8, and so on.

African Virtual University 54

Activity And Its Measurement

It is natural to ask how one can measure a very long and a very short half-life. It is

obvious that the equation 0

tN N e λ−= cannot be used for this purpose directly. Help comes from the fact that the members a radioactive series are comes from the fact that the embers a radioactive series are radioactive, too. Generally, the number of daughter nuclei is changing with time as well. This will continue until the decay rate of a radioactive product (daughter nuclei) becomes just equal to its rate of formation from the previous member of the chain (the parent nuclei). This condition is called ideal equilibrium. Thus, at ideal equilibrium

p dN N

t t

Δ Δ=

Δ Δ and so, at equilibrium the following relation holds

p p d pN Nλ λ=

or

p pd

d p d

N T

N Tλ

λ= =

At ideal equilibrium, the numbers of parent and daughter nuclei are proportional to their half-lives. This relation is used in cases where the half-life of a nuclear species

is either too short or too long for direct determination from equation 0

tN N e λ−=

In the International System (SI) of units, activity is expressed in 1s− . A source is said to have one unit of activity if it undergoes one decay every second.

Activity is often expressed in curies. One curie (Ci) is the activity of 1g of radium, that is, the number of decays per second occurring in one gram of radium. Let us find this number.

The curie is a very large unit, because radium is a very active element, and the mass of one gram is a firly large amount for any practical preparation.This is why in practice use is made of submultiples of the curie, namely the millicurie (mCi) and

the microcurie ( )C iμ

3

6

1m 10 Ci

1 10 Ci

Ci

Ciμ

−

−

=

=


An alternative unit is the rutherford (Rd), a unit of radioactivity equal to 610 de-

cays per second, 6 11 10R d s−= . Obviously, 41 3.7 10 .C i R d= ×

Example

The half-life of radium equal to 1590 years. Find its decay constantλ . and deter-mine the number of nuclei in one gram of radium.

Solution

The the number of radium atoms per gram. It is equal to Avogadro’s number, AN , divided by the mass of one kilomole, M:

2624 1

24 -1

6.023 10 1/ kmole/ 2.67 10 kg

226 kg/kmole

=2.67 10 g

AN N M −× ×= = = ×

×Then the activity of one gram of radium will be

21

10 1

0.6930.693 / 2.67 10

1590 365 24 3600 3.7 10

A N N T

s

λ

−

= = = ×× × ×

= ×

That is, the number of decays per second in one gram of radium is 37000 milion

The definition of the cirie used at present reads as follows: The curie is a unit of radioactivity defined as the quantity of any radioactive nuclide in which the num-

ber of decays per second is 103.7 10× .


Radioactive Decay As A Statistical Process

The law of radioactive decay, has been derived on the assumption that radioactive

decay in a given time interval tΔ . The point is that all nuclei of a given chemical element are undistinguishable. The best we can do is to find an average number of

nuclei decaying in the time interval from to t tΔ . Thus, what we have is a statisti-cal process, that is, the decay of a given nucleus is a random event having a certain probability of occurrence.

The decay probability per unit time per nucleus may be derived as follows. If we

have N original nuclei and the number decaying in a time tΔ is NΔ , then the rela-

tive decrease, /N N−Δ , in the number of nuclei per unit time, that is, the quantity

- ( / )N N tΔ Δ gives the decay probability per unit time per nucleus.

This definition agrees with the meaning of the decay constant, λ . By definition, the decay constant is the decay probability pre unit time per unit nucleus.

For further discussion of this point look in the compulsory reading by the same author.

2.3 Application of Radioactivity

Radioactive Dating

The decrease in the number of radioactive nuclei according to radioactive decay law, may be used as a means for measuring the time that passes since a specimen known

to contain 0N radioactive atoms initially and the instant when their number is N . In other words, radioactivity provides a kind of time scale. According to the law of

radioactivity: 0

tN N e λ−= , the time interval between the instants when the number

of radioactive nuclei is 0 N and N is

0 01 / 2

N N1ln 1.44 ln

N Nt t

λ⎛ ⎞ ⎛ ⎞⎛ ⎞= =⎜ ⎟ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ ⎝ ⎠

As a rule, N represents the number of unchanged nuclei at the present time, so that aboe equation gives the age the specimen containing the radioactive nuclei

In geologic studies, a different radioactive time scale is required for each application. In determining the age of rocks, for example, one should use a sufficiently slow ra-dioactive time scale, that is, radioactive decays with a half-life of the same order of magnitude as geological epochs, running in to hundreds of millions or even millions


of millions of years. This condition is satisfied by the half-live of 238 U and 235 U . Naturally occurring uranium is actually a mixture of both. Their half-lives are 4500 million and 900 million years, respectively.

At present, chemically pure and naturally occurring uranium contains 238

9299.28% U, 235

920.714% U, 23492 0.006% U the latter being the decay product of 238 U . Since

its content is very small, 234 U may be neglected. Each of the 238 U and 234 U iso-topes is the parent of a radioactive series of its own, both of which terminate in lead isotopes. Thus, lead nuclei are the end products of the radioactive decay of uranium nuclei. Using the ratio between uranium and the lead derived from it in natural ura-nium, one can readily determine the time interval during which this amount of lead has accumulated.

In archaeology, radioactivity is used to date the objects found in excavations. In such applications, the uranium time scale is unsuitable for at least two reasons. For one thing, artefacts have never contained uranium. For another, the uranium time scale clock is too slow for human history where time is usually measured in centuries or millennia. In other words, archaeological dating one needs a radioactive time scale with a half-life of a few centuries or millennia. Nature has provided such time sca-les.

The particles that make up the so-called primary cosmic rays are extremely energe-tic and, colliding with the nuclei of the elements that form the Earth’s atmosphere, break them up into fragments These fragments are highly energetic, too, and form the so-called secondary cosmic rays. The interaction of cosmic rays with the nuclei of atmospheric nitrogen turns them into the nuclei of carbon with mass number 14,

instead of 12, as with ordinary carbon. 146 C has a half life of about 5570 years,

which fits archaeologists well. Moreover, because the intensity of primary cosmic rays remains practically constant, there is an unvarying supply of radioactive carbon in the atmosphere. Radioactive carbon produces radioactive carbon dioxide through

plants and the food cahain 146 C , finds its way into animals and becomes part of their

organs and tissues.

In a living plant or animal, the per cent content of radioactive carbon in comparison with the ordinary carbon dos not change with time, because any losses are made good by food. If, however, a plant or an animal dies, food cannot replenish the loss of radioactive carbon any longer. Thus, one can determine the time passing since the death of the organism or the age of an artifice made of an organic material.

Using a charged particle counter, it has been found 146 C decays by emission of beta

particles that one gram of radioactive carbon contained in the in the cellulose of a living or a recently activity of the radioactive isotope is 17.5 particles per minute. That is, the activity of the radioactive isotope is 17.5 decays per minute. Converting


1 / 2 5570t = years into minutes, we find the number of 146 C nuclei that have this

magnitude of activity:

1/ 2

10

(1/ )( / )

1.44 ( / )

1.44 5570 365 24 60 1.75

7.5 10

N N tt N tλ= Δ Δ

= Δ Δ

= × × × × ×

≈ × Thus, one gram of carbon in the cellulose of a living or a recently cut tree contains 75 000 million nuclei of radioactive carbon. This number progressively decreases because it is not replenished (and this happens when the tree is cut), the original number will decrease with time. That is, the activity of the remaining radio active carbon will decrease progressively. If we compare its present activity to the activity that was present when the wood was cut down, we can determine the time interval between these two instants.

When this technique is applied to wooden artefacts usually found in archaeological excavations, one actually finds the time at which a tree was cut. This gives the age of the artefacts made from it.



1) How do the electric charges of alpha, beta and gamma rays differ? Ans. The alpha ‘ray’ consists of alpha particles. Each alpha particle has a + 2 charge. The beta ‘ray’ consists of electrons. Each electron has a -1 charge. A magnetic field will push the oppositely charged particles in opposite direc-tions. The gamma ray consists of photons of light. They are not charged at all.

2) How does the source differ for a beam of gamma rays and a beam of X rays. Ans. Gamma rays come from the nuclei of some atoms. X rays come from the reconfiguration of electrons surrounding the nucleus of an atom. They may also be produced when an electron undergoes a large acceleration.

3) Give two examples of a nucleon. Ans.. Protons and neutrons are found in the nuclei of atoms and are therefor called nucleons.

4) Give the atomic number for deuterium and for tritium. Ans. Deuterium and tritium are both isotopes of hydrogen. Deuterium has one proton and one neutron while tritium has one proton and two neutrons. The both have atomic number 1.

5) How does the mass of a nucleon compare with the mass of an electron. Ans. One nucleon is approximately 1800 times more massive than an electron.

6) When beta emission occurs, what change takes place in an atomic nucleus? Ans. Beta emission occurs when a neutron emits an electron. The neutron changes into a proton in the process. The atomic nucleus now has one more proton that before the emission and thus is now an atom of a different element.

7) Distinguish between an isotope and an ion. Ans.. An isotope of an element has a different number of neutrons than a different isotope of the same element. An ion is a charged atom. It is charged because it does not have the same number of protons as electrons.

8) What is meant by radioactive half-life? Ans. Radioactive half-life is the time required for one half the remaining radioactive nuclei to undergo radioactive decay.

9) When thorium, atomic number 90, decays by emitting an alpha particle, what is the atomic number of the resulting nucleus. What happens to its atomic mass? Ans. An alpha particle consists of two protons and two neutrons. When thorium undergoes alpha decay, the remaining nucleus will have 88 protons instead of 90. The new atom will be atomic number 88, which is radium-a different element than before. The alpha particle consists of two protons and two neutrons. Alpha decay reduces the atomic mass by four.


10) When thorium decays by emitting a beta particle(an electron), what is the atomic number of the resulting nucleus? What happens to its atomic mass? Ans. When a nucleus undergoes beta decay, one of its neutrons changes into a proton as it emits an electron. Therefore, the atomic number increases by one. The new atomic number will be 91. Although the fleeing electron carries a tiny bit of mass away with it, the atomic mass of the atom does not change.

11) What is the effect on the makeup of a nucleus when it emits an alpha particle? A beta particle? A gamma ray? Ans. When the nucleus of an atom emits an alpha particle, it loses two protons and two neutrons. When the nucleus of an atom emits a beta particle a neu-tron changes to a proton. When the nucleus of an atom emits a gamma ray the nucleus reconfigures itself to a less energetic state.

12) Which isotope of carbon is radioactive? Carbon-12 or Carbon -14 Ans. Carbon-14 is a radioactive isotope of carbon.

13) Why is there more C-14 in new bones than there is in old bones of the same mass? Ans. Carbon-14 changes to Nitrogen-14 with a half-life of 5,730 years. So the amount of Carbon-14 present in a substance is reduced over time

14) X rays are most similar to which of the following: alpha, beta, or gamma? Ans. X rays and gamma rays are most similar because they are both photons of light. The others are not.

15) Some people say that all things are possible. Is it at all possible for a hydro-gen nucleus to emit an alpha particle? Explain your answer. Ans. A hydrogen nucleus contains only one proton and zero, one or two neu-trons. An alpha particle consists of two protons and two neutrons. Therefore a hydrogen atom cannot emit an alpha particle. It cannot emit what it doesn’t have.

16) Why are alpha and beta rays deflected in opposite directions in a magnetic field? Why aren’t gamma rays deflected? Ans. Alpha rays consist of positively charged helium nuclei. Beta rays consist of negatively charged electrons. Gamma rays are uncharged photons of light. A magnetic field will apply a force to a moving charged particle. Positively charged particles are accelerated in one direction and negative charged par-ticles are accelerated in the opposite direction. Because gamma rays are not charged, they are unaffected by the magnetic field.

17) The alpha particle has twice the electric charge of the beta particle but, for the same velocity, accelerates less than the beta in a magnetic field. Why? Ans. From Newton’s second law of motion we know that acceleration is directly proportional to the net force applied to an object and inversely propor-tional to the objects mass. Although the force applied to the alpha particle is twice that applied to the beta particle, the alpha particle is approximately 3600 times more massive than the beta.


18) Which type of radiation results in the greatest change in atomic mass? Atomic number? Ans. Alpha radiation. Alpha radiation. The resulting nucleus will be missing two protons and two neutrons. The atomic mass will be four less than the original and the atomic number will be two fewer than the original.

19) Which type of radiation results in the least change in atomic mass? The least change in atomic number? Ans. Gamma radiation. There is no change in mass number or atomic num-ber because a gamma ray is a photon of light.

20) In bombarding atomic nuclei with proton «bullets», why must the protons be accelerated to high energies if they are to make contact with the target nuclei? Ans. Atomic nuclei are positively charged. The proton «bullets» are positi-vely charged. They will be repelled away from each other by the electroma-gnetic force.

21) The amount of radiation from a point source is inversely proportional to the distance from the source. If a Geiger counter 1 meter from a small sample reads 360 counts per minute, what will be its counting rate 2 meters from the source? 3 meters from the source?

Ans. Doubling the distance will result in a count of ( )2

11 2 4= the original count. 1/4 of 360 = 90 counts per minute. Tripling the distance will result in

( )2

11 3 9= the original count. 1/9 of 360 = 40 counts per minute.

22) When 22688 Ra decays by emitting an alpha particle, what is the atomic number

of the resulting nucleus? What is the name of the element? Ans. When the nucleus of an atom emits an alpha particle, it loses two protons and two neutrons. The remaining nucleus will be atomic number 86 and its mass number will be 222. The reaction can be written as follows:

226 222 4

88 86 2Ra Ra He→ +

23) When 21884 Po emits a beta particle, it transforms into a new element.

a) What are the atomic number and atomic mass of this new element? b) What are atomic number and atomic mass if the polonium instead emits an

alpha particle? Ans.a) Beta emission occurs when a neutron emits an electron as it changes into

a proton. When emits a beta particle, its atomic number increases by one and its atomic mass remains unchanged. The resulting atom will be ato-mic number 85 and its atomic mass is 218. The reaction can be written as follows:


218 218 084 85 1Po At 0

-1 where represents the emitted electron,−→ + β β b) When the nucleus of an atom emits an alpha particle, it loses two

protons and two neutrons. If 21884 Po emits an alpha particle its new ato-

mic number will be 82 and its new atomic mass will be 214. The reac-tion can be written as follows: 218 214 4

84 82 2Po Pb He→ +

24) State the number of protons and neutrons in each of the following nuclei:

2 12 56 197 90 2381 6 26 79 38 92H C Fe Au Sr and U, , , , , Ans. Hydrogen 2 has 1 proton and 1 neutron. Carbon 12 has 6 protons and 6 neutrons. Iron 56 has 26 protons and 30 neutrons. Gold 197 has 79 protons and 118 neutrons. Strontium 90 has 38 protons and 52 neutrons. Uranium 238 has 92 protons and 146 neutrons.

25) How is it possible for an element to decay forward in the periodic table-that is, to decay to an element of higher atomic number? Ans. When the nucleus of an atom of an element undergoes beta decay, one of its neutrons changes to a proton as it emits an electron. This will increase the number of protons and therefor the atomic number, by one.

26) If a sample of a radioactive isotope has a half-life of 1 year, how much of the original sample will be left:

a) At the end of one year? Ans.1/2

b) At the end of two years? Ans. 1/4

c) At the end of three years? Ans. 1/8

27) A sample of a particular radioisotope is placed near a Geiger counter, which is observed to register 160 counts per minute. Eight hours later the detector counts at a rate of 10 counts per minute. What is the half-life of the material? Ans. The half-life is 2 hours. Here is my reasoning. If you cut 160 in half you will have 80. 1/2 of 80 = 40. 1/2 of 40 = 20. 1/2 of 20 = 10. We repea-ted this process 4 times. Four half-lives have elapsed. Eight hours divided by 4, equals 2 hours.



Counting statistics, using GM tube may be a good approach to deliver contents on radioactivity. Introductory physics students will recognize that radioactivity is used in medicine, agriculture and industrial applications. Relating these applications to the demonstrations, laboratory exercises, and solutions of problems will help in teaching this concept.


Activity 3: Interaction of Radiation with Matter



• Describe interaction of light charged and heavy charged particles with mat-ter

• Identify and describe the four major interactions of photons with matter• Use cross sections and coefficients of interaction to solve problems• Describe gas filled, scintillation and semiconductor detectors (construction,

principle and use)


When charged particles pass through matter they lose energy to the medium by the following processes.

i. Inelastic collisions with orbital electrons (excitation and ionisation of atoms),

ii. Radiative losses in the field of nuclei (Bremsstrahlung emission), iii. Elastic scattering with nuclei and iv. Elastic scattering with orbital electrons.

Which of these interactions actually take place is a matter of chance. However ener-getic electrons lose energy mainly by inelastic collisions which produce ionisation and excitation, and also by radiation. Charged particles in general lose energy mainly by the coulomb interactions with the atomic electrons. If the energy transferred to the electrons in an atom is sufficient to raise it to higher energy state in the atom, this process is called excitation. If the energy transferred is more, the electron is ejected out of this system. This process is called ionisation.


Photons may interact with the atomic electrons, with the nucleons or with the field produced by them. The probability of interaction depends on the atomic number Z of the material and the energy of the photon. as summarized in the table below.

Type of interaction →

Interaction with

↓

Absorption Elastic scattering

(Coherent)

Inelastic scattering

(Incoherent)

I. Atomic electrons

Photoelectric effect:

4

pe

5

T (low energy)

(high energy)

Z

Z

∝

∝

Rayleigh scattering

2 (low energy limit)R Zσ ∝

Compton scattering

Zσ ∝

II. Nucleons Photonuclear reactions:

( )( )( ), , , etc,

Z (h 10 MeV)

n p fγ γ γ

ν∝ ≥

Elastic nuclear scattering Nuclear resonance Scattering

III. Electric field of charged particles

Pair production

a) ( 1.02MeV)

b) ( 2.04MeV)n

e

k Z h

k Z h

ν

ν

∝ ≥

∝ ≥

Delbrück scattering

IV. Mesons Photomeson production

140h MeVν ≥



Reading 3: CHAPTER THREE .

Complete reference: PHYSICS 481 Lecture Notes and Study Guide From Department of Physics Addis Ababa University, by Tilahun Tesfaye(PhD) . Abstract: This Reading contains a detailed account of interaction of heavy and li-ght charged particles with matter. Interaction of photons is also discussed in detail. Gas field, scintillation and solid-state detectors are also discussed. Rationale: This chapter tallies well with the first activity of this module.



Resource #3

Title : Cal Poly Physics Department’s Virtual Radiation Laboratory (Geiger Counter) URL:-: http://www.csupomona.edu/~pbsiegel/www/Geiger_Counter/Geiger.html Date Consulted:-Jan 2008 Description:- The virtual Geiger counter operates similar to the real one. The Gei-ger counter has two sample holders. In each sample holder you can pick either an empty holder, Ba137m or Mn54 (5 μ Ci). The detector has a dead time, and there is a background. The buttons are similar to a real Geiger counter. To operate: set the counting time and click start. Counting stops after the counting time. Then clear the counter. To record counts from the Ba137m samples, you need to select the sample and click on “squeeze out Ba”. Squeezing out the sample refreshes the Ba source, which has a short half life. The button refreshes both sources when clicked. The sources are only counted when they are in the sample holder.

Experiments that can be done using this virtual lab are

1. Dead time measurement: Measurement of the detector’s dead time2. Statistics of Nuclear Decay: Examine if the detector’s counts follow a Poisson

distribution. 3. Efficiency measurement of the detector 4. Half-life of Ba137: Take data on Ba137 and determine its half-life. Remember

to account for background and dead time


Resource #4

Title : Cal Poly Physics Department’s Virtual Radiation Laboratory (NaI Gamma Detector) URL:-: http://www.csupomona.edu/~pbsiegel/www/naidat/Detector.html

Date Consulted:-Jan 2008 Description:- Using this virtual NaI detector you can calibrate the detector for energy and determine the energy of unknown gamma source.

To run the applet, click on gamma detector (Calibration) . You will see the MCA screen with 1024 channels. The samples include three standards and an unknown. The unknown is a single isotope. Your goal is to determine the photopeak energies and the identity of the unknown. The energy of the detected gamma is (approxima-tely) proportional to the channel number. Use the standards Cs137 (661.64 KeV), Na22(511.0034 and 1274.5 KeV), and Mn54(834.827 KeV) to determine the para-meters of the linear (or quadratic) relationship between channel number and energy. Then find the channel numbers of the photopeaks of the unknown, determine their energies from your calibration line, and interpolate to find the gamma energies of the unknown. To assist you, a table of gamma energies (be patient, it takes a while to load) is supplied.

This virtual laboratory also helps you determine half life of K40; attenuation of Gamma radiation in Lead Experiment and attenuation of X-rays in Aluminium experiment.




Useful Link #3 MIT OPEN COURSEWARE

Title: Interaction of Radiation with Matter URL: http://en.wikipedia.org/wiki/Law_of_universal_gravitation

Screen Capture:

Description: Basic principles of interaction of electromagnetic radiation, ther-mal neutrons, and charged particles with matter. Introduces classical electro-dynamics, quantum theory of radiation, time-dependent perturbation theory, transition probabilities and cross sections describing interaction of various radiations with atomic systems. Applications include theory of nuclear magne-tic resonance; Rayleigh, Raman, and Compton scattering; photoelectric effect; and use of thermal neutron scattering as a tool in condensed matter research.. Rationale: The site provides a detailed description and solved problems on the topic. . Date Consulted: - JANUARY 2008



Introduction

When a charged particle, like electron, proton, alpha particle etc., passes through matter it loses energy as a result of electromagnetic interactions with the atoms and molecules of the surrounding medium. These interaction mechanisms are:

1. Inelastic collisions with orbital electrons (excitation and ionisation of atoms),

2. Radiative losses in the field of nuclei (Bremsstrahlung emission),3. Elastic scattering with nuclei and4. Elastic scattering with orbital electrons.

Which of these interactions actually take place is a matter of chance. The character of these interactions and the mechanism of the energy loss depends on the charge and velocity of the particle and on the characteristics of the medium

Charged particles are classified mainly into two groups: heavy particles of mass comparable with the nuclear mass (protons, alpha particles, mesons, and atomic and molecular ions), and electrons.

3.1 Interaction of Heavy and Light Charged Particles with Matter

Charged particles in general lose energy mainly by the coulomb interactions with the atomic electrons. If the energy transferred to the electrons in an atom is sufficient to raise it to higher energy state in the atom, this process is called excitation. If the energy transferred is more, the electron is ejected out of its atom. This process is cal-led ionisation. These two processes are closely associated and together constitute the energy loss by inelastic collision. The ejected electron will lose its kinetic energy and finally attach itself to another atom thereby making it a negative ion. These together constitute an ion pair. Some of the electrons ejected may have sufficient energy to

produce further ionisation. Such electrons are called delta ( )δ rays. In any case, the energy for these processes comes from the kinetic energy of the incident particle, which is slowed down.


3.1.1 Interaction of Heavy Charged Particles with Matter

Energy-Loss Mechanisms

• Coulombic interactions between the particle and electrons in the medium is the the basic mechanism for the slowing down of a moving charged particle in a material medium. This is common to all charged particles

• A heavy charged particle traversing matter loses energy primarily through the ionization and excitation of atoms

• The moving charged particle exerts electromagnetic forces on atomic electrons and imparts energy to them. The energy transferred may be sufficient to knock an electron out of an atom and thus ionize it, or it may leave the atom in an excited, nonionized state.

• A heavy charged particle can transfer only a small fraction of its energy in a single electronic collision. Its deflection in the collision is negligible.

• All heavy charged particles travel essentially straight paths in matter.

One of the quatntieties of interest in describing interaction of heavy charged particles

in matter is the stopping power ( )dE dx− defined by:

4 2

2coll o

2 2 2o

2 2

-dE 4 e zS NZB Beth formula for stopping power

dx m v

2m vwhere B ln ln 1

l

v vc c

π⎛ ⎞= =⎜ ⎟⎝ ⎠

⎡ ⎤⎛ ⎞≡ − − −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

where ze is the charge of the incident particle, v its velocity, N the number density of atoms (number of atoms per unit volume) of the material having atomic number

Z , om the electron rest mass and e the electron charge. The quantity I is a material property called the mean excitation energy, which is a logarithmic average of the excitation energies of the medium eighted by the corresponding oscillator strengths. Except for elements ith very low atomic number Z , the mean excitation energies in eV are pproximately to 10Z .


3.2 Interaction of Photons with Matter.

Interaction of photons with matter by which individual photons are removed or de-flected from a primary beam of x or γ-radiation, may be classified according to:

i. the kind of target, e.g. electrons, atoms or nuclei with which the photon inte-racts.

ii. the type of event, e.g. scattering, absorption, pair-production etc. which takes place.

The interactions taking place with atomic electrons are:

i. Photoelectric effect (Absorption)ii. Rayleigh scattering (Scattering)iii. Compton scattering (Scattering)iv. Two photon Compton scattering (Multi photon effect)

The interactions which occur with nucleons are:

i. Photonuclear reactions (γ,n), (γ,p), photo-fission etc. (Absorption).

ii. Elastic nuclear scattering (γ,γ) (Scattering)

iii. Inelastic nuclear scattering (γ,γ/) (Scattering)

The interactions with electric field surrounding charged particle are:

i. Electron-positron pair production in the field of nucleus (Absorption)ii. Electron-positron pair production in electron field (Absorption)iii. Nucleon-anti-nucleon pair production (Absorption)iv. The interactions occurring with mesons are:

i) Photo-meson production (Absorption)

ii) Modified (γ,γ) (Scattering)

But out of all these interaction processes, five main processes are:

i. Photoelectric effectii. Compton scatteringiii. Pair productioniv. Rayleigh scatteringv. Photo-nuclear interactions

And of these even, first three are the most important, as they result in the transfer of energy to electrons, which then impart that energy to matter in many coulomb-force interactions along their tracks. Rayleigh scattering is elastic, the photon is merely redirected through a small angle without any loss of energy. Photonuclear interactions are only significant for photon energies above a few MeV. In the following subsec-tions, the individual interaction processes are discussed.


Task 3.1 Question for discussion

Discuss the following questions with your colleagues or on the discussion forum of AVU

1. What are the most important interaction mechanisms by which photon energies are degraded in a material medium?

2. What is the reason for protection against ionizing radiation?

3.4 Nuclear Radiation Detectors

3.4.1 Gass Field Detectors

Gas Filled Radiation Detectors(GFRD) are the oldest of all radiation detectors and are still being used

GFRD’s principle of operation: When fast charged particles passes through a gas, the type of interaction is to create both excited molecules and ionized molecules along its path. After a neutral molecule is ionized, the resulting positive ion and free electron are called an ion pair, and it serves as the basic constituent of the electrical signal. Ions can be formed either by direct interaction with the incident particle, or through secondary process in which some of the particle energy is first transferred to an energetic electrons.

Regardless of the detailed mechanisms involved, the practical quantity of interest is the total number of ion pairs created along the track of the radiation The simplest of GFRD consists merely of two electrodes in a gas chamber; the walls of the chamber are constructed to permit penetration by the radiation of interest. The oldest but still very useful gas-filled nuclear radiation detector types are:

(i) The ionization chamber(ii) The proportional counter(iii) The Geiger Muller (GM) counter

Figure shows Gas Filled Radiation Detector (GFRD) and associated simplified cir-cuit. Voltage is applied between the cathode (the wall of the tubular gas container) and the anode (the central wire, insulated from the tube wall). Current in the external circuit is governed by the conductivity of the gas inside the tube and consequently by its ionization.


In the absence of ionization, the gas behaves like insulator and no current flows in the external circuit. However the behaviour of ion pairs generated inside the GFRD depends on electric field present, type of gas/gas-mixture, pressure inside the detector and detector geometry etc.

Figure above shows characteristic curves for GFRD with both

(i) for alpha and(ii) for beta particle radiation. Increasing voltage between anode to cathode reveals

five regions.


Region I: Recombination region

In the region I there is a competition between the loss of ion pairs by recombination and the removal of charge by collection on the electrodes. With increasing electric field the drift velocity of the ions increases;therefore the time available for recom-bination decreases, and the fraction of the charge which is collected becomes larger. GFRDs are not operated in this region.

Region II: Ionization Chamber region

Due to sufficient electric field the ion pairs are forced to drift towards the electrodes in region II, and because recombination is delayed or prevented, many reach the electrodes. Current in this region depends almost exclusively upon the number of ions generated by the radiation, and is almost independent of the exact value of the applied voltage. This region is referred to as the saturation region or the Ionization chamber region.

Region III: Proportional Counter region

In Region III, electrons are accelerated to high velocities and produce secondary ions by collision, leading to a multiplication of charge. This region, in which gas multipli-cation is employed while at the same time a dependence of the collected charge on the initial ionization remains, is known commonly as the proportional counter region.

Ion-multiplication gains of up to ~103-105 are attainable in this method of operation. (The upper end of Region III is generally known as ’the region of limited propor-tionality’ where output becomes more dependent on applied voltage than on initial ionization.)

Region IV: Geiger Region

Ion-multiplication escalates in region IV and, in the ensuing ’avalanche’, virtually all primary and secondary electrons are accelerated sufficiently to create more secondary and tertiary ions. Though the detector can no longer distinguish between the different kinds of radiation or between different energies in this region, detection sensitivity is excellent. Geiger Muller tubes operate in this region which is also often called the ’Geiger Muller plateau’.

Region V: Discharge region

Further escalation of avalanche in Region V produces total ionization of the gas between the electrodes. A self-sustaining discharge, which will continue as long as voltage is applied, can be instigated by a single pulse. This type of discharge can be harmful to the detector and lengthy operation in this region should be avoided.


2.2.2 Scintilation Detectors

Scintillatior can be used for ionizing radiation detection and spectroscopy of a wide assortment of radiation. Availability of scintillators in various physical forms (i.e. solid, liquid and gas), availability of excellent photon detectors like Photomultiplier tubes, solid-state photon detectors and microelectronics for processing signals makes these detectors quite useful for variety of applications.

Following are the sequential events which takes place while detecting ionizing ra-diation:

• The absorption of nuclear radiation in the scintillator, resulting in excitation and ionization within it.

• The conversion of the energy dissipated in the scintillator to light energy through the luminescence process.

• The transit of light photons to the photocathode of the photomultiplier tube.• The absorption of the light photons at the photo cathode and the emission of

the photoelectrons and subsequent electron multiplication process within the photomultiplier tube.

• The analysis of the current pulses furnished by the photo multiplier tube through the use of the succeeding electronic equipment like an electronic counter or a multi-channel analyser (MCA).



1) List four sources of ionizing radiation.

2) It is a primordial radioactive isotope and yet not part of naturally occurring decay series? Which isotope is it?

3) The energy of Compton scattered photon versus the energy of the incident photon is shown below

Figure Kinematic Relationship of incident and scattered photon

a) Interpret the graph for the incident photon energies < 0:01 keV.b) For which angle of photon scattering does the scattered electron took grea-

ter share of energy. For Á = 90± or Á = 45±.

4) charged particle radiation travel in straight line, except at distances close to the range, in materials. Explain

5) Compared to photon radiation, charged particle radiation causes more damage in a tissue despite its weak penetrating power. explain


Activity 4: Nuclear Forces and Elementary Particles



• Identify fundamental interactions in nature• Explain Yukawa’s theory of nuclear force• Identify elementary particles and describe their role in the process of interac-

tion


In this activity description of the four fundamental forces and their relative strength is described qualitatively. Yukawa’s theory of nuclear forces is explained

The terms antiparticle, fermion, boson, lepton, hadron, meson and baryon are explai-ned. The concepts of charge conservation, baryon number conservation, and lepton number conservation are explained and applied.

List of Required Readings (for the Learning Activity).

Copyright free readings should also be given in electronic form (to be provided on a CD with the module)


Reading 4: Fundamental Forces And Elementary Particle Classification

Complete reference: http://35.9.69.219/home/modules/pdf_modules/m255.pdf Abstract: I This is a module from the PHYSNET PROJECT, Elementary parti-cles are described in a lucid manner and the module has questions for revision and glossary at the end. Rationale: This chapter in the unit tallies with the content of this activity.



Introduction

Nuclear force is one of the four interactions existing in nature. The discussion and explanation of nuclear force is connected with the physics of elementary particles. In the first part of this activity you will study the four fundamental interactions in nature. In the second part theories explaining nuclear force will be studied in more detail. The final section of this activity you will look into elementary particles with emphasis in their role in the nuclear interaction and interaction between elementary particles. .

4.1 Fundamental Interactions in Nature

There are four fundamental interactions in nature vis strong (Nuclear); Electroma-gnetic; weak and gravitational. Table below shows therlative strengths of the four basic interactions.

Type of Interaction Relative Strength Range

Gravitational

3910−: ∞

Weak (eg. Beta decay)

1310−: almost zero

Electromagnetic

210−: ∞

Strong (Nuclear)

1 1410 m−:

The forces of gravity and electromagnetism are familiar forces in everyday life. The strong and weak interactions are new forces introduced when discussing nuclear phenomena. When two protons encounter each other, they experience all four of the fundamental forces of nature simultaneously. The weak force governs beta decay and neutrino interactions with nuclei. The strong force, which we generally call the nuclear force, is actually the force responsible for binding of nucleons.


Nuclear Forces

The forces operating between nucleons in a nucleus are called nuclear forces. An idea about these forces can be gained from general considerations. The stability of nuclei and the release of energy as a nucleus is formed from nucleons are indications that up to a certain distance between the nucleons, nuclear forces are those of attraction.

Nuclear forces cannot be ordinary electrostatic forces, for then a stable nucleus com-posed of a proton and a neutron would be inconceivable. Yet, such a nucleus does

exist as the neutron, the nucleus of heavy hydrogen or deuterium, 21 .D The deuteron

is a stable system with a binding energy of 2.2 MeV.

The nucleus occupies a finite element of space, and within this element the nucleons must be a definite distances apart. Obviously at a certain distance, attractive force gives way to repulsive force. The distance at which this transition occurs is expressed in terms of fermis (fm). The fermi defined as

151 10 cmfm −=

The fermi is not unlike the unit of the first Bohr radius in the hydrogen atom used in the measurement of distances in atomic physics. Observations and theory have revealed some other properties of nuclear forces.

Properties of Nuclear Forces

1. Nuclear Forces are Short range: nuclear forces have been found to be short-range forces,. very short range, with essentially no effect beyond nuclear dimensions The distance of 2.2 fm has come to be known as the range of nuclear forces.

2. Nuclear forces are charge-independent. That is, interactions between two nucleons are independent of whether one or both nucleons have electric charge. In other words, neutron-neutron, neutron proton and proton-proton interactions are almost identical in character. Thus, as regards specifically nuclear interactions, protons and neutrons are identical particles. The charge independence of nuclear forces has been established from experiments on the scattering of protons by neutrons and of neutrons by protons.

3. Nuclear forces are noncentral, or tensor, forces, that is, those whose direction depends in part on the spin orientation of the nucleons, which may be parallel or anti-parallel. This has clearly been shown by experiments on the scattering of neutrons by the molecules of parahydrogen and orthohydrogen. A molecule of parahydrogen differs from that of orthohydrogen in that in the former the protons have anti-parallel spin orientation, and in the latter, parallel spin orientation. If the interaction between nucleons were independent of spin orientation, neutrons would be scattered identically by orthohydrogen and parahydrogen. Observa-tions have testified to the opposite, that is, nuclear forces are dependent on spin orientation.

4. Nuclear forces are saturable: that is a nucleon can attract only a few of its nearest neighbors.


4.2 Elementary Particles

The discussion and explanation of nuclear force is connected with the physics of elementary particles. Among the particles that are of importance in nuclear physicsare the ones given in table below.

Many of these particles have their anti-matter counterpart. For example there is

anti proton -p for p, for β − there is β + , for κ + there is κ − for −Ξ there is +Ξ etc. When a particle and its antiparticle meet they annihilate each other.

Particles are in general classified into two types according to the statistics they

obey.

(I) Fermions:

a. Obey the FD statistics

b. have half integral spin i.e.3 5

, ,2 2 2

h h hL , , , ,n pβ λ− Σ are examples of

Fermions Fermions are further classified as Baryons (Fermions of mass m >mass of proton) and Leptons (Fermions of mass m < mass of protons).


(II) Bosons:

a. Obey the BE statistics

b. have integral spin i.e. , 2 , 3 ,h h h L , ,γ π κ are examples of Fermions

Bosons are further classified as Photons (Bosons of zero rest mass ) and mesons

(Bosons of non-zero rest mass)

Mesons and baryons, which interact strongly with nuclei (Nucleons) are also refer-red to in general as hadrons. On the other hand leptons and photons do not interact strongly with nuclei.

4.2 Yukawa’s Theory of Nuclear Forces

In covalent bonding, molecules are held together by sharing (exchanging) electrons. In 1936, Yukawa proposed a similar mechanism to explain nuclear forces.

According to Yukawa’s theory (also known as meson theory) all nucleons consist of identical cores surrounded by a cloud of one or more mesons and each nucleon conti-nuously emitting and absorbing pions. i.e. the force between nucleons is explained as being the exchange of elementary particles by nucleons by one of the following processes.

p Ä p + π 0

n Ä n + π 0

p Ä n + π +

n Ä p + π −

These equations violet the law of conservation of energy. A proton of mass equi-valence of 938 MeV becomes aneutron with 939.55 MeV and ejects a pion with 139.58MeV! This energy conservation violation can happen only if the violation exists for such short time that it can not be measured or observed by the Heisenberg’s uncertainty principle:


2

E t so the violation can exist only if

h h E t t =

E m

during this time, even if the pion moves with the speed of light,

the distance that it can move is

r = c t

the range of nuclear

cπ

Δ Δ ≥

Δ Δ ≤ → Δ ≤Δ

Δ Δ

h

h

-158

8

-11

force. i.e. the distance within which the

exchange of pions by nucleons takes place.

1.5 10 t = 0.3 10 sec

3 10

E = = 3.5152 10 J = 145.57MeVt

−×⇒ Δ ≈ ×

×

⇒ Δ ×Δ

h

This is close to the measured value of pion mass. Therefore Yukawa’s theory (the meson theory) satisfies the two important characteristics of nuclear forces

1. Nuclear force is the same between any two nucleons. i.e. p-p; p-n and n-n forces are the same. This is satisfied by the meson theory sice there are three types of mesons with the same mass.

2. Exchange of π meson (a particle of non-zero rest mass) by nucleons satis-fies the short range nature of nuclear forces. As reasoned above, the energy violation can happen only if the the exchange took place with in the limits of nuclear dimension.

This can be reasoned easily as follows.

When a nucleon ejects a π meson the change in energy that is involved is at least

the energy contained by a meson at rest, i.e 2m cπ . Thus during the interaction of nucleon and pions, the change in energy involved is:

2E m cπΔ =

So during the ejection or absorption of a pion by a nucleon, the low of conservation

of Energy seems to be violated by a magnitude of 2E m cπΔ = This can happen only if the violation exists for such a short time that it cannot be measured or observed by Heisenberg’s uncertainty principle as discussed above.

The potential for the π meson field is approximately given by:

2( )re

V rr

μ

γ−

= −


where γ is a constant and m cπμ =

h. This is commonly referred to as Yukawa

Potential.

The attractive force between nucleons does not exist for distance between nucleons below a certain limiting distance. For distances less than a limiting distance, the force between nucleons is a very strong repulsive force. The limiting distance is about 0.5 F. This repulsive force is believed to be due to exchange of π mesons. The repulsion is often taken to be a hard core, i.e., a region where the potential goes to infinity.

Task 4.1 Question for discussion

Discuss the following questions with your colleagues or on the discussion forum of AVU

1. What are cosmic rays, what kind of particles are coming to our earth from extra terrestrial sources?

2. Search form the internet the lattest number of elementary particles known.3. Why does exchang of mesons gives rise to attractive force.



1) Determine the minimum kinetic energy of protons requiered for the formation of

a) 0π -messon in the reaction 0p p p p π+ → + + ,

b) a proton anti proton pair in the reaction p p p p p p+ → + + +%

2) Knowing the mass of a neutral π -meson (135.0Mev/c2), determine the energy of

γ -quanta formed during the decay of a stationary neutral π meson: 0 2π γ→.

3) Determine the maximum energy of electrons emitted during the beta decay of a neutron if the neutron mass in 939.57 Mev/c2 , and the mass of the hydrogen atom is 938.73 Mev/c2

Optional Formative Evaluation 2


The search for the ultimate building blocks of matter is dated since the times of the Greeks. This search is not yet ended. We now not only know the existance of sub ato-mic particles (electrons, protons and neutrons) but also subparticles of the subatomic particles themselves. Historic account of Elementary particles through different era may be a good approach to present contnt at a school level.


XI.CompiledListOfAllKeyConcepts(Glossary)

Nuclear Terminology

1. Nuclear Terminology: There are several terms used in the field of nuclear physics that an RCT must understand.

a. Nucleon: Neutrons and protons are found in the nucleus of an atom, and for this reason are collectively referred to as nucleons. A nucleon is defined as a constituent particle of the atomic nucleus, either a neutron or a proton.

b. Nuclide:-A species of atom characterized by the constitution of its nucleus,

which is specified by its atomic mass and atomic number ( )Z , or by its num-

ber of protons ( )Z , number of neutrons ( )N , and energy content. A listing of all nuclides can be found on the “Chart of the Nuclides,” which will be introduced in a later lesson.

c. Isotope:- Isotopes are defined as nuclides which have the same number of protons but different numbers of neutrons. Therefore, any nuclides which have the same atomic number (i.e. the same element) but different atomic mass numbers are isotopes. For example, hydrogen has three isotopes, known as Protium, Deuterium and Tritium. Since hydrogen has one proton, any hydrogen atom will have an atomic number of 1. However, the atomic mass numbers of the three isotopes are different: Protium (H-1) has an mass number of 1 (1 proton, no neutrons), deuterium (D or H-2) has a mass number of 2 (1 proton, 1 neutron), and tritium (T or H-3) has a mass number of 3 (1 proton, 2 neutrons)

2. Mass Defect and Binding Energy:. The mass of an atom comes almost entirely from the nucleus. If a nucleus could be disassembled to its constituent parts, i.e., protons and neutrons, it would be found that the total mass of the atom is less than the sum of the masses of the individual protons and neutrons. This difference in mass is known

as the mass defect,( )Δ . computed for each nuclide, using the following equation

p

e

n

a

( )( )

( ) ( )( )

where = mass defect

Z=atomic number

M mass of a proton (1.00728 amu)

M mass of electoron (0.000548 amu)

A= mass number

M =mass of neutron (1.00867)

M =atomic mas

p e n a

H n a

ZM ZM A Z M M

Z M A Z M M

Δ = + + − −

= + − −

Δ

=

=

s (from chart of the nuclides)

mass of hydrogen atomHM =


3. Binding Energy: Binding energy is the energy equivalent of mass defect.

1amu 931.478 MeV=

4. Binding Energy Pernucleon: If the total binding energy of a nucleus is divided by the total number of nucleons in the nucleus, the binding energy per nucleon is obtained. This represents the average energy which must be supplied in order to remove a nucleon from the nucleus.

5. Radioactivity (Radioactive decay):- the spontaneous decomposition of a nucleus to form a different nucleus.

6. Radiocarbon dating (carbon-14 dating):- a method for dating ancient wood or cloth on the basis of the radioactive decay of the nuclide C-14.

7. Radiotracer:- a radioactive nuclide, introduced into an organism for diagnostic purposes, whose pathway can be traced by monitoring its radioactivity

8. Reactor core:- the part of a nuclear reactor where the fission reaction takes place

9. REM:- a unit of radiation dosage that accounts for both the energy of the dose and its effectiveness in causing biological damage (from roentgen equivalent for man)

10. Resonance:- a condition occurring when more than one valid Lewis structure can be written for a particular molecule. The actual electronic structure is represented not by any one of the Lewis structures but by the average of all of them

11. Nuclear Fission: The splitting of heavy nuclei into at least two smaller nuclei with an accompanying release of energy is called nuclear fission.

12. Nuclear Fusion:- Fusion is a reaction between nuclei which can be the source of power. Fusion is the act of combining or “fusing” two or more atomic nuclei. Fusion thus builds atoms. Fusion occurs naturally in the sun and is the source of its energy.

( ) ( ) ( )1 4 2+ +

1 24 H He 2 e 24.7MeV→ + + The reaction is initiated under the extremely high temperatures and pres-sure in the sun2(e+) + 24.7 MeV 1 2 What occurs in the above equation is the combination of 4 hydrogen atoms, giving a total of 4 protons and 4 electrons. 2 protons combine with 2 electrons to form 2 neutrons, which combined with the remaining 2 protons forms a helium nucleus, leaving 2 electrons and a release of energy.


XII. CompiledListofCompulsoryReadings


XIII. CompiledListof(Optional) MultimediaResources

Resource #1

Title: Motion of Centre of Mass URL: http://surendranath.tripod.com/Applets/Dynamics/CM/CMApplet.html Description: Applet shows the motion of the centre of mass of a dumbbell shaped object. The red and blue dots represent two masses and they are connected by a mass less rod. The dumbbell’s projection velocity can be varied by using the velo-city and angle sliders. The mass ratio slider allows shifting of centre of mass. Here m1 is the mass of the blue object and m2 is the mass of red object. Check boxes for path1 and path2 can be used to display or turn off the paths of the two masses. Rationale: This applet depicts the motion of centre of mass of two balls (shown in red and blue colour). The applets speed and angle of projection can be varied...

Resource #2

Title : Rotating Stool URL:- http://hyperphysics.phy-astr.gsu.edu/hbase/rstoo.html#sm Complete Reference:- Good animation graphics and applet to visualize the depen-dence of moment of inertia on distribution of matter on an object.. Rationale: Strengthens what is already discussed in Activity 2.

Resource #3

Title : Hyper Physics URL: http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html Date Consulted:-April 2007 Description:- This Java applet helps you to do a series of virtual experiments, . you can determine the escape and orbital velocities by varying different parameters of the projectile.


XIV. CompiledListofUsefulLinks

Useful Link #1

Title: Classical Mechanics URL: http://farside.ph.utexas.edu/teaching/301/lectures/ Description: Advanced description of the topics discussed in mechanics I and II of the AVU Physics module. Rationale: This site has comprehensive coverage of most of physics, in the me-chanics courses. The learner can consult chapters 7, 8 and 9 of the book. The PDF version is also available.

Useful Link #2

Title: Tutorial on torque from university of Guelph URL: http://www.physics.uoguelph.ca/tutorials/torque/index.html Description: The site gives detailed description of torque Rationale: Here you will find a good collection of tutorial problems on torque...

Useful Link #3

Title: Universal Gravitation URL: http://en.wikipedia.org/wiki/Law_of_universal_gravitation Description: This is a good collectionn of theory and historical account of the newtons low of universal gravitation. Rationale: The site provides a detailed description and solved problems on the topic.

Useful Link #4

Title: Universal Gravitation and Planetary Motion URL: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/circles/u6l3c.html Description: Lecture notes and discussion forum from the physics class room. Rationale: Reach in discussion topics and interactive problems.

Useful Link #5

Title: Gravitational Field URL: http://en.wikipedia.org/wiki/Gravitational_field Description: Gravitational field, its meaning in classical mechanics, and its mea-ning in general relativity are described in this section. Rationale: Useful for the one who needs to compare many references.

Useful Link #6

Title: Geostationary orbit URL: http://en.wikipedia.org/wiki/Geostationary Description: This link Explains geostationary orbit. The animated graphics helps visualization. Rationale: This supplements the theory given in Activity three...


XV. SynthesisoftheModule

Nuclear Physics

In this module (Nuclear Physics) dynamics of a system of particles, rotational motion and Gravitation are dealt in detail. The module began with the study of impulse of a force and its relation with momentum. The impulse force relation is generalized for a system of particle.

In the second activity is the kinematic and dynamic descriptions of rotational motion were done using new quantities. . It was shown that the equations of motion that describe linear motion possess a rotational counterpart.

The third activity is on Gravitation Up to now we have described various forces from an entirely empirical point of view. To gain a more unified understanding of such forces and to achieve greater predictive power, we shall now examine two of the four fundamental forces which are ultimately responsible for all other forces. Thus in the third activity we discussed the gravitational force which accounts for the interaction between all astronomical bodies, the motion of the planets and the moon, the trajec-tories of space vehicles, the occurrence of the tides, and the weights of objects.

The fourth activity has illustrated that motion is a relative concept. Quantities of mo-tion like position, displacement and velocity are not universal and yet Newton’s laws of motion hold in all inertial reference frames. The quantities of motion in different frames of reference are related by Galilean Transformation.


XVI. SummativeEvaluation

Multiple Choice questions

1 Which one of the following ejects photoelectrons of the highest energy under optimum condition of irradiation?

(a) ultraviolet radiation(b) infrared radiation(c) monochromatic yellow light(d) gamma rays

2 Assume that a particle is moving at a speed near that of light. In order to halve its Einsteins’s Energy equivalence, the particle’s speed must be reduced

(a) to ½ of its original value(b) to ¼ of its original value

(c) to 1 2 of its original value(d) until its relativistic mass is halved

3 Antimatter consists of atoms containing

(a) protons, neutrons and electrons(b) protons, neutrons and positrons(c) antiprotons, antineutrons and positrons(d) antiprotons, antineutons and elelctrons

4 A high energy gamm ray may materialize into

(a) a meson(b) an electon and a proton(c) a proton and a neutron(d) an electorn and a positron

5 Alpha rays can be detected by fog tracs mad in a

(a) scinitillation counter(b) Geiger-Muller tube(c) Wilson Cloud chamber(d) nuclear reactor


6 Which one of the following kinds of rays will usually be produced by bombard-ment of a metal target by cathode rays?

(a) alpha rays(b) cosmic rays(c) gamma rays(d) x-rays

7 Whch one of the following is Most closely related to radiant heat?

(a) x-rays(b) infra-red light(c) ultraviolet light(d) yellow light

8 Which principle states our inability to measure both momentum and position simultaneously with unlimited accuracy.

(a) The principe of least square(b) The principle of uncertainty(c) The Pauli exclusion principle(d) The principle of conservation of momentum

9 If 21084 Po emits beta particle (electron), atomic number of the resulting nucleus

will be

(a) 82(b) 83(c) 84(d) 85

10 Of the following, one can not be accelerated in a cyclotron. Identify

(a) deuteron(b) neutron(c) electron(d) triton

11 The energy of an electron in a stationery orbit of hydrogen atom is

(a) positive(b) negative(c) zero(d) infinity


12 Which of the following sources give discrete emission spectrum

(a) candle(b) mercury vapor lamp(c) sun(d) incandescent bulb

13 In the following figure the energy levels of hydrogen atom have been shown along with some transitions marked A,B,C, D and E.

0ev-0.544ev-0.850ev

-1.500ev

-3.400ev

-13.600ev

A

B

C D

E

The transitions A, B, and C respectively represent

(a) The series limit of Lyman series, third member of Balmer series and second member of Paschen series

(b) The series limit of Lyman series, second member of Balmer series and second member of Paschen series

(c) The ionisation potential of hydrogen, second member of Balmer series and third member of Paschen series

(d) The first member of Lyman series, third member of Balmer series and second member of Paschen series

14 With reference to the energy level diagram of the above question D and E cor-respond to

(a) An emission line of Lyman series and absorption at wavelength higher than the Paschen series respectively

(b) An emission line of the Balmer series and an emission wavelength longer than Lyman series limit respectively.

(c) An absorption line of Balmer series and an emission at a wavelength shorter than Lyman series limit respectively

(d) The absorption line of Balmer series and ionisation potential of hydrogen respectively.


15 Which of the following statements are true for both X-rays and α -rays

(a) They cause ionisation of air when they pass through it (b) They can be deflected in electric and magnetic fields. (c) They can be used to detect flaws in metal coatings(d) They travel with the speed of light

16 The rate of disintegration of a given sample of radionuclides is 1710 atoms/s and half-life is 1445 years. The number of atoms is

(a) 171.44 10×

(b) 171.4 10×

(c) 276.57 10×(d) none of these.

17 In a breeder reactor, useful fuel obtained from 238 U is

(a) 239 Pu

(b) 235 U

(c) 235 Th

(d) 233 Ac

18 The average life τ and the decay constant λ of a radioactive nucleus are related as

(a) /Cτ λ=

(b) / 1τ λ =

(c) 0693 /=τ λ

(d) 1τλ =

19 Atomic mass number of an element is 232 and its atomic number is 90. The end product of this radioactive element is an isotope of lead (atomic mass 208 and atomic number 82). The number of alpha and beta particles emitted are

(a) 4 and =6α β=

(b) 6 and =0α β=

(c) 6 and =4α β=

(d) 3 and =3α β=


20 γ -rays consist of

(a) electromagnetic waves (b) fast moving electrons(c) helium nuclei(d) singly ionised gas atoms

21 Emission of β -rays in a radioactive decay results in a daughter element showing a

(a) change in charge but not in mass (b) change in mass but not in charge(c) change in both(d) change in neither

22 In the reaction represented by 4 4 4

2 2 1

A A A AZ Z Z ZX Y Y K− − −

− − −→ → → The decay in

sequence are

(a) , ,α γ β

(b) , ,γ α β

(c) , ,β γ α

(d) , ,α β γ

23 The main source of solar energy is

(a) combustion(b) gravitational contraction (c) nuclear fusion(d) nuclear fission

24 The radioactivity of an element becomes 1/64th of its original value in 60 second. The half value period is

(a) 30s(b) 15s(c) 10s(d) 5s


25 When the radioactive isotope 23888 R a decays in a series by the emission of three

alpha particles and a β -particle. The isotope finally formed is

(a) 22084 R A

(b) 21588 R A

(c) 27286 R A

(d) 22683 R A

26 Half life period of lead is

(a) 1590 years(b) 1590days(c) infinite(d) zero

27 The half life period of a radioactive sample depends upon

(a) nature of substance(b) pressure(c) temperature(d) all of the above

28 A positron is emitted by a radioactive nucleus of atomic number 90. The product nucleus will have atomic number

(a) 90(b) 91(c) 89(d) 88

29 What is a curie

(a) measurement of electric field(b) measurement of magnetism(c) measurement of temperature(d) measurement of radioactivity

30 Which of the following is not a mode of radioactive decay

(a) alpha decay(b) fusion(c) electron capture(d) positron emission


31 Particles which can be added to the nucleus of an atom without changing its chemical properties are called

(a) alpha particles(b) protons(c) electrons(d) neutrons

32 What is the mass of 1 curie of 234 14 /( 8.8 10 )sU λ −= ×

(a) 103.7 10 g×

(b) 232.348 10 g×(c) 20 days

(d) 3.8 20× days

33 The half life of radioactive radon 3.8 days. the time at the end of which 1/20th

of the radon sample will remain undecayed is nearly ( 10e 0 4343log .= )

(a) 1.6 days(b) 16.4 days(c) 20 days

(d) 3 8 20days. ×

34 The radioactive decay rate of a radioactive element is found to be 310 disinte-grations/s at a certain time. If the half life of the element is 1 second the decay rate after one second and three seconds respectively is

(a) 100, 10

(b) 310 , 310(c) 125, 500(d) 500, 125

35 A freshly prepared radioactive source of half-life 2 hours emits radiations of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

(a) 128 hours(b) 24 hours(c) 12 hours(d) 6 hours


36 The equation 0

1 1A A

Z ZX Y e υ+ −→ + + represents

(a) fission(b) fusion

(c) β -decay

(d) γ -decay

37 During a negative β -decay

(a) An atomic electron is ejected(b) An electron which is already present within the nucleus is ejected (c) A neutron in the nucleus decays emitting an electron(d) A part of binding energy of nuclei is converted into an electron

38 When 94 B e is bombarded with α -particle, one of the products of nuclear

transmutations is 126 C . The other is

(a) 1

0 n

(b) 21 H

(c) 11 H

(d) 01 e−

39 In the nuclear reaction, given by 4 14 1He N 172 + → +bX Hq The nucleus X is

(a) oxygen of mass 16(b) oxygen of mass 17(c) nitrogen of mass 16(d) nitrogen of mass 17

40 The energy released per fission of a 23592 U nucleus is nearly

(a) 200 MeV(b) 200 keV(c) 200 eV(d) 20 eV

41 If 10% of the radioactive material decay in 5 days. What would be percentage of amount of original material left after 20 days?

(a) 55.6%(b) 65.6%(c) 75.6%(d) 85.6%


42 In the nuclear process 11 11

6 5C B Xβ +→ + + , X stands for

(a) photon(b) neutrino(c) antineutrino(d) neutron

43 If the nuclei of X and Y are fused to form a nucleus of mass M and some energy is released, then

(a) X-Y=M(b) X+Y>M(c) X+Y<M(d) X+Y=M

44 The nuclei 136 C and 14

7 N can be described as

(a) isotones(b) isotopes of carbon(c) isobars(d) isotopes of nitrogen

45 If M is the atomic mass, A is mass number, then (M-A)/A is called

(a) packing fraction(b) mass defect(c) Fermi energy(d) binding energy

46 When the number of nucleons in nuclei in crease, the binding energy per nu-cleon

(a) First increases and then decreases with increase of mass number(b) Remains constant with mass number (c) Decreases continuously with mass number(d) Increases continuously with mass number

47 The average binding energy of a nucleus is

(a) 8BeV(b) 8 MeV(c) 8 keV(d) 8eV


48 The mass defect for the nucleus of helium is 0.0303 a.m.u. What is the binding energy per nucleon for helium in MeV

(a) 27(b) 7 (c) 4 (d) d. 1

49 In stable nuclei, the number of neutrons (N) is related to the number of Z in a neutral atom in general as

(a) N Z≥(b) N=Z(c) N<Z(d) N>Z

50 Fission of a nucleus is achieved by bombarding it with

(a) electrons(b) protons(c) neutrons(d) X-rays

51 The more readily fissionable isotope of uranium has an atomic mass of

(a) 238(b) 236(c) 235(d) 234

52 The equation ( )1

1

44 2 2 26H He e MeV+ + + +→ + + represents

(a) fission(b) fusion

(c) γ -decay

(d) β -decay

53 From the following equations pick out the possible nuclear fusion reactions.

(a) 13 1 14

6 1 6 4.3Mev+ → +C H C

(b) 12 1 13

6 1 7 2+ → +C H N M ev

(c) 14 1 15+ +7 1 8N H O 7.3Mev→

(d) 235 1 140 94 1

92 0 54 38 0U+ n Xe+ Sr+2( n)200MeV

→+ +λ


54 Consider a nuclear reaction 200 110 90 + Energyx A B→ + If the binding energy per nucleon for X,A and B is 7.4 MeV, 8.2 MeV and 8.2 MeV respectively, what is the energy released

(a) 90 MeV(b) 110 MeV(c) 160 MeV(d) 200 MeV

55 Which of the following undergo fission reaction easily by slow moving neu-trons?

(a) 235 239,U Pu

(b) 239 234,P Th

(c) 238 232,U Rn

(d) 238 206

92 82U pb→

56 A radioactive substance has a half-life of 60 minutes. During 3 hours the fraction of atom that have decayed would be

(a) 12.5%(b) 87.5%(c) 8.5% (d) 25.1%

57 The element used for radioactive carbon dating for more than 5600 years is

(a) 14C

(b) 234U

(c) 238U

(d) 94P o

58 After two hours one sixteenth of the starting amount of a certain radioactive isotope remaine un decayed. The half-life of the isotope is

(a) 15 minutes (b) 30 minutes (c) 45 minutes(d) one hour


59 A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2:1 what will be the ratio of their nuclear size (nuclear radius)?

(a) 1/ 32 :1

(b) 1 / 32 :1

(c) 1/ 33 :1

(d) 1/ 21 : 3

60 A radioactive reaction is 238 206

92 82U pb λ→ . How many α - and β -particles are emitted?

(a) 10α ,6 β(b) 4 protons, 8 neutron (c) 6 electron, 8 proton

(d) 6 β and 8α

61 Which of the following is the fusion reaction

(a) 21 H 2 4

1 2H He+ →

(b) 1 14 14 1

0 7 6 1n H C H+ → +

(c) 1 236 239

0 92 93n U Np β γ−+ → + +

(d) 3 31 2H H e β γ−→ + +

62 Which of the following statements is true?

(a) 192

78 has 78 neutrons Pt

(b) 214 210 -84 82 + P o P b β→

(c) 238 234 4

92 90 2U Th+ He →

(d) 234 234 4

90 91 2 + Tj Pa He→

63 The binding energy of deutron ( )2

1 H is 1.112 MeV per nucleon and an alpha

particle ( )42 H has a binding energy of 7.074 MeV per nucleon. Then in the

reaction 2 2 4

1 1 2H H He Q+ → + the energy Q released is

(a) 1MeV(b) 11.9 MeV(c) 23.8 MeV(d) 931 MeV


64 The half-life of radium is 1620 year and its atomic weight is 226 kg/kilomole. The number of atoms that will decay from its 1g sample per second will be

(a) 103.61 10×

(b) 123.61 10×

(c) 153.11 10×

(d) 1531.1 10×

(e) (Avagadro’s number 266.02 10N = × atom /kilomole)s

65 A parent nucleus mn P decays into a daughter nucleus D through α emission in

the following way 04 C . The subscript and superscript on the daughter nucleus D will be written as

(a) mn P

(b) 4mn P +

(c) 4mn P −

(d) 4

2

mn D −

−

66 Given 1.0087, 1.0073, 4.0015neutr on pr otonm m mα= = = (in amu units, 1 amu=931 MeV). Binding energy of helium nucleus is

(a) 28.4 MeV(b) 20.8 MeV(c) 27.3 MeV(d) 14.2Mev

67 16g of sample of a radioactive element is taken from Bombay to Delhi in 2 hours and it was found that 1g of the element remained (undisintegrated). Half life of element is

(a) 2 hours(b) 1 hour(c) 1/2 hour(d) ¼ hour


68 0I -rays radiations can be used to create electron positron pair. In this process of pair production, γ -rays energy can not be less than

(a) 5.0 MeV(b) 4.02 MeV(c) 15.0 MeV(d) 1.02 MeV

69 The half life of Po is 140 days. If 16g of Po is present then what is the time taken for 1g of po to be present

(a) 10 days(b) 280 says(c) 560 days(d) 840 days

70 A radioactive sample has a half life of 5 day. To decay from 8 microcurie to one microcurie, the number of days will be

(a) 40(b) 25(c) 15(d) 10

71 The activity of the radioactive sample decreases to one-third of the original

intensity 0I in a period of 9 years. After 9 years more, its activity would be

(a) same

(b) 0I /6

(c) 0I /4

(d) 0I /9

72 R a d o n - 2 2 0 w i l l e v e n t u a l l y d e c a y t o B i s m u t h 2 1 2 a s

220 216 4

86 84 2 ; half life =55sRn Po He→ +

216 212 4

84 82 2 ; half life =0.16sPo Pb He→ +

212 212 0

82 83 1 ; half life =10.6 hoursPb Bi e−→ + If a certain mass of radon-220 is allowed to decay in a certain container, after five minutes the element with the greatest mass will be

(a) Radon(b) Polonium(c) Lead(d) Bismuth


73 Which is heavy water?

(a) water in which soap does not lather (b) compound of heavy oxygen and hydrogen(c) compound of deuterium and oxygen

(d) water at 04 C

74 The critical mass of nuclear reaction is

(a) the initial mass to start a nuclear fission (b) the minimum mass for the chain reaction (c) the size of the reactor core(d) the size of the nuclear fuel + size of the moderator

75 Carbon-14 decays with half-life of about 5,800 years. In a sample of bone, the ratio of carbon-14 to carbon-12 is found to be ¼ of what it is in free air. This bone may belong to a period about x centuries ago, where x is nearest to

(a) 58(b) 58/2

(c) 3 58×

(d) 2 58×

76 A radioactive sample contains 05 atoms and has a half life of one year. Then the time required for all the atoms to decay is

(a) 610 years (b) one year (c) 10 years (d) ∞

77 A fast reactor does not use

(a) a coolant (b) control system(c) a moderator(d) nuclear level

78 When 23592U undergoes fission 0.1%of its original mass is changed into energy.

How much energy is released if 1 kg of 23592U undergoes fission?

(a) 109 10 J×

(b) 119 10 J×

(c) 129 10 J×

(d) 139 10 J×


79 The half-life of the isotope 2411 H a is 15 hrs. How much time does it take for

7/8th of a sample of this isotope to decay?

(a) 75 hrs(b) 65 hrs(c) 55 hrs(d) 45 hrs

80 200MeV of energy may be obtained per fission of 235 U . A reactor is generating 100 kW of power.

(a) 1000

(b) 82 10 ×

(c) 931

(d) 1 2 to that of X X

81 N atoms of a radioactive element emit n alpha particles per second. The half-life of the element

(a) n/N sec (b) N/n sec

(c) 0.693

secN

n

(d) 0.693

secn

N

82 The combinations of radioactive emissions will not change the mass number of radioactive nuclear not change the mass number of radioactive nuclear

(a) alpha and beta decays(b) alpha and gamma decays(c) alpha beta and gamma decays (d) beta and gamma decays

83 Thermal neutrons are incident on a sample of Uranium containing both

235 235

92 92 and U U . Then

(a) both the isotopes will undergo fission(b) none of the isotopes will undergo fission

(c) only 235

92 U will undergo fission

(d) only 235

92 U will under go fusion


84 If 27 Al is bombarded with neutron and produce 28 Al and a proton. What will

be Q value of this reaction? Given mass of 27 27.98154=Al in amu.

(a) 36.79 10 MeV−×(b) 3.16 MeV(c) 6.32 MeV(d) 6.32eV

85 The activity of a radioactive sample is measured as 9750 counts per minute at t=0 and as 975 counts per minute at t=5 minute at t=0 and as 975 counts per minutes. The decay constant is approximately in per minute

(a) 0.230(b) 0.461(c) 0.691(d) 0.922

86 Half-lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes Initially the sample of A and B have equal number of nuclei. After 80 minutes the ratio of remaining number of A and B nuclei is

(a) 1:16(b) 4:1(c) 1:4(d) 1:1

87 Two radioactive materials 1 2 and X X have decay constants 10λ and λ res-pectively. If initially they have the same number of nuclei, then the ratio of the

number of nuclei of 1 2 to that of X X will be 1/e after a time

(a) 1/(10λ )

(b) 1/(11λ )

(c) 11/(10λ )

(d) 1/(9λ )


Answers to Formative Evaluation 1

1. C

2. A

3. A

4. A

5. B

6. C

7. B

8. A

9. A

10. C

11. D

12. D

13. D

14. A

15. C

16. D

17. B

18. C

19. D

20. B

21. D

22. D

23. B

24. A


XVII.References

This is a compiled list of the references, like standard reference books for the discipline, used in the development of the module. (Not for the learner do not have to be copyright free) Atleast 10 in APA style

Raymond A. Serway (1992). PHYSICS for Scientists & Engineers. Updated Version.

Douglas D. C. Giancoli Physics for scientists and engineers. Vol. 2. Prentice Hall.

Irving Kaplan (1962) Nuclear Physics.Sena L.A. (1988) Collection of Questions and Problems in physics, Mir Publishers

Moscow.Nelkon & Parker (1995) Advanced Level Physics, 7th Ed, CBS Publishers &

Ditributer, 11, Daryaganji New Delhi (110002) India. ISBN 81-239-0400-2.Godman A and Payne E.M.F, (1981) Longman Dictionary of Scientific Usage.

Second impression, ISBN 0 582 52587 X, Commonwealth Printing press Ltd, Hong Kong.

Beiser A., (2004) Applied Physics, 4th ed., Tata McGraw-Hill edition, New Delhi, India

Halliday D., Resnick R., and Walker J. (1997), Fundamentals of Physics, 5th ed., John Wiley and Sons

James O’Connell (1998), Comparison of the Four Fundamental Interactions of Physics, The Physics Teacher 36, 27.


XVIII.MainAuthoroftheModule

About the author of this module

Tilahun Tesfaye, Dr.

Department of physics, Addis Ababa University,Ethiopia, East Africa.P.O.Box 80359 (personal), 1176 (Institutional)E-mail: [email protected]; [email protected]: +251-11-1418364

Breif Biography: The author is currently the chairperson of the department of physics at Addis Ababa University. He has authored school textbooks that are in use all over Ethiopian schools. His teaching experience spans from junior secondary school physics to postgraduate courses at the university level. He also worked as a curriculum development expert and Educational materials development panel head at Addis Ababa Education Bureau.

You are always welcome to communicate with the author regarding any question, opinion, suggestions, etc this module.


XIX.FileStructure

Name of the module (WORD) file :

• Nuclear PhysicsV1.doc

Name of all other files (WORD, PDF, PPT, etc.) for the module.

• Compulsory readings Nuclear_Physics.pdf Abstract: Lecture notes, in the university of Addis Ababa, by the author are com-piled in one PDF file.

Prepared by Tilahun TESFAYE African Virtual university Université Virtuelle Africaine Universidade Virtual Africana

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