Download nuclear physics - Thierry Karsenti

Nuclear Physics
Prepared by Tilahun Tesfaye, Ph.D.
NOTICE
TABLE OF CONTENTS
FOREWORD
This module has four major sections
The first one is the INTRODUCTORY section that consists of five parts vis:
1.
TITLE:- The title of the module is clearly described
2.
PRE-REQUISIT KNOWLEDGE: In this section you are provided with
information regarding the specific pre-requisite knowledge and skills you
require starting the module. Carefully look into the requirements as this will
help you to decide whether you require some revision work or not.
3.
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.
4.
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
borrow by some other means.
5.
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:
6.
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.
7.
GENERAL OBJECTIVE(S):
Clear informative, concise and
understandable objectives are provided to give you what knowledge skills
and attitudes you are expected to attain after studying the module.
8.
SPECIFIC LEARNING OBJECTIVES (INSTRUCTIONAL OBJECTIVES):
Each of the specific objectives, stated in this section, is 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:
9.
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.
10.
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
11.
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.
12.
COMPILED LIST OF COMPULSORY READINGS: A minimum of three
compulsory reading materials are provided. It is mandatory to read the
documents.
13.
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.
14.
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.
15.
SYNTHESIS OF THE MODULE: Summary of the module is presented.
16.
SUMMATIVE EVALUATION:Enjoy your work on this module.
I.
NUCLEAR PHYSICS
BY TILAHUN TESFAYE ADDIS ABABA UNIVERSITY ETHIOPIA
II
PREREQUISITE COURSE OR KNOWLEDGE
In order to study this module you need to complete the QUANTUM MECHANICS
of the AVU Teachers’ Training Module.
III
TIME
This module can be completed in 120hrs.
IV
MATERIALS
The 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 RATIONALE
We 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
o Nuclear Magnetic Resonance (cancer),
o Security (e.g. mine detection),
o Fundamental studies such as neutrino properties (double beta decay)
 Medical applications
o Cancer therapy using radiation
o Historic use to kill cells - e.g. radium
o Modern use with ion beams (e.g. GSI)
 Medical imaging
o MRI (Nuclear magnetic imaging)
o Positron Emission Tomography
o X-ray imaging etc
 The environment
o Carbon dating 12C/14C ratio
o Argon gas dating
o Rb/Sr dating of rocks
 Biology
o Archaeology (dating by isotope ratios)
o Use of radioactivity to trace fluids in organs
o Forensic
 Security and industry
o Oil well logging
o 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
nucleus. 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 information 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
OVERVIEW
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 applications.
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
applications 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.
6.1 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
 Fundamental Interaction in nature.
 Survey of elementary particles.
 Yukawa’s theory of nuclear forces.
(20 hours)
6.2 GRAPHIC ORGANIZER
A. Basic Properties
of the Atomic Nucleus
C. Interaction of Radiation
With Matter
Basic properties of the atomic nucleus.
Nuclear constituents. Isotopes,
Interaction of heavy and light
charged particles with matter.
Nuclear binding energy,
Interaction of photons with matter.
Nuclear stability,
Interaction cross-sections
and interaction coefficients.
Nuclear radiation detectors.
Mass and isotopic abundance,
NUCLEAR
Physics
D. Nuclear Forces and
Elementary Particles
Nuclear models
B. Radioactivity
Fundamental interactions in nature.
Yukawa’s theory of nuclear force.
Survey of elementary particles.
Radioactivity. Its discovery, alpha,
beta and gamma radiation,
Laws of radioactive disintegration.
Natural radioactivity (series and non series)
radioactive equilibrium,
Applications of radioactivity.
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
VIII. Specific Learning Objectives
(Instructional Objectives)
Content
Learning objectives
After Completing this section you
should be able to:
Basic Properties of the Atomic
Nucleus (30 hours)

Identify constituents of the atomic
nucleus and their collective properties.
 Basic Propertiesof the atomic nucleus,

Describe mass defect

Relate neutron: proton ratio to stability

Describe the shell and liquid drop
models of the nucleus
Radioactivity: (35 hours)

Describe radiations from the nucleus
 Radioactivity, discovery, alpha, bet and

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

Describe interaction of light charged
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 (construction,
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
1.
Nuclear constituents, Iosotopes,
 Nuclear Binding Energy.
 Nuclear Stability,
 Mass and Isotopic Abundance;
 Nuclear Models.
2.
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.
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)  -rays
(c)  -rays
5
The half life period of radioactive nuclide is 3 hours, its activity will be reduced
by a factor of
(a)
6
7
8
9
(d)  -rays
1
8
(b)
1
6
(c)
1
27
(d)
1
9
Which of the following radioactive decay emits  -particle
(a)
82
pb 214 93 Bi 214  ...
(c)
92
U 238 90 Th 234  ...
(b)
91
Th 234 91 pa 234  ...
(d)
91
pa 234 92 U 234  ...
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
(c) 0.25g
(b) 0.5g
(d) <1 mg
A nuclide A (with mass number m and atomic number n) disintegrates emitting
an  -particle. The resulting nuclide B has mass number and atomic number
respectively equal to
(a) m-2 and n
(c) m-4 and n-1
(b) m-4 and n-2
(d) m+4 and n+1
As a result of radioactive decay a 238
92 U nucleus is changed to
During this decay the particles emitted are
234
91
Pa nucleus.
(a) two  -particles and one proton
(b) two  -particles and one neutron
(c) one  -particle and one  -particle
(d) one proton and two neutrons
10 The relation between half life T1/ 2 of a radioactive sample and its mean life 
is
(a)   2.718T1/ 2
(c)   0.693T1/ 2
(b)   T1/ 2
(d) T1/ 2  0.693
11 The decay constant  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 1 H 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) 93.1MeV
(b) 931 MeV
(c)10078 MeV
(d) 9310 MeV
16 A  0 meson at rest decays into two gamma rays  0     then which of the
following is correct
(a) the two  ’s move in the directions opposite to each other
(b) the two  ’s have unequal energies
(c) both the  ’s move in the same direction
(d) the  ’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  -particles, radioactive phosphorus is
formed i.e. 13 Al 27  2 He 4 15 P 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  -particle is emitted. The residual
nucleus is
(a) 0 n1
(b) 1 D 2
(c) 1 H 3
(d)
13
Li 7
20 What is X in the following relation 13 Li 7 1 H 1 2 He4  X
(a) 1 H 3
(b) 0 D1
(c) 1 D 2
(d) 2 He 4
21 If  ,  and  -rays have ionising powers I , I  and I  respectively then
(a) I ,  I  >I 
(c) I  I  =I 
(b) . I ,  I  <I 
(d) none of these
22 Which of the following is a correct statement
(a)  -radioactivity is the process in which an electron is emitted from an
unstable atom whose atomic number Z remains unchanged
(b)  -radioactivity is the process in which the daughter nucleus has atomic
number 1 unit more than that of the parent nucleus
(c)  -radioactivity is the process in which an unstable atom emits the nucleus
of a helium atom
(d)   -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
24
(b) 300
(c) 200
(d) 150
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/ log e 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
(c) 920 MeV
(b) 92 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
(c) 2.38MeV
(b) 23.8MeV
(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
released will be
(a) 3  104 J
(c) 9  1010 J
(b) 9  107 J
(d) 9  1014 J
30 A radioactive nucleus undergoes a series of decay according to the scheme.




A 
 A1 
 A 2 
 A3 
 A 4 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
(c) radium
(b) uranium
(d) cadmiu
m
32 Thermal neutrons have energy around
(a) 100eV
(c) 1eV
(b) 10eV
(d)
92
U 238 82 pb 206
(e)
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
(c) to slow down neutrons
(b) slow down the neutrons
(d) produce neutrons
35 Cadmium rods are used in a nuclear reactor to
(a) generate neutrons
(c) slow down neutrons
(b) absorb neutrons
(d) produce neutorns
36 How many radioactive disintegrations per second are defined as Becquerel
(a) 106
(c) 1
(d) none of the above
(b) 3.7  1010
37 In the nuclear reactor at Trombay which of the following is used as moderator
(a) ordinary water
(c) copper
(b) cadmium
(d) heavy water
38 Which of the following particles is used to cause fission in an atomic reactor?
(a) proton
(c)  -particle
(b)  -particle
(d) neutron
39 Which of the following is the best nuclear fuel?
(a) Neptunium 293
(c) Uranium 236
(b) plutonium 239
(d) Thorium 236
40 The moderator in a reactor
(a) absorbs thermal energy
(c) accelerate neutron
(b) slows down 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
(c) A and C are isotopes
(b) A and B are isotopes
(d) A and B are isobars
43 A radioactive sample with a half-life of 1 month has the label: ``Activity =2
microcuries on 1.8.1991’’. What was its activity two moths later in microcuries?
(a) 1.0
(c) 4
(b) 0.5
(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 He 4 6 C12  0 n 1
(b)
92
U 238 82 pb 206
(c)
56
Ba144 56 Kr 92 92 U 235  0 n 1
(d)
26
Fe56  48 Ca112 74 W 167  0 n1
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)
92
U 233
(c)
92
U 238
(b)
92
U 235
(d)
90
Th 232
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 period
50 Heavy water is used as moderator in a nuclear reactor. The function of the moderator
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
11. A
21. A
31. D
41. C
2. D
12. D
22. C
32. A
42. B
3. B
13. B
23. C
33. D
43. A
4. D
14. C
24. D
34. B
44. A
5. A
15. B
25. B
35. B
45. B
6. C
16. A
26. A
36. C
46. A
7. D
17. D
27. A
37. D
47. B
8. B
18. B
28. A
38. D
48. A
9. C
19. D
29. B
39. B
49. C
10. D
20. D
30. A
40. C
50. D
9.3 PEDAGOGICAL COMMENT FOR THE LEARNER:
Nuclear physics can be seen, historically, as the child of chemistry and atomic
physics 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 four activities. Each activity has examples and reading
assignments. You are required to to complete all the learning activities and
complet the compulsory material. The compulsory material is an extensive lecture
notes and study guide with excercises. 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 estimates, 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:
A
Z
X
The atomic nuclei has some properties of interest:
 Nuclear Size: In general atomic nuclei have spherical shape with radius
roughly given by:
R  R AA/3
where R o =1.2  0.2 fm
 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 .. and spin s
combine to the total angular momentum j The total angular momentum of a
nucleus I is therefore the vector sum of the angular momenta of the
nucleons
A
j=l+s
I=  ji
odd-A: half-integer I, even-A: integer I
i=1
 Angular momentum: The angular momentum I has all of the usual
properties of quantum mechanical angular momentum vectors:
I 2  2 I ( I  1)
Iz  m
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 Fermigas 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
problems.
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 nucleus 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
because 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 126 C atom.
1u  1.6603 1027 kg
Spin And Magnetic Moment of The Nucleus:
o
D 1(5890A )
o
D 1 (5 8 9 6 A )
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.
l+1/2
l-1/2
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
 N=eh/2m p
where  N 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
possibilities, 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 1/2000 th the
electronic magneton.
Data on nuclear spin also witnessed against the proton-electron model. For
example, according to this model the beryllium nucleus, 94 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, 94 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
uncertainty principle. If the nucleus contained electrons, then the uncertainty in the
electron position, x, would be comparable with the linear dimensions of the
nucleus, that is, 10 14 or 10 15 m. Let us choose the greater value, x  1014 From
the Heisenberg uncertainty relation for the electron momentum we have
ΔP>>h/Δx>>10-14 =10-19 kg m/s
The momentum P is directly related to its uncertainty, that is P : P  P Once the
momentum of the electro is known, one can readily find its energy. Since in the
above example P>>me c  1030 kg  3 108 m/s , one should use the relativistic
relation for energy and momentum
E 2 =c 2 p 2 +m e2 c 4
Then we get
E  c p  me c  3  108 1038  (1030  3 108 ) 2
2
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:
A
Z
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)me
mn =1.008982±0.000003 amu=(1838.63±0.01)me
The proton and the neutron have the same mass number equal to unity. In the
nucleus, 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
magnetic 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 physics.
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 ). With an
odd number of nucleons, its spin will be half-integral (in units of ).
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, E0 , is related to its rest mass m0
by:
o
E 0 =m0c 2
where c is the velocity of light in a vacuum. Designating the energy given upon the
formation of a nucleus as Eb , then the mass equivalent of the total binding
energy
o
Δm 0 =ΔE b /c 2
is the decrease in the rest mass as the nucleons combine to make up the nucleus.
The quantity mo 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 m0 is given by
Δ mo =Zmp +(A-Z)mn -M
The quantity m0 gives a measure of the binding energy:,
ΔEb =Δm0c2 =[Zmp +(A-Z)mn -M]c2
In nuclear physics, energies are expressed in atomic energy units (aeu)
corresponding to atomic mass units:
1aeu = c2 1amu =  9 1016 m 2 /s 2  1.660kg
= 1.49110-10 J
 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.
10
Cu-63
Binding Energy per Nucleon (MeV)
9
Sn-120
Al-27
Th-232
8
Pt-195
U-238
He-4
7
B-10
6
Li-6
5
4
3
He-3
2
H-1
1
0
0
40
20
80
60
120
100
160
140
200
180
240
220
Mass Number (A)
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
28
Si to 138
range 28<A<138, that is, from 14
56 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), Δε b is about 7.6 MeV.
In the region of small mass numbers, the binding energy per nucleon shows
characteristic maximua and minima. Minima in the binding energy per nucleon are
shown by nuclei containing an odd number of protons and neutrons, such as
6
10
14
3 Li, 5 B and 7 N
Maxima in the binding energy per nucleon are associated with nuclei having an
even number of protons and neutrons, such as 42 He, 126 C and 168 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-dimensional box is given by E n  n 2 E1 , 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  E1  19 E1 as shown in diagram A . In contrast, if 3 were
neutrons and 2 were protons (as shown in B), the energy would be
 4   4 1  E1  8 E1 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
energies; 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
24
water contains 8.23  10 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
uranium-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) .
Eb  C1 A  C2 A
2/3
N  Z
Z ( Z  1)
 C3
 C4
1/ 3
A
A
2
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.
C2  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, 4 R 2 . Using R  R A1/ 3 , the surface area becomes
4 R 2 A2 / 3 which is proportional to A2 / 3 . This the surface effect.
3. C3  0.71MeV The repulsive force between protons reduces the binding
Z  Z  1
pairs of protons, each with a Coulomb potential
2
Z  Z  1
k e2
of e , where R  A1/ 3 R . Thus we subtract a term proportional to
R
A1/ 3
This is the Coulomb effect
energy. There are
4.
C4  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  -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  particles in
B’
B
A
A’
C
C’
(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  -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
92
U 235 and 92U 238 atoms is that
(a) U 238 contains 3 more neutrons
(b) U 238 contains 3 more neutrons nd three more electrons
(c) U 238 contains 3 more protons and 3 more electrons
(d) U 238 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
nucleus
(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  ,  and 
are 1.1 MeV and 7.0 MeV respectively. The energy released when two
neutrons form a helium nucleus  2 He 4  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  -radiation with a neutrino
15 In the disintegration chain 92 U 238  X Z Z 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 K 40 , Ar 40 and Ca 40 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 1 H 2
(b) 1 H 2 and 1 H 3
(c) 6 C12 and 6C13
(d)
20
15
P30 and 14 Si 30
Consider the following forces in nature I Gravitation II Strong III Electrostatic
IV Weak. If the forces are arranged in decreasing magnitude the correct
combination 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
92
U 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 )M P
(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
the radio of
10
10
B5 and 5 B11 . Then
B10 and 5 B11 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.
Specific Teaching and Learning Objectives

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
Summary of the Learning Activity
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 to  ,  or  radiations.
The fundamental law of radioactive decay states the rate of transformation of a
radioactive nuclei is proportional to the number of atoms of the nuclei.
N  N e  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 transformation, i.e
one element decays into a radioactive substance that is also radioactive. 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,
N P  P N P  0
or
dN D
 D N D  0
dt
P N P  D N D
P N P  G NG
etc.
where subscripts P, D and G stand for parent, daugheter and granddaughter respectively.
Study of radioactivty and radioisotopes has several applications in science and
technology. Some of them are:
1. Radioactive dating:
2. Trace element analysis:
3. Medical application as diagnostic and treatment etc.
List of Required Readings
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;  ,  and  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.
List of Relevant MM Resources (for the Learning Activity).
Software, Interactive online exercises Videos, animations etc
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.
url:- http://michele.usc.edu/java/fission/nuclear.html
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.
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 #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..
Detailed Description of the Activity (Main Theoretical Elements)
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
40
K , and the
naturally radioactive light nuclei, such as the potassium isotope 19
carbon isotope
14
6
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
226
substances which they named polonium, 210
84 Po , and radium, 88 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
holding a sample of radon, a radioactive gas  222
86 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
spectrum of helium, and this confirmed that the alpha-particles emitted by the
radon sample turned to helium. Applying the methods of magnetic and
q
electrostatic deflection. Rutherford determined the specific charge,
, of alpha
m
particles (where m 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, 42 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 , where m  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 radioactive atoms. The disintegration of radium in
RaC12 and RaBr2 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 betaparticles are called alpha- and beta-decay, respectively. Gamma-decay is nonexistent. 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:
A
z
For alpha decay:
For beta decay:
A
z
4
X 
 A-4
Z-2Y  2 He
 decay
A
X 
 Z+1
Y  10
 decay
Where X is the chemical symbol of the parent nucleus, Y is that of a daughter
nucleus, 42 He is the helium nucleus (the end product), and 10 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:
226
88
4
Ra 
 222
86 Rn  2 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 betadisintegration 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
 the Thorium series (starts from
238
92
U and terminates in a stable
206
82
Pb )
Th and terminates in a stable
208
82
Pb ) and
232
90
 the Actinium series, (starts from
238
92
thus called after the respective parents,
U and terminates in a stable
238
92
U, 23290Th, and
235
89
207
82
Pb )
AC There is one more
radioactive series produced artificially and starting with neptunium, 237
93 Np , a
transuranic 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 83 Bi 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:
238
92
U


206
82
Pb.
The number n 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, n  ( A1  A2 ) / 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  n
2n  n  10
From the value of n , we find that n  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 t 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  N untransformed nuclei existing
at time t  t then change in the number of untransformed nuclei that is the
number of nuclei decaying in time t will be proportional to N, that is:
N N t ; or N  - N t
where  is a positive proportionality factor called the decay constant; it has a
definite value for each nuclear species. The minus sign on the right-hand side of
the above equation indicates that N decreases with time. Thus it follows that the
decay constant is the fractional decreases in the number of nuclei decaying per
unit time:

 N
N
t
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   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  N0 exp(t )
where N 0 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  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 constant
.
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  t1/ 2 , if N (t1/ 2 ) 
N0
2
By this definition and on the basis of the exponential decay law, t1/ 2 and  are
related as
N0
 N 0 exp (-t1/ 2 )
2
Cancelling N 0 and taking a logarithm, we obtain
t1/ 2 
ln 2


0.693

or
1


T
 1.44T
0.693
The half-lives of naturally radioactive elements range between wide limits. For
uranium 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  ) 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 2t1/ 2 . This
is not so because if the number of nuclei remaining after the time t1/ 2 is N0 / 2 ,
then after the time 2t1/ 2 this number will be falf the number N 0 /2, or one-quarter of
N 0 , and in the time 3t1/ 2 this number will be half of N 0 /4 that is, N 0 /8, and so on.
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 N  N 0 e t 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
N p
N d
t
t
and so, at equilibrium the following relation holds

 p N p  d N p
or
Np
Nd

d Tp

 p Td
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
N  N 0 e  t
In the International System (SI) of units, activity is expressed in s 1 . 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 ( Ci )
1mCi  103 Ci
1Ci  106 Ci
An alternative unit is the rutherford (Rd), a unit of radioactivity equal to 106 decays
per second, 1Rd  106 s 1 . Obviously, 1Ci  3.7 104 Rd .
Example
The half-life of radium equal to 1590 years. Find its decay constant  . and
determine 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, N A ,
divided by the mass of one kilomole, M:
6.023 1026 1/ kmole
N  NA / M 
 2.67 1024 kg 1
226 kg/kmole
=2.67 10 24g -1
Then the activity of one gram of radium will be
A   N  0.693N / T 
0.693
2.67 1021
1590  365  24  3600
 3.7 1010 s 1
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 number
of decays per second is 3.7  1010 .
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 t . 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 t to t . Thus, what we have is a
statistical 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 t is N , then the
relative decrease, N / N , in the number of nuclei per unit time, that is, the
quantity - (N / N )t gives the decay probability per unit time per nucleus.
This definition agrees with the meaning of the decay constant,  . 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 N 0 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: N  N 0 e t , the time interval between the
instants when the number of radioactive nuclei is N0 and N is
N 
1 N 
t    ln  0   1.44t1/ 2ln  0 
  N 
 N 
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 radioactive 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 halflive 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
235
99.28% 238
0.006% 234
92 U, , 0.714% 92 U,
92 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 isotopes 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 uranium, 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 scales.
The particles that make up the so-called primary cosmic rays are extremely
energetic 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 t1/ 2  5570 years into minutes, we find the number of 146 C nuclei that
have this magnitude of activity:
N  (1/  )(N / t )
 1.44t1/ 2 (N / t )
 1.44  5570  365  24  60 1.75
 7.5  1010
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.
Formative Evaluation 2
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 directions.
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 neutron
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 hydrogen
nucleus to emit an alpha particle? Explain your answer.
Ans. A hydrogen nucleus contains only one proton and zero, one or two
neutrons. 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
particles 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 proportional 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
number 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 positively
charged. They will be repelled away from each other by the electromagnetic
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?
2
Ans. Doubling the distance will result in a count of 1 2  1 4 the original
count. 1/4 of 360 = 90 counts per minute. Tripling the distance will result in
2
1 3  1 9 the original count. 1/9 of 360 = 40 counts per minute.
 
 
22) When 226
88 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
88
23) When
218
84
Ra 
222
86
Ra  24 He
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 atomic number
85 and its atomic mass is 218. The reaction can be written as follows:
0
Po  218
where -10  represents the emitted electron
85 At  1,
b) When the nucleus of an atom emits an alpha particle, it loses two protons
and two neutrons. If 218
84 Po emits an alpha particle its new atomic number will
be 82 and its new atomic mass will be 214. The reaction can be written as
follows:
218
214
4
84 Po  82 Pb  2 He
218
84
24) State the number of protons and neutrons in each of the following nuclei:
2
12
56
197
90
238
1 H, 6 C, 26 Fe, 79 Au, 38 Sr, and 92 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 repeated this
process 4 times. Four half-lives have elapsed. Eight hours divided by 4,
equals 2 hours.
Teaching the Content in Secondary School 2
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
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.
Specific Teaching and Learning Objectives

Describe interaction of light charged 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 (construction,
principle and use)
Summary of the Learning Activity
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
energetic 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)

Photoelectric effect:
I. Atomic electrons
Tpe  Z 4 (low energy)
 Z (high energy)
5
Rayleigh scattering
Inelastic
scattering
(Incoherent)
Compton
scattering
 R  Z 2 (low energy limit)   Z
Photonuclear reactions:
II. Nucleons
 , n  , p  , f  etc,
 Z (h  10 MeV)
Elastic nuclear
scattering
Nuclear
resonance
Scattering
Pair production
III. Electric field of
charged particles
a) kn  Z (h  1.02MeV)
b) ke  Z (h  2.04MeV)
Delbrück scattering
Photomeson production
IV. Mesons
h  140MeV
List of Required Readings 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
light 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.
List of Relevant MM Resources (for the Learning Activity).
Software, Interactive online exercises Videos, animations etc
Resource #3; 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
Geiger counter has two sample holders. In each sample holder you can pick
either an empty holder, Ba137m or Mn54 (5  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 time
2. 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; 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 (approximately) 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 parameters 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.
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 #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, thermal
neutrons, and charged particles with matter. Introduces classical electrodynamics,
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 magnetic 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
Detailed Description of the Activity (Main Theoretical Elements)
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 and
4. 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 called 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   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 e 4 z 2
 -dE 
S
NZB
 
mo v2
 dx coll
Beth formula for stopping power
 2m o v 2
 v2  v2 
where B  ln
 ln 1  2   2 
l
 c  c 

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 , m o 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
deflected from a primary beam of x or -radiation, may be classified according to:
i.
the kind of target, e.g. electrons, atoms or nuclei with which the
photon interacts.
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 (,n), (,p), photo-fission etc. (Absorption).
ii.
Elastic nuclear scattering (,) (Scattering)
iii.
Inelastic nuclear scattering (,) (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 (,) (Scattering)
But out of all these interaction processes, five main processes are:
i.
Photoelectric effect
ii.
Compton scattering
iii.
Pair production
iv.
Rayleigh scattering
v.
v) 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 subsections, 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
circuit. 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 recombination 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
multiplication 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
proportionality’ 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.
3.4.2 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
radiation:

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).
Formative Evaluation 3
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
greater 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
You will require 20 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.
Specific Teaching and Learning Objectives

Identify fundamental interactions in nature

Explain Yukawa’s theory of nuclear force

Identify elementary particles and describe their role in the process of
interaction
Summary of the Learning Activity
*Max 100 words of the synopsis of the activity
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
explained. 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)
List of Required Readings
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 particles
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.
Detailed Description of the Activity (Main Theoretical Elements)
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);
Electromagnetic; weak and gravitational. Table below shows therlative strengths of
the four basic interactions.
Type of Interaction
Relative Strength
Range
Gravitational
10 39

Weak (eg. Beta decay)
10 13
almost zero
Electromagnetic
10 2

Strong (Nuclear)
1
1014 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
composed 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, 1 D 2 . 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
1 fm  1015 cm
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 protonproton 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. Observations
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   there is   , for   there is   for  there is  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
3 5
b. have half integral spin i.e. , ,
2 2 2
Fermions
  , n, p,  ,  are examples of
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 ,
 ,  ,  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
referred 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
continuously 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
p  0
n
n  0
p
n  
n
p  
These equations violet the law of conservation of energy. A proton of mass
equivalence 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:
E t 
Et 
so the violation can exist only if
h
h
 t 
=
E
m c 2
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 force. i.e. the distance within which the
exchange of pions by nucleons takes place.
 t=
 E=
1.5 10-15
 0.3  108sec
8
3 10
= 3.5152 10-11J = 145.57MeV
t
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  meson (a particle of non-zero rest mass) by nucleons
satisfies 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  meson the change in energy that is involved is at least
the energy contained by a meson at rest, i.e m c 2 . Thus during the interaction of
nucleon and pions, the change in energy involved is:
E  m c 2
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 E  m c 2 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  meson field is approximately given by:
V (r )   2
e  r
r
where  is a constant and  
Potential.
m c
. This is commonly referred to as Yukawa
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
 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.
Formative Evaluation 4
1) Determine the minimum kinetic energy of protons requiered for the formation of
a)  0 -messon in the reaction p  p  p  p   0 ,
b) a proton anti proton pair in the reaction p  p  p  p  p  p
2) Knowing the mass of a neutral  -meson (135.0Mev/c2), determine the energy
of  -quanta formed during the decay of a stationary neutral  meson:
 0  2 .
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
Teaching the Content in Secondary School 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
atomic 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 COMPILED
(GLOSSARY)
LIST
OF
ALL
KEY
CONCEPTS
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 number 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,    . computed for each
nuclide, using the following equation
  ZM p  ZM e  ( A  Z )( M n )  M a
 Z ( M H )  ( A  Z )( M n )  M a
where  = mass defect
Z=atomic number
M p  mass of a proton (1.00728 amu)
M e  mass of electoron (0.000548 amu)
A= mass number
M n =mass of neutron (1.00867)
M a =atomic mass (from chart of the nuclides)
M H  mass of hydrogen atom
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.
4  11 H    42 He 2+   2  e +   24.7MeV
The reaction is initiated under the extremely high temperatures and pressure
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
COMPILED LIST OF COMPULSORY READINGS
XIII COMPILED LIST OF (OPTIONAL) MM RESOURCES
Resource #1
Title: Motion of Centre of Mass
URL: http://surendranath.tripod.com/Applets/Dynamics/CM/CMApplet.html
Screen Capture:
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 velocity 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 Rotating Stool
url:- http://hyperphysics.phy-astr.gsu.edu/hbase/rstoo.html#sm
Complete Reference:- Good animation graphics and applet to visualize the
dependence of moment of inertia on distribution of matter on an object..
Rationale: Strengthens what is already discussed in Activity 2.
Resource #3;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 COMPILED LIST OF USEFUL LINKS
Useful Link #1 Classical Mechanics
Title: Classical Mechanics
URL: http://farside.ph.utexas.edu/teaching/301/lectures/
Screen Capture:
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
mechanics courses. The learner can consult chapters 7, 8 and 9 of the
book. The PDF version is also available.
Useful Link #2 Tutorial on torque from university of Guelph
Title: Torque
URL: http://www.physics.uoguelph.ca/tutorials/torque/index.html
Screen Capture:
Description: The site gives detailed description of torque
Rationale: Here you will find a good collection of tutorial problems on torque...
Useful Link #3 Universal Gravitation from Wikipedia
Title: Universal Gravitation
URL: http://en.wikipedia.org/wiki/Law_of_universal_gravitation
Screen Capture:
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 From The physics Class room
Title: Universal Gravitation and Planetary Motion
URL:
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/circles/u6l3c.html
Screen Capture:
Description: Lecture notes and discussion forum from the physics class room.
Rationale: Reach in discussion topics and interactive problems.
Useful Link #5 Wikipedia
Title: Gravitational Field
URL: http://en.wikipedia.org/wiki/Gravitational_field
Screen Capture:
Description: Gravitational field, its meaning in classical mechanics, and its meaning in
general relativity are described in this section.
Rationale: Useful for the one who needs to compare many references.
Useful Link #6 Geostationary Orbit
Title: Geostationary orbit
URL: http://en.wikipedia.org/wiki/Geostationary
Screen Capture:
Description: This link Explains geostationary orbit. The animated graphics helps
visualization.
Rationale: This supplements the theory given in Activity three...
XV SYNTHESIS OF THE MODULE
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 trajectories 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
motion 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. Summative Evaluation
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
bombardment 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 210
84 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.
C
0ev
-0.544ev
-0.850ev
D
-1.500ev
B
-3.400ev
A
E
-13.600ev
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
correspond 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  -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 1017 atoms/s
and half-life is 1445 years. The number of atoms is
(a) 1.44  1017
(c) 6.57 1027
(b) 1.4  1017
(d) none of these.
17 In a breeder reactor, useful fuel obtained from
(a)
239
Pu
(b)
238
U is
235
U
(c)
235
233
(d)
Th
Ac
18 The average life  and the decay constant  of a radioactive nucleus are
related as
(a)   C / 
(c)   0693/ 
(b)  /   1
(d)   1
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  =6
(c)   6 and  =4
(b)   6 and  =0
(d)   3 and  =3
20  -rays consist of
(a) electromagnetic waves
(c) helium nuclei
(b) fast moving electrons
(d) singly ionised gas atoms
21 Emission of  -rays in a radioactive decay results in a daughter element
showing a
(a) change in charge but not in
mass
(c) change in both
(d) change in neither
(b) change in mass but not in
charge
22 In the reaction represented by
sequence are
A
Z
X
A 4
Z 2
Y
A 4
Z 2
Y
A 4
Z 1
(a)  ,  , 
(c)  ,  , 
(b)  ,  , 
(d)  ,  , 
K
The decay in
23 The main source of solar energy is
(a) combustion
(c) nuclear fusion
(b) gravitational contraction
(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 88 Ra 238 decays in a series by the emission of
three alpha particles and a  -particle. The isotope finally formed is
(a)
84
RA220
(b)
88
RA215
(c)
86
RA272
(d)
83
RA226
26 Half life period of lead is
(a) 1590 years
(c) infinite
(b) 1590days
(d) zero
27 The half life period of a radioactive sample depends upon
(a) nature of substance
(c) temperature
(b) pressure
(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
(c) electron capture
(b) fusion
(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
(c) electrons
(b) protons
(d) neutrons
32 What is the mass of 1 curie of U 234 (  8.8 1014/ s )
(a) 3.7 1010 g
(c) 20 days
(d) 3.8  20 days
(b) 2.348 1023 g
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 ( log10e  0. 4343 )
(a) 1.6 days
(c) 20 days
(b) 16.4 days
(d) 3. 8  20days
34 The radioactive decay rate of a radioactive element is found to be 103
disintegrations/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
(c) 125, 500
(b) 103 , 103
(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
(c) 12 hours
(b) 24 hours
(d) 6 hours
36 The equation
A
Z
X Z A1Y  10e
(a) fission
(b) fusion
represents
(c)  decay
(d)  -decay
37 During a negative  -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 4 Be9 is bombarded with  -particle, one of the products of nuclear
transmutations is 6 C 12 . The other is
(a) 0 n1
(b) 1 H 2
39 In the nuclear reaction, given by
(c) 1 H 1
4 He14 N X b  H1
q
1
7
2
(d)
(c) nitrogen of mass 16
(b) oxygen of mass 17
(d) nitrogen of mass 17
92
e0
The nucleus X is
(a) oxygen of mass 16
40 The energy released per fission of a
1
U 235 nucleus is nearly
(a) 200 MeV
(c) 200 eV
(b) 200 keV
(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%
C115 B11    X
42 In the nuclear process 6
, X stands for
(a) photon
(c) antineutrino
(b) neutrino
(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
(c) X+Y<M
(b) X+Y>M
(d) X+Y=M
13
6
44 The nuclei
14
7
C and
N can be described as
(a) isotones
(c) isobars
(b) isotopes of carbon
(d) isotopes of nitrogen
45 If M is the atomic mass, A is mass number, then (M-A)/A is called
(a) packing fraction
(c) Fermi energy
(b) mass defect
(d) binding energy
46 When the number of nucleons in nuclei in crease, the binding energy per
nucleon
(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
52 The equation
4

1
H
1
(c) 235
 2 He4  2e  26MeV
(d) 234
represents
(a) fission
(c)  -decay
(b) fusion
(d)  -decay
53 From the following equations pick out the possible nuclear fusion reactions.
(a)
(b)
(c)
(d)
13
1
14
6 C 1 H  6 C  4.3Mev
12
1
6 C 1 H  7
7
N13  2 Mev
N14 +1H18 O15 +7.3Mev
235
92
94
1
U+ 01 n 140
54 Xe+ 38 Sr+2( 0 n)
  200MeV
54 Consider a nuclear reaction x 200  A110  B90 + Energy 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
neutrons?
(a) U 235 , Pu 239
(c) U 238 , Rn232
(b) P 239 , Th234
(d)
92
U 238 82 pb 206
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%
(c) 8.5%
(b) 87.5%
(d) 25.1%
57 The element used for radioactive carbon dating for more than 5600 years is
(a) C14
(b) U 234
(c) U 238
(d) Po94
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
(c) 45 minutes
(b) 30 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) 21/ 3 :1
(b) 21/ 3 :1
60 A radioactive reaction is
emitted?
92
(c) 31/ 3 :1
(d) 1: 31/ 2
U 238 82 pb 206  . How many  - and  -particles are
(a) 10  ,6 
(c) 6 electron, 8 proton
(b) 4 protons, 8 neutron
(d) 6  and 8 
61 Which of the following is the fusion reaction
a. 1 H 2 1 H 2  2 He 4
b. 0 n1  7 H 14 6 C14 1 H 1
c. 0 n1 92 U 236 93 Np 239     
d. 1 H 3  2 He3     
62 Which of the following statements is true?
a. 78 Pt192 has 78 neutrons
Po 214 
b.
84
c.
238
92
d.
90
U
82
Pb 210 + -
234
90
Tj 234 
Th+ 24 He
91
Pa 234 + 2 He4
63 The binding energy of deutron
particle

2

1
H 2  is 1.112 MeV per nucleon and an alpha
H 4  has a binding energy of 7.074 MeV per nucleon. Then in the
reaction 1 H 2 1 H 2 2 He 4  Q the energy Q released is
(a) 1MeV
(c) 23.8 MeV
(b) 11.9 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) 3.61 1010
(c) 3.11 1015
(b) 3.61 1012
(d) 31.1 1015
(e) (Avagadro’s number N  6.02 1026 atom /kilomole)s
65 A parent nucleus n P m decays into a daughter nucleus D through  emission
in the following way 4 0 C . The subscript and superscript on the daughter
nucleus D will be written as
(a) n P m
(c) n P m 4
(b) n P m 4
(d)
n2
D m4
66 Given mneutron  1.0087, m proton  1.0073, m  4.0015 (in amu units, 1 amu=931
MeV). Binding energy of helium nucleus is
(a) 28.4 MeV
(c) 27.3 MeV
(b) 20.8 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 I 0 -rays radiations can be used to create electron positron pair. In this process
of pair production,  -rays energy can not be less than
(a) 5.0 MeV
(c) 15.0 MeV
(b) 4.02 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
(c) 560
(d) 840
says
days
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 I 0 in a period of 9 years. After 9 years more, its activity would be
(a) same
(c) I 0 /4
(b) I 0 /6
(d) I 0 /9
72 Radon-220 will eventually decay to Bismuth 212 as
220
84 Po 216  2 He4 ; half life =55s
86 Rn
84
Po 216 82 Pb 212  2 He4 ; half life =0.16s
Pb 212 83 Bi 212  1 e0 ; half life =10.6 hours
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
82
(a) Radon
(c) Lead
(b) Polonium
(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 4 0 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
(c) 3  58
(b) 58/2
(d) 2  58
76 A radioactive sample contains 50 atoms and has a half life of one year. Then
the time required for all the atoms to decay is
(a) 106 years
(c) 10 years
(b) one year
(d) 
77 A fast reactor does not use
(a) a coolant
(c) a moderator
(b) control system
(d) nuclear level
78 When
92
U 235 undergoes fission 0.1%of its original mass is changed into
energy. How much energy is released if 1 kg of
92
U 235 undergoes fission?
(a) 9 1010 J
(c) 9 1012 J
(b) 9  1011 J
(d) 9 1013 J
79 The half-life of the isotope 11 Ha 24 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 U 235 . A reactor is
generating 100 kW of power.
(a) 1000
(c) 931
(b) 2  108
(d) X1 to that of X 2
81 N atoms of a radioactive element emit n alpha particles per second. The halflife of the element
(a) n/N sec
(d)
(b) N/n sec
(c)
0.693n
sec
N
0.693 N
sec
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
(c) alpha beta and gamma decays
(b) alpha and gamma decays
(d) beta and gamma decays
83 Thermal neutrons are incident on a sample of Uranium containing both
235
235
92 U and 92 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 Al  27.98154 in amu.
(a) 6.79 103 MeV
(c) 6.32 MeV
(b) 3.16 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 X 1 and X 2 have decay constants 10  and 
respectively. If initially they have the same number of nuclei, then the ratio of
the number of nuclei of X1 to that of X 2 will be 1/e after a time
(a) 1/(10  )
(b) 1/(11  )
(c) 11/(10  )
(d) 1/(9  )
Answers to Formative Evaluation 1
1. C
6. C
11. D
16. D
21. D
2. A
7. B
12. D
17. B
22. D
3. A
8. A
13. D
18. C
23. B
4. A
9. A
14. A
19. D
24. A
5. B
10. C
15. C
20. B
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
1. Raymond A. Serway (1992). PHYSICS for Scientists & Engineers. Updated
Version.
2. Douglas D. C. Giancoli Physics for scientists and engineers. Vol. 2. Prentice
Hall.
3. Irving Kaplan (1962) Nuclear Physics.
4. Sena L.A. (1988) Collection of Questions and Problems in physics, Mir
Publishers Moscow.
5. Nelkon & Parker (1995) Advanced Level Physics, 7th Ed, CBS Publishers &
Ditributer, 11, Daryaganji New Delhi (110002) India. ISBN 81-239-0400-2.
6. 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.
7. Beiser A., (2004) Applied Physics, 4th ed., Tata McGraw-Hill edition, New
Delhi, India
8. Halliday D., Resnick R., and Walker J. (1997), Fundamentals of Physics, 5th
ed., John Wiley and Sons
9. James O’Connell (1998), Comparison of the Four Fundamental Interactions of
Physics, The Physics Teacher 36, 27.
10.
XVIII. Main Author of the Module
About the author of this module:
Name: -
Tilahun Tesfaye
Title:
Dr.
Address:
Department of physics, Addis Ababa University,
Ethiopia, East Africa.
P.O.Box 80359 (personal), 1176 (Institutional)
E-mail: [email protected]; [email protected].
Tel: +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.
XX. File Structure
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 compiled in one
PDF file. .