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Nuclear Physics
Nuclear Physics
Prepared by Tilahun TESFAYE
African Virtual university
Université Virtuelle Africaine
Universidade Virtual Africana
African Virtual University Notice
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African Virtual University Table of Contents
I.
Nuclear Physics_ ___________________________________________ 5
II.
Prerequisite Course or Knowledge_ _____________________________ 5
III. Time_____________________________________________________ 5
IV. Materials__________________________________________________ 5
V.
Module Rationale_ __________________________________________ 5
VI. Content___________________________________________________ 7
6.1 Overview ____________________________________________ 7
6.2 Outline_ _____________________________________________ 7
6.3 Graphic Organizer _____________________________________ 7
VII. General Objective(s)_________________________________________ 9
VIII. Specific Learning Objectives__________________________________ 10
IX. Pre-assessment_ __________________________________________ 11
X.
Teaching and Learning Activities_______________________________ 23
XI. Glossary of Key Concepts____________________________________ 85
XII. List of Compulsory Readings_ ________________________________ 87
XIII. Compiled List of (Optional) Multimedia Resources_________________ 88
XIV. Compiled List of Useful Links_________________________________ 89
XV. Synthesis of the Module_____________________________________ 90
XVI. Summative Evaluation_______________________________________ 91
XVII.References_ _____________________________________________ 109
XVIII. Main Author of the Module _________________________________ 110
XIX. File Structure _ ___________________________________________ 111 African Virtual University Notice
Foreword
This module has four major sections.
The first one is the INTRODUCTORY section that consists of five parts vis:
TITLE:- The title of the module is clearly described
PRE-REQUISITE KNOWLEDGE: In this section you are provided with information regarding the specific pre-requisite knowledge and skills you require to start the
module. Carefully look into the requirements as this will help you to decide whether
you require some revision work or not.
TIME REQUIRED: It gives you the total time (in hours) you require to complete
the module. All self tests, activities and evaluations are to be finished in this specified
time.
MATERIALS REQUIRED: Here you will find the list of materials you require
to complete the module. Some of the materials are parts of the course package you
will receive in a CD-Rom or access through the internet. Materials recommended
to conduct some experiments may be obtained from your host institution (Partner
institution of the AVU) or you may acquire or borrow by some other means.
MODULE RATIONALE: In this section you will get the answer to questions like
“Why should I study this module as pre-service teacher trainee? What is its relevance
to my career?”
The second is the CONTENT section that consists of three parts
OVERVIEW: The content of the module is briefly presented. In this section you will
fined a video file (QuickTime, movie) where the author of this module is interviewed
about this module. The paragraph overview of the module is followed by an outline
of the content including the approximate time required to complete each section. A
graphic organization of the whole content is presented next to the outline. All these
three will assist you to picture how content is organized in the module.
GENERAL OBJECTIVE(S): Clear informative, concise and understandable objectives are provided to give you what knowledge skills and attitudes you are expected
to attain after studying the module.
SPECIFIC LEARNING OBJECTIVES (INSTRUCTIONAL OBJECTIVES):
Each of the specific objectives, stated in this section, are at the heart of a teaching
learning activity. Units, elements and themes of the module are meant to achieve the
specific objectives and any kind of assessment is based on the objectives intended to
African Virtual University be achieved. You are urged to pay maximum attention to the specific objectives as
they are vital to organize your effort in the study of the module.
The third section is the bulk of the module. It is the section where you will spend
more time and is referred to as the TEACHING LEARNING ACTIVITIES. The
gist of the nine components is listed below:
PRE-ASSESSMENT: A set of questions, that will quantitatively evaluate your level
of preparedness to the specific objectives of this module, are presented in this section.
The pre-assessment questions help you to identify what you know and what you need
to know, so that your level of concern will be raised and you can judge your level
of mastery. Answer key is provided for the set of questions and some pedagogical
comments are provided at the end.
TEACHING AND LEARNING ACTIVITIES: This is the heart of the module.
You need to follow the learning guidance in this section. Various types of activities
are provided. Go through each activity. At times you my not necessarily follow the
order in which the activities are presented. It is very important to note:
•
•
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formative and summative evaluations are carried out thoroughly
all compulsory readings and resources are done
as many as possible useful links are visited
feedback is given to the author and communication is done
COMPILED LIST OF ALL KEY CONCEPTS (GLOSSARY): This section
contains short, concise definitions of terms used in the module. It helps you with
terms which you might not be familiar with in the module.
COMPILED LIST OF COMPULSORY READINGS: A minimum of three compulsory reading materials are provided. It is mandatory to read the documents.
COMPILED LIST OF (OPTIONAL) MULTIMEDIA RESOURCES: Total list
of copyright free multimedia resources referenced in, and required for completion
of, the learning activities is presented.
COMPILED LIST OF USEFUL LINKS: a list of at least 10 relevant web sites that
help you understand the topics covered in the module are presented. For each link,
complete reference (Title of the site, URL),a screen capture of each link as well as
a 50 word description are provided.
SYNTHESIS OF THE MODULE: Summary of the module is presented.
SUMMATIVE EVALUATION:
Enjoy your work on this module.
African Virtual University 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
- Nuclear Magnetic Resonance (cancer),
- Security (e.g. mine detection),
- Fundamental studies such as neutrino properties (double beta decay)
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•
•
•
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Medical applications
- Cancer therapy using radiation
- Historic use to kill cells - e.g. radium
- Modern use with ion beams (e.g. GSI)
Medical imaging
- MRI (Nuclear magnetic imaging)
- Positron Emission Tomography
- X-ray imaging etc
The environment
- Carbon dating 12C/14C ratio
- Argon gas dating
- Rb/Sr dating of rocks
Biology
- Archaeology (dating by isotope ratios)
- Use of radioactivity to trace fluids in organs
- Forensic
Security and industry
- Oil well logging
- Detection of bomb material etc
Study of atomic nucleus is the basis to harness the tremendous amount of energy
locked by nature inside the nucleus and to use radiations emitted by the atomic 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.
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African Virtual University VI. Content
6.1 Overwiew
This module (Nuclear Physics) introduces the basic properties of the atomic nucleus
nuclear constituents; the binding energy; isotopes; and nuclear models are concepts
dealt in the first activity.
Most atoms found in nature are stable and do not emit particles or energy that change
form over time. Heavy elements, such as uranium or thorium, and their decay chain
elements do not have stable nuclei. They emit radiation in their naturally occurring
state. The second activity of the module dwells on radioactivity and related 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.
6.2 Outline
1 Basic Properties of the Atomic Nucleus
(30 hours)
&Basic Propertiesof the atomic nucleus, Nuclear constituents, Iosotopes,
&Nuclear Binding Energy.
&Nuclear Stability,
&Mass and Isotopic Abundance;
&Nuclear Models.
2 Radioactivity
(35 hours)
&Radioactivity, discovery, alpha, bet and gamma radiation, Laws of Radioactive
Distegration.
&Natural Radioactivity (Series and non Series), radioactive equilibrium,
&Applications of Radioactivity.
3 Interaction of Radiation With Matter
&Interaction of heavy and light Charged Particles with matter,
&Interaction of photons with matter,
&Interaction cross-sections and interaction coefficients.
&Nuclear Radiation Detectors.
(35 hours)
African Virtual University 4 Nuclear Forces and Elementary Particles
(20 hours)
&Fundamental Interaction in nature.
&Survey of elementary particles.
&Yukawa’s theory of nuclear forces.
6.3 Graphic Organizer
A . B asi c P r o pe rt ies
o f the At om i c N uc leus
C. I n te ra ct io n of R adia tio n
W it h M att er
Basi c proper ti es of th e atom i c nu cl eu s.
Nuc lear const itu ents. I sot opes,
I nter ac ti on of h eavy and li ght
c harged part icl es w ith m atter .
Nuc lear bin ding energ y,
I nter acti on of phot ons w ith m atter .
Nuc lear stabili ty ,
I nt eract ion cr oss- secti ons
an d i nter ac ti on coeff ici ents.
Nuc lear radi ation detect ors.
D . N u c lear Fo rc es a n d
Elem en ta ry P ar tic les
F undam ental int eract ions in n atur e.
M ass an d iso topi c abun dance,
N U CL EAR
P hy sics
Nu clear m odels
B . R adi o ac tiv ity
R ad ioact iv it y. I t s d isc over y, alp ha,
beta and gamm a radi at ion,
Law s of radi oac ti ve d isi ntegr ation .
Y uk aw a’s th eor y of nuc lear forc e.
Sur vey of elem entar y parti cl es.
Natur al radi oacti vi ty ( seri es and n on s er ies)
radi oacti ve equili b riu m,
App li cati ons of radi oacti v ity .
African Virtual University VII. General Objective(S)
After completing the module you should be able to
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Understand the basic properties of nuclei and the atomic nucleus
Describe radioactivity and related phenomena
Explain the various interactions of nuclear radiation with matter
Understand nuclear interactions and elementary particles involved in the
interactions
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VIII.Specific Learning Objectives
(Instructional Objectives)
Content
Learning objectives
After Completing this section you should be able to:
1. Basic Properties of the Atomic Nucleus (30 hours)
&Basic Propertiesof the atomic
nucleus, Nuclear constituents,
Iosotopes,
&Nuclear Binding Energy.
&Nuclear Stability,
&Mass and Isotopic Abundance;
&Nuclear Models.
2. Radioactivity: (35 hours)
&Radioactivity, discovery, alpha,
bet and gamma radiation, Laws of
Radioactive Distegration.
&Natural Radioactivity (Series and non
Series), radioactive equilibrium,
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•
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•
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
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
&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.
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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
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IX. Pre-assessment
Are You Ready For Nuclear Physics?
Dear Learner
In this section, you will find self-evaluation questions that will help you test your
preparedness to complete this module. You should judge yourself sincerely and do
the recommended action after completion of the self-test. We encourage you to take
time and answer the questions.
Dear Instructor
The Pre-assessment questions placed here guide learners to decide whether they are
prepared to take the content presented in this module. It is strongly suggested to abide
by the recommendations made on the basis of the mark obtained by the learner. As
their instructor you should encourage learners to evaluate themselves by answering
all the questions provided below. Education research shows that this will help learners
be more prepared and help them articulate previous knowledge.
9.1
Self Evaluation Associated With Nuclear Physics
Evaluate your preparedness to take the module on thermal physics. If you score
greater than or equal to 60 out of 75, you are ready to use this module. If you score
something between 40 and 60 you may need to revise your school physics on topics
of heat. A score less than 40 out of 75 indicates you need to physics.
Try the following questions and evaluate whether you have the necessary background
to take on topics related to Nuclear Physics.
1 Which statement best describes the structure of an atom?
(a) A positive core surrounded by electrons packed tightly around it.
(b) A particle comprised of a mixture of protons, electrons and neutrons.
(c) A tiny nucleus of protons and neutrons with electrons orbiting around it.
(d) A large core of protons and electrons surrounded by neutrons.
2 Of the following, when an atom emits an alpha particle its mass number is
(a) decreased by 4 and its atomic number is increased by 2
(b) increased by 4 and its atomic number is decreased by 2
(c) increased by 4 and its atomic number is increased by 2
(d) decreased by 4 and its atomic number is decreased by 2
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3
An electron moves with a speed equal to 4/5 that of light, Which one of the
following is the ratio the electron’s mass to its rest mass.
(a) 5/4
(b) 5/3
(c) 25/9
(d) 25/16
4 Of the following the one which can penetrate through 20cm thick steel plate is
(a) positive rays
(b) α -rays
(c) β -rays
(d) γ -rays
5
The half life period of radioactive nuclide is 3 hours, its activity will be reduced
by a factor of
(a)
1
8
(b)
1
6
(c)
1
27
(d)
1
9
6 Which of the following radioactive decay emits α -particle
(a)
7
82
pb214 →93 Bi 214 + ...
(b)
91
Th234 →91 pa 234 + ...
(c)
92
U 238 →90 Th234 + ...
(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
(b) 0.5g
(c) 0.25g
(d) <1 mg
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8
A nuclide A (with mass number m and atomic number n) disintegrates emitting
an α -particle. The resulting nuclide B has mass number and atomic number
respectively equal to
(a) m-2 and n
(b) m-4 and n-2
(c) m-4 and n-1
(d) m+4 and n+1
9
As a result of radioactive decay a 238
U nucleus is changed to
92
During this decay the particles emitted are
234
91
Pa nucleus.
(a) two β -particles and one proton
(b) two β -particles and one neutron
(c) one α -particle and one β -particle
(d) one proton and two neutrons
10 The relation between half life T1/ 2 of a radioactive sample and its mean life τ
is
(a) τ = 2.718T1/ 2
(b) τ = T1/ 2
(c) τ = 0.693T1/ 2
(d) T1/ 2 = 0.693τ
11 The decay constant λ of a radioactive sample
(a) is independent of the age
(b) depends on the nature of activity
(c) increases as the age of atoms increases
(d) decreases as the age of atoms increases
12 Of the three isotopes of hydrogen 1 H 1 ,1 H 2 and 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
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13 A certain radioactive substance has a half-life of 5 years. Thus for a nucleus in
a sample of the element, probability of decay in 10 years is
(a) 100%
(b) 75%
(c) 60%
(d) 50%
14 A gamma ray photon creates an electron positron pair. If the rest mass of electron
is 0.5 MeV and the total kinetic energy of the electron positron pair is 0.78 MeV,
the energy of gamma ray photon must be
(a) 0.28 MeV
(b) 1.28 MeV
(c) 1.78 MeV
(d) 0.78 MeV
15 If the mass of proton is completely converted into energy, it will be about
(a) 3.1MeV
(b) 931 MeV
(c) 10078 MeV
(d) 9310 MeV
16 A π 0 meson at rest decays into two gamma rays π 0 → γ + γ then which of
the following is correct
(a) the two γ ’s move in the directions opposite to each other
(b) the two γ ’s have unequal energies
(c) both the γ ’s move in the same direction
(d) the γ ’s will be periodically approaching and receding from each other
17 If the half life of a radioactive metal is 2 years
(a) The metal will completely disintegrate in 2 years
(b) 1/4th of it will remain after 8 years
(c) the metal will completely disintegrated in to 4 years
(d) it will never disintegrate completely
18 When aluminium is bombarded with α -particles, radioactive phosphorus is
formed i.e.
is
13
Al 27 + 2 He4 →15 P 30 one more particle formed in this reaction
(a) an electron
(b) a neutron
(c) negatively charged helium atom
(d) a negatively charged hydrogen atom
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19 If 5 B 10 is bombarded with neutrons and α -particle is emitted. The residual
nucleus is
(a) 0 n1
(b) 1 D 2
(c) 1 H 3
(d)
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 D 1
(c) 1 D 2
(d) 2 He4
21 If α,β and γ -rays have ionising powers I α , I β and I γ respectively then
(a) I α ,> I β >I γ
(b) . I α ,< I β <I γ
(c) I α = I β =I γ
(d) none of these
22 Which of the following is a correct statement
(a) β -radioactivity is the process in which an electron is emitted from an unstable
atom whose atomic number Z remains unchanged
(b) γ -radioactivity is the process in which the daughter nucleus has atomic
number 1 unit more than that of the parent nucleus
(c) α -radioactivity is the process in which an unstable atom emits the nucleus
of a helium atom
(d) α γ -radioactivity is the process in which a heavy atom emits electromagnetic
radiations of very high frequency
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23 The counting rate observed from a radioactive source at t=0s was 1600 counts
per second and at t=8s it was 100 counts per second. The counting rate observed
as counts per second at t=6 seconds will be
(a) 400
(b) 300
(c) 200
(d) 150
24 Consider a radioactive material of half life 1.0 minute. If one of the nuclei decays
now, the next one will decay
(a) after 1 minute
(b) after 1/ 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
(b) 92 MeV
(c) 920 MeV
(d) 0.92 Mev
26 The binding energy per nucleus were to split into two eequal size nuclei, about
how much energy would be released in the process.
(a) 238MeV
(b) 23.8MeV
(c) 2.38MeV
(d) 119MeV
27 Most suitable element for nuclear fission is the element with atomic number
near
(a) 92
(b) 52
(c) 21
(d) 11
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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
(b) 9 × 107 J
(c) 9 × 1010 J
(d) 9 × 1014 J
30 A radioactive nucleus undergoes a series of decay according to the scheme.
A ⎯α⎯
→ A1 ⎯β⎯
→ A 2 ⎯α⎯
→ A 3 ⎯λ⎯
→ 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
(b) uranium
(c) radium
(d) cadmium
32 Thermal neutrons have energy around
(a) 100eV
(b) 10eV
(c) 1eV
(d)
92
U 238 →82 pb206
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33 On an average how many neutrons are released per fission
(a) 2
(b) 1
(c) 3
(d) 2.5
34 Moderators are used in the nuclear reactors to
(a) accelerate the neutrons
(b) slow down the neutrons
(c) to slow down neutrons
(d) produce neutrons
35 Cadmium rods are used in a nuclear reactor to
(a) generate neutrons
(b) absorb neutrons
(c) slow down neutrons
(d) produce neutorns
36 How many radioactive disintegrations per second are defined as Becquerel
(a) 106
(b) 3.7 × 1010
(c) 1
(d) none of the above
37 In the nuclear reactor at Trombay which of the following is used as moderator
(a) ordinary water
(b) cadmium
(c) copper
(7) heavy water
38 Which of the following particles is used to cause fission in an atomic reactor?
(a) proton
(b) α -particle
(c) β -particle
(d) neutron
39 Which of the following is the best nuclear fuel?
(a) Neptunium 293
(b) plutonium 239
(c) Uranium 236
(d) Thorium 236
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40 The moderator in a reactor
(a) absorbs thermal energy
(b) slows down neutron
(c) accelerate neutron
(d) absorbs neutrons
41 For an atomic reactor being critical the ratio of the average number of neutrons
produced and used in chain reaction
(a) depends on the mass of fissionable material
(b) is greater than one
(c) is equal to one
(d) is less than one
42 An element A decays into element C by a two step process
A → B + 2 He4 , B → C + 2e− . Then
(a) A and C are isobars
(b) A and B are isotopes
(c) A and C are isotopes
(d) A and B are isobars
43 A radioactive sample with a half-life of 1 month has the label: ``Activity =2 microcuries on 1.8.1991’’. What was its activity two moths later in microcuries?
(a) 1.0
(b) 0.5
(c) 4
(d) 8
44 Isotopes are atoms having
(a) Same number of protons but different number of neutrons
(b) Same number of protons but different number of protons
(c) Same number of protons and neutrons
(d) None of the above
45 Which one of the following nuclear reactions is a source of energy in the sun?
(a) 4 Be9 + 2 He4 →6 C 12 + 0 n−1
(b)
92
U 238 →82 pb206
(c)
56
Ba144 + 56 K r 92 →92 U 235 + 0 n−1
(d)
26
F e56 + 48 Ca112 →74 W 167 + 0 n1
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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
(b)
92
U 235
(c)
92
U 238
(d)
90
Th232
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
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9.2
Answer Key
1. C
30. A
2. D
31. D
3. B
32. A
4. D
33. D
5. A
34. B
6. C
35. B
7. D
36. C
8. B
37. D
9. C
38. D
10. D
39. B
11. A
40. C
12. D
41. C
13. B
42. B
14. C
43. A
15. B
44. A
16. A
45. B
17. D
46. A
18. B
47. B
19. D
48. A
20. D
49. C
21. A
50. D
22. C
23. C
24. D
25. B
26. A
27. A
28. A
29. B
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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 five activities. Each activity has examples and reading
assignments. You are required to complete all the learning activities and complete the
compulsory reading material. This material is an extensive lecture notes and study
guide with exercises. These lecture notes are developed by the author of this module
from 2004 to 2007 in the University of Addis Ababa, Ethiopia.
Research in recent years has shown that the students who do best in physics (and
other subjects) are those who involve themselves actively in the learning process.
This involvement can take many forms: writing lots of questions in the margins of
the module; asking questions by email; discussing physics in the AVU discussion
forums etc. So you are strongly advised to exhaust all possiblities given to you by
the AVU.
A Final Word
Physics, in general, is not so much a collection of facts as a way of looking at the
world. The author of this module hopes that your first course in nuclear physics will
be a big plus to your appreciation of nature and will contribute to improve your skills
in careful thinking, problem solving, and precise communication. In this course you
will gain lots of experience with qualitative explanations, rough numerical 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.
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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 =1.2 ± 0.2 fm
o
o
• Charge: - The elelctric charge distribution within the nucleus is the same as
thenuclear mass distribution Experimental results suggest that the ‘elelctrical
radius of the nucleus’ and ‘nuclear matter radius’ are nearly the same.
• Nuclear Spin: For each nucleon orbital angular momentum l .. and spin s com-
bine to the total angular momentum j The total angular momentum of a nucleus I is therefore the vector sum of the angular momenta of the nucleons
A
j=l+s
I=∑ ji
i=1
odd-A: half-integer I, even-A: integer I
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• Angular momentum: The angular momentum I has all of the usual
properties of quantum mechanical angular momentum vectors:
I 2 = h 2 I (I + 1)
I z = mh
m= - I , - I + 1, L, I
• The total angular momentum I is usually referred to as nuclear spin and the
corresponding spin quantum number I is used to describe nuclear states.
Nuclear stability is related to the number of nucleons constituting the nucleus. Stable
nuclei only occur in a very narrow band in the Z-N plane. All other nuclei are unstable
and decay spontaneously in various ways.
There are three models of the atomic nucleus. the liquid drop model, the Fermi-gas
model and the shell model. Each model explain certain observations of nuclear
property. No single model explain all observations.
List of Required Readings
Copyright free readings should also be given in electronic form (to be provided on a CD
with the module)
Reading 1: CHAPTER ONE.
Complete reference: PHYSICS 481 Lecture Notes and Study Guide
From Department of Physics Addis Ababa University, by Tilahun Tesfaye(PhD) .
Abstract: This Reading is structured in terms early atomic hypothesis; properties
of the nucleus; theories of nuclear composition; binding energy; nuclear force and
nuclear structure models. Each section is ended with a set of questions and 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.
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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
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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
1/1836 th that of a proton. It is customary to measure the mass of an atom in atomic
African Virtual University 27
mass units, abbreviated amu. The atomic mass unit is equal to one-twelfth of the
mass of the neutral
12
6
C atom.
1u = 1.6603 × 10−27 kg
Spin And Magnetic Moment of The Nucleus
In atomic physics module you have seen that the spin of an electron results in the
fine structure of atomic spectrum. For atoms having one valence electron the relative
orientation of the orbital and spin moments of the electron leads to the splitting of
all energy levels (except the s-level) and as a result, to the splitting of spectral lines.
With further improvement of spectroscopic instruments, investigators were able to
investigate such lines. It was found that each of the two D-lines of sodium was in
turn a doublet, that is , consisting of two very closely spaced spectral lines.
Fig. D-lines of Na
Pauli suggested that the hyperfine structure might be due to an occurrence of angular
momentum in the atomic nucleus. The total angular momentum, or nuclear spin,
along with nuclear charge and nuclear mass, is the most important characteristic of
the nucleus.
The nucleus is made up of protons and neutrons each of which has spin h 2 . The
nuclear spin is the vector sum of the spin angular momenta of all the component
particles. A ucleus made up of an even number of nucleons has integral spin (in units
of h ) or zero spin. In addition to nuclear spin, the nucleus has a magnetic moment.
Thus, all atomic particles (the nucleus and electrons) have a magnetic moment.
The magnetic moment of a nucleus is determined by those of its component particles.
By analogy with the Bohr magneton, the magnetic moments of nuclei are expressed
in terms of the so-called nuclear magneton defined as
μN=eh/2m p
where μN is the nuclear gyromagnetic ratio.
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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 1/2000th 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
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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, Δx, would be comparable with the linear dimensions of the nucleus, that is,
10−14 or 10−15 m. Let us choose the greater value, Δx = 10−14 From the Heisenberg
uncertainty relation for the electron momentum we have
nP>>h/nx>>10-14 =10-19 kg m/s
The momentum P is directly related to its uncertainty, that is ΔP : P ≈ ΔP Once the
momentum of the electro is known, one can readily find its energy. Since in the above
example P>>m e c = 10−30 kg × 3 × 108 m/s , one should use the relativistic relation
for energy and momentum
E 2 =c 2 p2 +m e2 c 4
Then we get
E = c p2 + me c 2 = 3 × 108 10−38 + (10−30 × 3 × 108 )2
≈ 2 × 108 eV = 200 MeV
This figure is greatly in excess of that (7-8MeV)found for the total binding energy
by experiment and is many times the energy of electrons emitted in beta-decay. If,
on the other hand, the electrons in the nucleus were assumed to have the energy
comparable with that associated with the particles emitted in beta-decay (usually a
few MeV), then the region where the electrons must be localized, that is, the size of
the nucleus as found from the uncertainty relations would be much greater than that
found by observation.
A way out was found when in 1932 Chadwick discovered a new fundamental particle.
From an analysis of the paths followed by the particles produced in some nuclear
reactions and applying the law of conservation of energy and momentum, Chadwick
concluded that these paths could only be followed by a particle with a mass slightly
greater than that of the proton and with a charge of zero. Accordingly, the new particle
was called the neutron.
According to the present views, a nucleus consists of nucleons: protons and neutrons.
As the mass of a nucleon is about 2000 times the mass of an electron the nucleus
carries practically all the mass of an atom
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A nuclid is a specific combination of a number of protons and neutrons. The complete
symbol for a nuclide is written as:
A
X
Z
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
m p =1.0075975±0.000001 amu=(1836.09±0.01)m e
m n =1.008982±0.000003 amu=(1838.63±0.01)m e
The proton and the neutron have the same mass number equal to unity. In the 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 h ). With an odd
number of nucleons, its spin will be half-integral (in units of h ).
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1.2
Nuclear Binding Energy
Atomic nuclei containing positively charged protons and uncharged neutrons make
up stable systems despite the fact that the protons experience Coulomb repulsion.
The stability of nuclei is an indication that there must be some kind of binding force
between the nucleons. The binding force can be investigated on the energy basis
alone, without invoking any considerations concerning the nature and properties of
nuclear forces.
An idea about the strength of a system can be gleaned from the effort required to break
it up i.e. to do work against the binding. This approach leads to several important
facts about the forces that hold the nucleons in a nucleus.
The energy required to remove any nucleon from the nucleus is called the binding (or
separation) energy of that nucleon in the nucleus. It is equal to the work that must be
done in order to remove the nucleon from the nucleus without imparting it any kinetic
energy. The total binding energy of a nucleus is defined as the amount of work that
must be done in order to break up the nucleus into its constituent nucleons. From the
law of conservation of energy it follows that in forming a nucleus, the same amount
of energy must be released as is put in to break it up.
The magnitude of the binding energy of nuclei may be estimated from the following
considerations. The rest mass of any permanently stable nucleus has been found to
be less than the sum of the rest masses of the nucleons that it contains. It appears
as if in “packing up’’ to form a nucleus the protons and neutrons lose some of their
masses.
An explanation of this phenomenon is given by the special theory of relativity. This
fact is accounted for by the conversion of part of the mass energy of the particles into
binding energy. The rest energy of a body, E 0 , is related to its rest mass m0 by:
o
E0 =m 0 c 2
where c is the velocity of light in a vacuum. Designating the energy given upon the
formation of a nucleus as ΔE b , then the mass equivalent of the total binding energy
o
Δmo = ΔE b / c 2
is the decrease in the rest mass as the nucleons combine to make up the nucleus. The
quantity Δm o is also known as mass defect or mass decreament. If a nucleus of
mass M is composed of a number Z of protons with a mass m p and of a number A-Z
of neutrons with a mass m n , the quantity Δm0 is given by
Δmo = Zmp + ( A − Z )mn − M
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The quantity Δm0 gives a measure of the binding energy:,
ΔE = Δm c 2 = [Zm + ( A − Z )m − M ]c 2
b
o
p
n
In nuclear physics, energies are expressed in atomic energy units (aeu) corresponding
to atomic mass units:
(
)
1aeu = c 2 × 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 = [Zm + ( A − Z )m − M ] × 931.1MeV
b
p
n
Where the masses of the nucleons and the mass of the nucleus are expressed in atomic
mass units. On the average, the binding energy per nucleon is about 8MeV, which is
a fairly large amount.
Fig: A plot of the binding energy per nucleon as a function of mass number A
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As is seen from the plot, the strength of binding varies with the mass number of the
nuclei. The binding is at its strongest in the middle of the periodic Table, in the range
28
28<A<138, that is, from 14
Si to 138
Ba. In these nuclei, the binding energy is very
56
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 63 Li,
10
5
B and
14
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,
12
6
C and
16
8
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.
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1.3
Nuclear Stability
Not all nuclei are stable. Unstable nuclei undergo radioactive decay into different
nuclei. Stable nuclei have approximately equal numbers of neutrons and protons
N = Z for small A < 20 and a small excess of neutrons for large A as shown in
the diagram.
The Pauli exclusion principle helps to understand the fact that nuclei with equal N
and Z are stable. Imagine filling a 1-deminsional box with protons and neutrons.
We want the minimum energy configuration for a given value of A , say 5. Since both
neutrons and protons have spin ½ they are fermions (like electrons) and so obey the
Pauli exclusion principle. This principle restricts the number of protons and neutrons
to 2 of each at each energy level. Recall that the energy of the nth energy in a 1-di-
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mensional box is given by E n = n2 E 1 , where E 1 is the energy of the round level.
If all 5 nucleons were neutrons, the total energy of the nucleus would be
(
) (
)
⎡9 + 2 × 4 + 2 × 1 ⎤ E 1 = 19E 1 as shown in diagram A . In contrast, if 3 were neu⎣
⎦
(
)
trons and 2 were protons (as shown in B), the energy would be ⎡⎣ 4 + 4 × 1 ⎤⎦ E 1 = 8E 1
which is far less. This simple picture shows that it is more favourable energetically
to have N : Z
If we include the Coulomb repulsion between the protons, the energy levels of the
protons become higher than the energy levels of the neutrons. As A increases, it
becomes more favourable to have a small excess of neutrons.
Some elements have more stable isotopes than others. The elements with the most
number of stable isotopes have Z values of 2, 8, 20, 28, 50, 82 and 126. These are
called magic numbers, as the reason for stability was not understood at the time they
(
)
were discovered. For example, calcium Z = 20 has 6 stable isotopes whereas
(
)
(
)
potassium Z = 19 and scandium Z = 21 have only 2 stable isotopes each.
Similarly, nuclei with N equal to a magic number have a larger than average number
of isotones (an isotone has the same N value but a different Z value).
Nuclei with A : 60 are more tightly bound together and so they are at lower energy
compared to the rest. (Binding energy is analogous to the energy required to lift a
bucket of water from a well. A large binding energy means the water is low in the
well, i.e. the water is at a low energy). If two light nuclei with A << 60 are brought
together they create a new nuclei at lower rest energy (this is called fusion). Also
a heavy with A >> 60 can split into two nuclei of lower rest energy (this is called
fission).
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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 water contains
8.23 × 1024 atoms of oxygen, and the isotopic abundance of oxygen-18 is 0.20%,
then there are 1.65 × 1022 atoms of oxygen-18 in the cup.
The atomic weight for an element is defined as the average atomic weight of the
isotopes of the element. The atomic weight for an element can be calculated by
summing the products of the isotopic abundance of the isotope with the atomic mass
of the isotope.
Example
Calculate the atomic weight for the element lithium. Lithium-6 has an atom percent
abundance of 7.5% and an atomic mass of 6.015122 amu. Lithium-7 has an atomic
abundance of 92.5% and an atomic mass of 7.016003 amu.
Solution:
(
)(
) (
)(
)
Atomic Mass Lithium = 0.75 6.015122amu + 0.925 7.016003 amu
=6.9409 amu
The other common measurement of isotopic abundance is weight percent (w/o).
Weight percent is the percent weight of an element that is a particular isotope. For
example, if a sample of material contained 100 kg of uranium that was 28 w/o uranium-235, then 28 kg of uranium-235 was present in the sample.
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1.5
Nuclear Models
There are two basic types of simple nuclear model
Collective body with no individual particle states. An example is the Liquid Drop
Model which is the basis of the semi-empirical mass formula.
Individual particle model with nucleons in discrete energy states for example the
Fermi Gas Model or the Shell Model.
The Liquid Drop Model
This model is based on the fact that the density of the nucleus is roughly constant. It
predicts the total binding energy of the number from values of atomic number(Z);
neutron number (N) and and mass number (A) .
E b = C1 A − C 2 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. C 1 = 15.7MeV The constant density of the nucleus implies that the distance
between nucleons and the number of nearest neighbours (i.e. those within 3
fm) is also constant. Thus the binding energy of each nucleon should also be
constant. Hence, the total binding energy should be proportional to the number
A of nucleons. This is called the volume effect.
2.
C 2 = 17.8MeV The first term is an overestimate because it ignores the
fact that the nucleons near the surface of the nucleus have fewer neighbours
compared to a nucleon inside. We have to subtract a term proportional to the
surface area, 4π R 2 . Using R = Ro A1/ 3 , the surface area becomes 4π Ro2 A2 / 3
which is proportional to A2 / 3 . This the surface effect.
3. C 3 = 0.71MeV The repulsive force between protons reduces the binding
energy. There are
tial of
(
(
)
Z Z −1
2
pairs of protons, each with a Coulomb poten-
ke e2
, where R = A1/ 3 Ro . Thus we subtract a term proportional to
R
)
Z Z −1
A
1/ 3
This is the Coulomb effect
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4.
C 4 = 23.6MeV We found in the simple 1-dimensional box model that a
departure from N = Z increases the energy of the nucleus and thus lowers
(
)
2
the binding energy, hence we subtract a term proportional to N = Z 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.
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Formative Evaluation 1
1
A beam of fast moving α -particles were directed towards thin film of gold.
The path A ' , B' , and C ' of the transmitted beams corresponding to incident
parts A,B and C of the beam are shown in the figure below The number of α
-particles in
(a) C ' will be minimum and in B’ maximum
(b) A ' will be minimum and C’ maximum
(c) A ' will be maximum and B’ minimum
(d) B' will be minimum and in C’ will be maximum.
2
An α -particle of energy 6MeV is projected toward a nucleus of atomic number
50. The distance of nearest approach is
(a) 2.4 × 10−10 m
(b) 2.4 × 10−12 m
(c) 2.4 × 10−14 m
(d) 90,2.4 × 10−20 m
3 The nucleus radius is of the order of
(a) 10−14 m
(b) 10−15 m
(c) 10−6 m
(d) 10−10 m
4 The difference between
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
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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 α,β and γ
are 1.1 MeV and 7.0 MeV respectively. The energy released when two neutrons
form a helium nucleus
(a) 11.8MeV
(b) 32.4MeV
(c) 23.6MeV
(d) 28MeV
(
2
)
He4 is
African Virtual University 41
11 which of the following does not obey inverse square law force
(a) electrostatic force
(b) magnetic force between two poles
(c) gravitational force
(d) nuclear force
12 The mass density of a nucleus varies with mass number A as
(a) A2
(b) A
(c) constant
(d) 1/A
13 According to Yukawa the nuclear force arises though the exchange between
nucleons of
(a) proton
(b) photon
(c) positron
(d) meson
14 A neutron when disintegrates, gives
(a) a proton and an electron with a neutrino
(b) a positron and an electron with a neutrin9o
(c) a proton and a positron with a neutrino
(d) a proton and λ -radiation with a neutrino
15 In the disintegration chain 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
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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 C 12 and 6 C 13
(d) 15 P 30 and 14 Si 30
20 Consider the following forces in nature I Gravitation II Strong III Electrostatic
IV Weak. If the forces are arranged in decreasing magnitude the correct 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
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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/m 2
(b) 1017 kg/m 3
(c) 10−15 kg/m 3
(d) 1034 kg/m 3
24 Atomic weight of Boron is 10.81 and it has two isotopes 10 B 5 and 5 B 11 . Then
the radio of
10
B 10 and 5 B 11 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.
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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 α , β or γ 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 o e− λ t
This is the basic law equation for radiactivity.
The intensity measurement of radioactivity is done in two units which are:
• Curie: Defined as the that quantity of radioactive material which gives
3.7 × 1010 disintegration per second .
• Rutherford (Rd): It is defined as that amount of radioactive substance which
gives 106 disintegrations/sec.
In nature there are radioactive elements that exhibit successive transformation, i.e one element decays into a radioactive substance that is also radioactive. In successive radioactive transformation, if the number of nuclides of
African Virtual University 45
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 = −λP N P = 0
dN D
or
= −λD N D = 0
dt
λP N P = λD N D
λP N P = λG N G
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; α , β and γ decays
are explained. There are a number of solved numerical problems in each section
and a set of problems provided at the end. of each section of the cahpter.
Rationale: This chapter in the unit tallies with the content of this activity.
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.
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The Sequence Info button displays a chart that depicts the path of the series with
atomic number indicated on the vertical axis on the left, and number of neutrons
shown along the bottom. Colored arrows represent alpha and beta decays. To return
to the main user interface, click the Dismiss button.
Initially, a selected series contains all parent material, and the amount is represented
by a colored bar on a vertical logarithmic scale. Each line represents a factor of ten.
In order to step forward through the sequence by a specified number of years, you
may type the appropriate number into the Time Step field and hit Enter. By hitting
Enter repeatedly, you can view the series at successive intervals. A negative time step
will backtack through the sequence.
Click the Animate button to automate the progress through the series. You can either
choose a time step before you animate, or leave it at zero. If the time step is left at
zero, the system will choose time steps to optimize viewing performance.
The scrollable Activity Log on the right keeps a record of the amounts of the parent
and all daughter products for each time increment.
Resource #3: Nuclear Decay Simulator.
U R L : - h t t p : / / m i c h e l e . u s c . e d u / j a v a / f i s s i o n / n u c l e a r. h t m l
Complete Reference:- A Java simulator. Allows the user to set up a square box full of
two different types of particles. Each can have distinct values for spontaneous decay
rate, neutrons generated/fission and neutron capture rate. There is also an external
neutron source which can be set to inject a varying number of neutrons
This applet is designed to mimic a sample of a radioactive material. When the applet
starts up, you should get three windows: the simulator itself, the control panel and
the graph window.
Inside the simulator window you will see a number of unmoving blue (and possibly
green) spheres. These mimic atoms in a solid, which may fission when hit by a neutron,
or might fission spontaneously. The blue and green atoms may behave differently from
each other- the settings are in the control panel. There are also moving red balls- these
are neutrons. When a neutron passes close to an atom, it may be absorbed by that
atom. This may cause the atom to fission, releasing more neutrons and making the
atom disappear. It’s also possible that an atom may just fission on it’s own, releasing
neutrons. Once a neutron has left the simulator, it disappears.
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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..
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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 naturally radioactive light
40
nuclei, such as the potassium isotope 19
K , and the carbon isotope 14
C , to name but
6
a few.
2.1
Radioactivity, Discovery and Laws:
Pierre and Marie Curie found that the radiation from pitchblende was four times as
strong as from uranium. This led to an intensive search for the source of this stronger
radiation. Finally, in 1898, the curies succeeded in discovering two new substances
which they named polonium,
210
84
Po , and radium,
226
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.
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Further investigations showed that alpha-rays were helium nuclei. A glass vial hol-
(
)
ding a sample of radon, a radioactive gas 222
Rn was placed in a glass vessel from
86
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 electrostatic deflection.
Rutherford determined the specific charge,
q
, of alpha particles (where m
α
mα
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 / mβ , where mβ 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
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a compound. These facts have led to the conclusion that radioactive transformations
are the property of nuclei which can undergo these transformations spontaneously.
The nuclear transformations accompanied by the emission of alpha- and beta-particles
are called alpha- and beta-decay, respectively. Gamma-decay is non-existent. The
nucleus that undergoes a decay is called the parent, the intermediate products are
called daughters, and the final stable element is called the end product.
Experimental studies into radioactive disintegrations have led to the formulation of
transition rules:
For alpha decay:
For beta decay:
A
z
A
z
X ⎯α⎯⎯
→ A-4
Y + 42 He
decay
Z-2
X ⎯β⎯⎯
→ Z+1AY + −10 β
decay
Where X is the chemical symbol of the parent nucleus, Y is that of a daughter nucleus,
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.
4
2
He is the helium nucleus (the end product), and
0
−1
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
Ra ⎯α⎯
→ 222
Rn + 42 He
86
Thus, the alpha-transformation removes four units of mass and two units of charge,
producing an element two steps down in the periodic Table. The beta-disintegration
removes one negative charge and essentially no mass, producing an element one step
higher in the periodic Table.
The daughter nucleus produced by radioactive decay is, as a rule, capable of further
decay, and so is the next daughter produced by the decay of the first. Thus we have
a radioactive series or chain. Each member of a radioactive series is a radioactive
isotope (radioisotope) of the element occupying the respective square in the periodic
Table.
The naturally radioactive nuclei form three radioactive series, namely:
• the Uranium series, (starts from
• the Thorium series (starts from
238
92
232
• the Actinium series, (starts from
90
U and terminates in a stable 206
Pb )
82
Th and terminates in a stable 208
Pb ) and
82
238
92
U and terminates in a stable 207
Pb )
82
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thus called after the respective parents,
238
92
U, 23290Th, and
235
89
AC There is one more
radioactive series produced artificially and starting with neptunium, 237
Np , a transu93
ranic element. In each radioactive series, each nuclide transforms into the next through
a chain of alpha- and beta disintegrations, each chain terminating in a stable isotopic
nucleus. The neptunium series terminates in the
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 →L→L→
206
82
Pb.
The number nα of alpha transitions can be found at once by dividing the difference
in mass number between the parent and the end product by four, because each alpha
transition removes four units of mass. In our example, nα = ( A1 − 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 = 2nα − nβ
2nα − nβ = 10
From the value of nα , we find that nβ = 6 . Thus, the uranium nucleus undergoes eight
alpha transitions and six beta transitions before it transforms to the lead nucleus.
With time, the number of parent nuclei decreases because of radioactive decay. This
decrease obeys a certain law which we seek to find. Let at the initial instant of time,
t = 0 there be Δt nuclei of the same element that will remain untransformed by an
arbitrary time t. Since we are dealing with spontaneous transformations, it is natural
to assume that a greater number of nuclei will decay over a longer interval of time.
Furthermore, the number of nuclei under going decay per unit of time (say, a minute)
will be greater with a law of radioactive decay. If we have N untransformed nuclei
present at time t, and N − ΔN untransformed nuclei existing at time t + Δt then
change in the number of untransformed nuclei that is the number of nuclei decaying
in time Δt will be proportional to N, that is:
ΔN : N Δt; or ΔN = -λN Δt
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where λ 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 ΔN decreases with time. Thus it follows that the decay
constant is the fractional decreases in the number of nuclei decaying per unit time:
λ=
( −ΔN N )
Δt
In other words, the decay constant represents the proportion of nuclei decaying per
unit time, or the decay rate. The decay constant is independent of ambient conditions
and is solely determined by the internal properties of the nucleus. It has dimensions
of λ = T −1 .
In order to find the time dependence for radioactive decay. we can show that the
number of atoms of the original kind remaining after time t is
N = N 0 exp(−λt)
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 / N 0 ) as a function of
time shows the decrease is exponential. The decay constant λ can be found from
the slope of the curve.
In practice the stability of radioactive nuclei against decay and the decay rate are most
often estimated in terms of the half life, t1/ 2 , rather than the decay constant λ .
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 λ are related as
N0
= N 0 exp (-λt1/ 2 )
2
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Cancelling N 0 and taking a logarithm, we obtain
or
t1/ 2 =
ln 2 0.693
=
λ
λ
1
T
=
= 1.44T λ 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 hundredmillionths of a second.
The constancy of t1/ 2 (or λ) for a given radioactive element implies that these
quantities represent huge numbers of atomic nuclei. Thus, radioactive decay is a
statistical process.
The above definition of the half-life is sometimes incorrectly construed as implying
that the total number of nuclei in a sample will decay in a time equal to 2t1/ 2 . This is
not so because if the number of nuclei remaining after the time t1/ 2 is N 0 / 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.
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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− λ 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
ΔN p
Δt
=
ΔN d
Δt
and so, at equilibrium the following relation holds
or
λ p N p = λd N p
Np
N
=
λd T p
=
λ p Td
d
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− λ 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 ( μ C i )
1mCi = 10− 3 Ci
1μ Ci = 10− 6 Ci
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An alternative unit is the rutherford (Rd), a unit of radioactivity equal to 10 6 decays per second, 1R d = 10 6 s − 1 . Obviously, 1C i = 3.7 × 10 4 R d .
Example
The half-life of radium equal to 1590 years. Find its decay constant λ . 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: N = NA / M =
6.023 ×1026 ×1/ kmole
= 2.67 ×1024 kg − 1
226 kg/kmole
=2.67 ×1024 g -1
Then the activity of one gram of radium will be
A = λ N = 0.693 N / 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 .
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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 Δ 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 Δ 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 Δ t is Δ N , then the relative decrease, −Δ N / N , in the number of nuclei per unit time, that is, the quantity
- ( Δ N / N ) Δ t gives the decay probability per unit time per nucleus.
This definition agrees with the meaning of the decay constant, λ . By definition, the
decay constant is the decay probability pre unit time per unit nucleus.
For further discussion of this point look in the compulsory reading by the same
author.
2.3
Application of Radioactivity
Radioactive Dating
The decrease in the number of radioactive nuclei according to radioactive decay law,
may be used as a means for measuring the time that passes since a specimen known
to contain 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− λ t , the time interval between the instants when the number
of radioactive nuclei is N 0 and N is
⎛N ⎞
⎛1⎞ ⎛N ⎞
t = ⎜ ⎟ ln ⎜ 0 ⎟ = 1.44t1 / 2 ln ⎜ 0 ⎟
⎝λ⎠ ⎝ 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
African Virtual University 57
of millions of years. This condition is satisfied by the half-live of 238 U and 235 U .
Naturally occurring uranium is actually a mixture of both. Their half-lives are 4500
million and 900 million years, respectively.
At present, chemically pure and naturally occurring uranium contains 99.28%
0.714%
235
92
U,
0.006%
234
92
U the latter being the decay product of
238
238
92
U,
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
organs and tissues.
14
6
C , finds its way into animals and becomes part of their
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
African Virtual University 58
t1 / 2 = 5570 years into minutes, we find the number of
magnitude of activity:
14
6
C nuclei that have this
N = (1/ λ )(ΔN / Δt)
= 1.44t1 / 2 (ΔN / Δt)
= 1.44 × 5570 × 365 × 24 × 60 ×1.75
≈ 7.5 ×10
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.
10
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.
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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.
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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.
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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
(1 3 ) = 1 9 the original count. 1/9 of 360 = 40 counts per minute.
2
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
Ra →
23) When
218
84
222
86
Ra + 42 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:
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218
84
Po →
218
85
At +
0
−1
β,
where -10 β represents the emitted electron
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
84
Po →
214
82
Pb + 42 He
24) State the number of protons and neutrons in each of the following nuclei:
2
1
H,
12
6
C,
56
26
Fe,
197
79
Au,
90
38
Sr, and
238
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.
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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.
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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.
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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 (low energy)
4
Rayleigh scattering
σ R ∝ Z 2 (low energy limit)
Photonuclear reactions:
Elastic nuclear scattering
(γ , n)(γ , p)(γ , f ) etc,
∝ Z (hν ≥ 10 MeV)
III. Electric field of
charged particles
Pair production
a) kn ∝ Z (hν ≥ 1.02MeV)
b) ke ∝ Z (hν ≥ 2.04MeV)
IV. Mesons
Photomeson production
hν ≥ 140 MeV
(Incoherent)
Compton
scattering
σ ∝Z
∝ Z 5 (high energy)
II. Nucleons
Inelastic
scattering
Delbrück scattering
Nuclear
resonance
Scattering
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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
Title : Cal Poly Physics Department’s Virtual Radiation Laboratory (Geiger
Counter)
URL:-: http://www.csupomona.edu/~pbsiegel/www/Geiger_Counter/Geiger.html
Date Consulted:-Jan 2008
Description:- The virtual Geiger counter operates similar to the real one. The Geiger counter has two sample holders. In each sample holder you can pick either an
empty holder, Ba137m or Mn54 (5 μ Ci). The detector has a dead time, and there
is a background. The buttons are similar to a real Geiger counter. To operate: set
the counting time and click start. Counting stops after the counting time. Then
clear the counter. To record counts from the Ba137m samples, you need to select
the sample and click on “squeeze out Ba”. Squeezing out the sample refreshes
the Ba source, which has a short half life. The button refreshes both sources when
clicked. The sources are only counted when they are in the sample holder.
Experiments that can be done using this virtual lab are
1. Dead time measurement: Measurement of the detector’s dead 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
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Resource #4
Title : Cal Poly Physics Department’s Virtual Radiation Laboratory (NaI
Gamma Detector)
URL:-: http://www.csupomona.edu/~pbsiegel/www/naidat/Detector.html
Date Consulted:-Jan 2008
Description:- Using this virtual NaI detector you can calibrate the detector for
energy and determine the energy of unknown gamma source.
To run the applet, click on gamma detector (Calibration) . You will see the MCA
screen with 1024 channels. The samples include three standards and an unknown.
The unknown is a single isotope. Your goal is to determine the photopeak energies
and the identity of the unknown. The energy of the detected gamma is (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.
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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
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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 (δ ) rays. In any case, the
energy for these processes comes from the kinetic energy of the incident particle,
which is slowed down.
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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:
4π e 4 z 2
⎛ -dE ⎞
S=⎜
=
NZB
⎟
mo v2
⎝ dx ⎠coll
⎡ 2m o v 2
⎛ v2
where B ≡ ⎢ln
− ln ⎜1 − 2
l
⎝ c
⎣
Beth formula for stopping power
⎞ v2 ⎤
⎟− 2 ⎥
⎠ 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 .
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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 γ-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.
ii.
iii.
iv.
Photoelectric effect (Absorption)
Rayleigh scattering (Scattering)
Compton scattering (Scattering)
Two photon Compton scattering (Multi photon effect)
The interactions which occur with nucleons are:
i. Photonuclear reactions (γ,n), (γ,p), photo-fission etc. (Absorption).
ii. Elastic nuclear scattering (γ,γ) (Scattering)
iii. Inelastic nuclear scattering (γ,γ/) (Scattering)
The interactions with electric field surrounding charged particle are:
i.
ii.
iii.
iv.
Electron-positron pair production in the field of nucleus (Absorption)
Electron-positron pair production in electron field (Absorption)
Nucleon-anti-nucleon pair production (Absorption)
The interactions occurring with mesons are:
i) Photo-meson production (Absorption)
ii) Modified (γ,γ) (Scattering)
But out of all these interaction processes, five main processes are:
i.
ii.
iii.
iv.
v. Photoelectric effect
Compton scattering
Pair production
Rayleigh scattering
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.
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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.
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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.
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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.
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2.2.2
Scintilation Detectors
Scintillatior can be used for ionizing radiation detection and spectroscopy of a wide
assortment of radiation. Availability of scintillators in various physical forms (i.e.
solid, liquid and gas), availability of excellent photon detectors like Photomultiplier
tubes, solid-state photon detectors and microelectronics for processing signals makes
these detectors quite useful for variety of applications.
Following are the sequential events which takes place while detecting ionizing 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).
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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
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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
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.
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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
∞
1
: 10 − 14 m
Strong (Nuclear)
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.
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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 proton-proton interactions are almost
identical in character. Thus, as regards specifically nuclear interactions, protons
and neutrons are identical particles. The charge independence of nuclear forces
has been established from experiments on the scattering of protons by neutrons
and of neutrons by protons.
3. Nuclear forces are noncentral, or tensor, forces, that is, those whose direction
depends in part on the spin orientation of the nucleons, which may be parallel
or anti-parallel. This has clearly been shown by experiments on the scattering of
neutrons by the molecules of parahydrogen and orthohydrogen. A molecule of
parahydrogen differs from that of orthohydrogen in that in the former the protons
have anti-parallel spin orientation, and in the latter, parallel spin orientation. If
the interaction between nucleons were independent of spin orientation, neutrons
would be scattered identically by orthohydrogen and parahydrogen. 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.
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4.2
Elementary Particles
The discussion and explanation of nuclear force is connected with the physics of
elementary particles. Among the particles that are of importance in nuclear physicsare
the ones given in table below.
Many of these particles have their anti-matter counterpart. For example there is
anti proton p - for p, for β − there is β + , for κ + there is κ − for Ξ − there is Ξ + etc.
When a particle and its antiparticle meet they annihilate each other.
Particles are in general classified into two types according to the statistics they
obey.
(I) Fermions:
a. Obey the FD statistics
h 3h 5 h
have half integral spin i.e. , , L
β − , n, p, λ , Σ are examples of
2 2 2
Fermions
Fermions are further classified as Baryons (Fermions of mass m >mass of proton)
and Leptons (Fermions of mass m < mass of protons).
b.
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(II)Bosons:
a. Obey the BE statistics
b. have integral spin i.e. h, 2 h, 3h, L
γ , π , κ are examples of Fermions
Bosons are further classified as Photons (Bosons of zero rest mass ) and mesons
(Bosons of non-zero rest mass)
Mesons and baryons, which interact strongly with nuclei (Nucleons) are also 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 Ä
p + π0
n Ä
n + π0
p Ä
n +π+
n Ä
p +π−
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:
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ΔE Δt ≥ h so the violation can exist only if
h
h
ΔEΔt ≤ h → Δt ≤
=
ΔE
mπ c 2
during this time, even if the pion moves with the speed of light,
the distance that it can move is
Δr = cΔ t
the range of nuclear force. i.e. the distance within which the
exchange of pions by nucleons takes place.
1.5 ×10-15
≈ 0.3 × 10− 8 sec
8
3 ×10
h
⇒Δ E=
= 3.5152 ×10-11 J = 145.57MeV
Δt
⇒ Δt=
This is close to the measured value of pion mass. Therefore Yukawa’s theory (the
meson theory) satisfies the two important characteristics of nuclear forces
1. Nuclear force is the same between any two nucleons. i.e. p-p; p-n and n-n
forces are the same. This is satisfied by the meson theory sice there are three
types of mesons with the same mass.
2. Exchange of π meson (a particle of non-zero rest mass) by nucleons 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 π meson the change in energy that is involved is at least
the energy contained by a meson at rest, i.e mπ c 2 . Thus during the interaction of
nucleon and pions, the change in energy involved is:
ΔE = m c 2
π
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 ΔE = mπ 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 π meson field is approximately given by:
V ( r ) = −γ 2
e− μ r
r
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mc
where γ is a constant and μ = π . This is commonly referred to as Yukawa
h
Potential.
The attractive force between nucleons does not exist for distance between nucleons
below a certain limiting distance. For distances less than a limiting distance, the force
between nucleons is a very strong repulsive force. The limiting distance is about 0.5
F. This repulsive force is believed to be due to exchange of π mesons. The repulsion
is often taken to be a hard core, i.e., a region where the potential goes to infinity.
Task 4.1
Question for discussion
Discuss the following questions with your colleagues or on the discussion forum of
AVU
1. What are cosmic rays, what kind of particles are coming to our earth from
extra terrestrial sources?
2. Search form the internet the lattest number of elementary particles known.
3. Why does exchang of mesons gives rise to attractive force.
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Formative Evaluation 4
1) Determine the minimum kinetic energy of protons requiered for the formation
of
a) π 0 -messon in the reaction p + p → p + p + π 0 ,
b) a proton anti proton pair in the reaction p + p → p + p + p%+ p
2) Knowing the mass of a neutral π -meson (135.0Mev/c2), determine the energy of
γ -quanta formed during the decay of a stationary neutral π meson: π 0 → 2γ
.
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.
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XI.Compiled List Of All Key Concepts (Glossary)
Nuclear Terminology
1. Nuclear Terminology: There are several terms used in the field of nuclear physics
that an RCT must understand.
a. Nucleon: Neutrons and protons are found in the nucleus of an atom, and for
this reason are collectively referred to as nucleons. A nucleon is defined as a
constituent particle of the atomic nucleus, either a neutron or a proton.
b. Nuclide:-A species of atom characterized by the constitution of its nucleus,
which is specified by its atomic mass and atomic number (Z ) , or by its 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, (Δ ) . computed for each nuclide, using the following equation
Δ = ZM p + ZM e + ( A − Z )( M n ) − M a
= Z ( M H ) + ( A − Z )( M n ) − M a
where Δ = 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
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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.
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XII.
Compiled List of Compulsory Readings
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XIII. Compiled List of (Optional)
Multimedia Resources
Resource #1
Title: Motion of Centre of Mass
URL: http://surendranath.tripod.com/Applets/Dynamics/CM/CMApplet.html
Description: Applet shows the motion of the centre of mass of a dumbbell shaped
object. The red and blue dots represent two masses and they are connected by a
mass less rod. The dumbbell’s projection velocity can be varied by using the 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
Title : 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
Title : Hyper Physics
URL: http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html
Date Consulted:-April 2007
Description:- This Java applet helps you to do a series of virtual experiments, .
you can determine the escape and orbital velocities by varying different parameters
of the projectile.
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XIV. Compiled List of Useful Links
Useful Link #1
Title: Classical Mechanics
URL: http://farside.ph.utexas.edu/teaching/301/lectures/
Description: Advanced description of the topics discussed in mechanics I and II of
the AVU Physics module.
Rationale: This site has comprehensive coverage of most of physics, in the mechanics courses. The learner can consult chapters 7, 8 and 9 of the book. The PDF
version is also available.
Useful Link #2
Title: Tutorial on torque from university of Guelph
URL: http://www.physics.uoguelph.ca/tutorials/torque/index.html
Description: The site gives detailed description of torque
Rationale: Here you will find a good collection of tutorial problems on torque...
Useful Link #3
Title: Universal Gravitation
URL: http://en.wikipedia.org/wiki/Law_of_universal_gravitation
Description: This is a good collectionn of theory and historical account of the
newtons low of universal gravitation.
Rationale: The site provides a detailed description and solved problems on the topic.
Useful Link #4
Title: Universal Gravitation and Planetary Motion
URL: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/circles/u6l3c.html
Description: Lecture notes and discussion forum from the physics class room.
Rationale: Reach in discussion topics and interactive problems.
Useful Link #5
Title: Gravitational Field
URL: http://en.wikipedia.org/wiki/Gravitational_field
Description: Gravitational field, its meaning in classical mechanics, and its meaning in general relativity are described in this section.
Rationale: Useful for the one who needs to compare many references.
Useful Link #6
Title: Geostationary orbit
URL: http://en.wikipedia.org/wiki/Geostationary
Description: This link Explains geostationary orbit. The animated graphics helps
visualization.
Rationale: This supplements the theory given in Activity three...
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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.
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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
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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
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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
A
-3.400ev
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.
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15 Which of the following statements are true for both X-rays and α -rays
(a) They cause ionisation of air when they pass through it
(b) They can be deflected in electric and magnetic fields.
(c) They can be used to detect flaws in metal coatings
(d) They travel with the speed of light
16 The rate of disintegration of a given sample of radionuclides is 1017 atoms/s and
half-life is 1445 years. The number of atoms is
(a) 1.44 × 1017
(b) 1.4 × 1017
(c) 6.57 × 10 27
(d) none of these.
17 In a breeder reactor, useful fuel obtained from
(a)
239
238
U is
Pu
(b)
235
U
(c)
235
Th
(d)
233
Ac
18 The average life τ and the decay constant λ of a radioactive nucleus are related
as
(a) τ = C / λ
(b) τ / λ = 1
(c) τ = 0693 / λ
(d) τλ = 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) α = 4 and β =6
(b) α = 6 and β =0
(c) α = 6 and β =4
(d) α = 3 and β =3
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20 γ -rays consist of
(a) electromagnetic waves
(b) fast moving electrons
(c) helium nuclei
(d) singly ionised gas atoms
21 Emission of β -rays in a radioactive decay results in a daughter element showing
a
(a) change in charge but not in mass (b) change in mass but not in charge
(c) change in both
(d) change in neither
22 In the reaction represented by
sequence are
A
Z
X →
Y→
A−4
Z −2
Y→
A−4
Z −2
A−4
Z −1
K
The decay in
(a) α , γ , β
(b) γ , α , β
(c) β , γ , α
(d) α , β , γ
23 The main source of solar energy is
(a) combustion
(b) gravitational contraction
(c) nuclear fusion
(d) nuclear fission
24 The radioactivity of an element becomes 1/64th of its original value in 60 second.
The half value period is
(a) 30s
(b) 15s
(c) 10s
(d) 5s
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25 When the radioactive isotope
88
R a 238 decays in a series by the emission of three
alpha particles and a β -particle. The isotope finally formed is
(a)
84
R A 220
(b)
88
R A 215
(c)
86
R A 272
(d)
83
R A 226
26 Half life period of lead is
(a) 1590 years
(b) 1590days
(c) infinite
(d) zero
27 The half life period of a radioactive sample depends upon
(a) nature of substance
(b) pressure
(c) temperature
(d) all of the above
28 A positron is emitted by a radioactive nucleus of atomic number 90. The product
nucleus will have atomic number
(a) 90
(b) 91
(c) 89
(d) 88
29 What is a curie
(a) measurement of electric field
(b) measurement of magnetism
(c) measurement of temperature
(d) measurement of radioactivity
30 Which of the following is not a mode of radioactive decay
(a) alpha decay
(b) fusion
(c) electron capture
(d) positron emission
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31 Particles which can be added to the nucleus of an atom without changing its
chemical properties are called
(a) alpha particles
(b) protons
(c) electrons
(d) neutrons
32 What is the mass of 1 curie of U 234 (λ = 8.8 × 10− 14 / s )
(a) 3.7 × 1010 g
(b) 2.348 × 1023 g
(c) 20 days
(d) 3.8 × 20 days
33 The half life of radioactive radon 3.8 days. the time at the end of which 1/20th
of the radon sample will remain undecayed is nearly ( log10 e = 0 . 4343 )
(a) 1.6 days
(b) 16.4 days
(c) 20 days
(d) 3 . 8 × 20days
34 The radioactive decay rate of a radioactive element is found to be 10 3 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
(b) 10 3 , 10 3
(c) 125, 500
(d) 500, 125
35 A freshly prepared radioactive source of half-life 2 hours emits radiations of
intensity which is 64 times the permissible safe level. The minimum time after
which it would be possible to work safely with this source is
(a) 128 hours
(b) 24 hours
(c) 12 hours
(d) 6 hours
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36 The equation
A
Z
X → Z +A1Y + − 10 e+υ
represents
(a) fission
(b) fusion
(c) β -decay
(d) γ -decay
37 During a negative β -decay
(a) An atomic electron is ejected
(b) An electron which is already present within the nucleus is ejected
(c) A neutron in the nucleus decays emitting an electron
(d) A part of binding energy of nuclei is converted into an electron
38 When
4
B e9 is bombarded with α -particle, one of the products of nuclear
transmutations is 6 C 12 . The other is
(a) 0 n1
(b) 1 H
2
(c) 1 H 1
(d)
−1
e0
39 In the nuclear reaction, given by
4
14
b
1
He + N → q X +1 H
7
2
The nucleus X is
(a) oxygen of mass 16
(b) oxygen of mass 17
(c) nitrogen of mass 16
(d) nitrogen of mass 17
40 The energy released per fission of a
92
U
235
nucleus is nearly
(a) 200 MeV
(b) 200 keV
(c) 200 eV
(d) 20 eV
41 If 10% of the radioactive material decay in 5 days. What would be percentage
of amount of original material left after 20 days?
(a) 55.6%
(b) 65.6%
(c) 75.6%
(d) 85.6%
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C
42 In the nuclear process 6
11 → B 11 + β + + X
5
, X stands for
(a) photon
(b) neutrino
(c) antineutrino
(d) neutron
43 If the nuclei of X and Y are fused to form a nucleus of mass M and some energy
is released, then
(a) X-Y=M
(b) X+Y>M
(c) X+Y<M
(d) X+Y=M
44 The nuclei
13
6
C and
14
7
N can be described as
(a) isotones
(b) isotopes of carbon
(c) isobars
(d) isotopes of nitrogen
45 If M is the atomic mass, A is mass number, then (M-A)/A is called
(a) packing fraction
(b) mass defect
(c) Fermi energy
(d) binding energy
46 When the number of nucleons in nuclei in crease, the binding energy per 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
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48 The mass defect for the nucleus of helium is 0.0303 a.m.u. What is the binding
energy per nucleon for helium in MeV
(a) 27
(b) 7
(c) 4
(d) d. 1
49 In stable nuclei, the number of neutrons (N) is related to the number of Z in a
neutral atom in general as
(a) N ≥ Z
(b) N=Z
(c) N<Z
(d) N>Z
50 Fission of a nucleus is achieved by bombarding it with
(a) electrons
(b) protons
(c) neutrons
(d) X-rays
51 The more readily fissionable isotope of uranium has an atomic mass of
(a) 238
(b) 236
(c) 235
(d) 234
52 The equation
4
(
1
H
1+
)→
2
He4 + + + 2e+ + 26 MeV represents
(a) fission
(b) fusion
(c) γ -decay
(d) β -decay
53 From the following equations pick out the possible nuclear fusion reactions.
(a)
6C
13
(b)
6C
12
(c)
7
(d)
+1 H 1 → 6 C 14 + 4.3M ev
1
+1 H → 7 N
13
+ 2 M ev
N14 +1H1 → 8 O15 + 7.3Mev
235
92
U+ 01 n → 140
Xe+ 94
Sr+2( 01 n)
54
38
+λ + 200MeV
African Virtual University 101
54 Consider a nuclear reaction x 200 → A110 + B 90 + 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 , Pu239
(b) P 239 , Th234
(c) U 238 , Rn232
(d)
92
U 238 →82 pb206
56 A radioactive substance has a half-life of 60 minutes. During 3 hours the fraction
of atom that have decayed would be
(a) 12.5%
(b) 87.5%
(c) 8.5%
(d) 25.1%
57 The element used for radioactive carbon dating for more than 5600 years is
(a) C 14
(b) U
234
(c) U
238
(d) P o94
58 After two hours one sixteenth of the starting amount of a certain radioactive
isotope remaine un decayed. The half-life of the isotope is
(a) 15 minutes
(b) 30 minutes
(c) 45 minutes
(d) one hour
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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
(c) 31 / 3 :1
(d) 1 : 31 / 2
60 A radioactive reaction is
are emitted?
92
U 238 →82 pb206 λ . How many α - and β -particles
(a) 10 α ,6 β
(b) 4 protons, 8 neutron
(c) 6 electron, 8 proton
(d) 6 β and 8 α
61 Which of the following is the fusion reaction
(a) 1 H 2 +1 H 2 → 2 He4
(b) 0 n1 + 7 H 14 →6 C 14 +1 H 1
(c) 0 n1 + 92 U 236 →93 Np239 + β − + γ
(d) 1 H 3 → 2 H e3 + β − + γ
62 Which of the following statements is true?
(a)
78
Pt192 has 78 neutrons
(b)
84
P o 214 →
(c)
238
92
(d)
90
U→
234
90
Tj 234 →
82
P b210 + β -
Th+ 42 He
91
Pa 234 + 2 He4
63 The binding energy of deutron
particle
( H ) is 1.112 MeV per nucleon and an alpha
2
1
( H ) has a binding energy of 7.074 MeV per nucleon. Then in the
4
2
reaction 1 H 2 +1 H 2 →2 He4 + Q the energy Q released is
(a) 1MeV
(b) 11.9 MeV
(c) 23.8 MeV
(d) 931 MeV
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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
(b) 3.61 × 1012
(c) 3.11 × 1015
(d) 31.1 × 1015
(e) (Avagadro’s number N = 6.02 × 10 26 atom /kilomole)s
65 A parent nucleus n P m decays into a daughter nucleus D through α 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
(b) n P m + 4
(c) n P m − 4
(d)
n− 2
D m− 4
66 Given mneutr on = 1.0087, mpr oton = 1.0073, mα = 4.0015 (in amu units, 1
amu=931 MeV). Binding energy of helium nucleus is
(a) 28.4 MeV
(b) 20.8 MeV
(c) 27.3 MeV
(d) 14.2Mev
67 16g of sample of a radioactive element is taken from Bombay to Delhi in 2 hours
and it was found that 1g of the element remained (undisintegrated). Half life of
element is
(a) 2 hours
(b) 1 hour
(c) 1/2 hour
(d) ¼ hour
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68 I 0 -rays radiations can be used to create electron positron pair. In this process of
pair production, γ -rays energy can not be less than
(a) 5.0 MeV
(b) 4.02 MeV
(c) 15.0 MeV
(d) 1.02 MeV
69 The half life of Po is 140 days. If 16g of Po is present then what is the time taken
for 1g of po to be present
(a) 10 days
(b) 280 says
(c) 560 days
(d) 840 days
70 A radioactive sample has a half life of 5 day. To decay from 8 microcurie to one
microcurie, the number of days will be
(a) 40
(b) 25
(c) 15
(d) 10
71 The activity of the radioactive sample decreases to one-third of the original
intensity I 0 in a period of 9 years. After 9 years more, its activity would be
(a) same
(b) I 0 /6
(c) I 0 /4
(d) I 0 /9
72 R a d o n - 2 2 0 w i l l e v e n t u a l l y d e c a y t o B i s m u t h 2 1 2 a s
86
Rn220 →84 Po216 + 2 He4 ; half life =55s
84
Po216 →82 Pb212 + 2 He4 ; half life =0.16s
82
Pb212 →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
(a) Radon
(b) Polonium
(c) Lead
(d) Bismuth
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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
(b) 58/2
(c) 3 × 58
(d) 2 × 58
76 A radioactive sample contains 5 0 atoms and has a half life of one year. Then the
time required for all the atoms to decay is
(a) 10 6 years
(b) one year
(c) 10 years
(d) ∞
77 A fast reactor does not use
(a) a coolant
(b) control system
(c) a moderator
(d) nuclear level
78 When
92
U
235
undergoes fission 0.1%of its original mass is changed into energy.
How much energy is released if 1 kg of
(a) 9 × 1010 J
(b) 9 × 1011 J
(c) 9 × 1012 J
(d) 9 × 1013 J
92
U
235
undergoes fission?
African Virtual University 106
79 The half-life of the isotope 11 H a 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
100 kW of power.
235
. A reactor is generating
(a) 1000
(b) 2 × 10 8
(c) 931
(d) X 1 to that of X 2
81 N atoms of a radioactive element emit n alpha particles per second. The half-life
of the element
(a) n/N sec
(b) N/n sec
(c)
(d)
0.693 N
n
0.693n
N
sec
sec
82 The combinations of radioactive emissions will not change the mass number of
radioactive nuclear not change the mass number of radioactive nuclear
(a) alpha and beta decays
(b) alpha and gamma decays
(c) alpha beta and gamma decays
(d) beta and gamma decays
83 Thermal neutrons are incident on a sample of Uranium containing both
235
92
U and
U . Then
235
92
(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
African Virtual University 107
84 If
27
Al is bombarded with neutron and produce
be Q value of this reaction? Given mass of
27
28
Al and a proton. What will
Al = 27.98154 in amu.
(a) 6.79 × 10 − 3 M eV
(b) 3.16 MeV
(c) 6.32 MeV
(d) 6.32eV
85 The activity of a radioactive sample is measured as 9750 counts per minute at
t=0 and as 975 counts per minute at t=5 minute at t=0 and as 975 counts per
minutes. The decay constant is approximately in per minute
(a) 0.230
(b) 0.461
(c) 0.691
(d) 0.922
86 Half-lives of two radioactive substances A and B are respectively 20 minutes and
40 minutes Initially the sample of A and B have equal number of nuclei. After
80 minutes the ratio of remaining number of A and B nuclei is
(a) 1:16
(b) 4:1
(c) 1:4
(d) 1:1
87 Two radioactive materials X 1 and X 2 have decay constants 10 λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the
number of nuclei of X 1 to that of X 2 will be 1/e after a time
(a) 1/(10 λ )
(b) 1/(11 λ )
(c) 11/(10 λ )
(d) 1/(9 λ )
African Virtual University 108
Answers to Formative Evaluation 1
1. C
2. A
3. A
4. A
5. B
6. C
7. B
8. A
9. A
10. C
11. D
12. D
13. D
14. A
15. C
16. D
17. B
18. C
19. D
20. B
21. D
22. D
23. B
24. A
African Virtual University 109
XVII. References
This is a compiled list of the references, like standard reference books for the discipline,
used in the development of the module. (Not for the learner do not have to be copyright free)
Atleast 10 in APA style
Raymond A. Serway (1992). PHYSICS for Scientists & Engineers. Updated
Version.
Douglas D. C. Giancoli Physics for scientists and engineers. Vol. 2. Prentice
Hall.
Irving Kaplan (1962) Nuclear Physics.
Sena L.A. (1988) Collection of Questions and Problems in physics, Mir Publishers
Moscow.
Nelkon & Parker (1995) Advanced Level Physics, 7th Ed, CBS Publishers &
Ditributer, 11, Daryaganji New Delhi (110002) India. ISBN 81-239-0400-2.
Godman A and Payne E.M.F, (1981) Longman Dictionary of Scientific Usage.
Second impression, ISBN 0 582 52587 X, Commonwealth Printing press
Ltd, Hong Kong.
Beiser A., (2004) Applied Physics, 4th ed., Tata McGraw-Hill edition, New Delhi,
India
Halliday D., Resnick R., and Walker J. (1997), Fundamentals of Physics, 5th ed.,
John Wiley and Sons
James O’Connell (1998), Comparison of the Four Fundamental Interactions of
Physics, The Physics Teacher 36, 27.
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XVIII. Main Author of the Module
About the author of this module
Tilahun Tesfaye, Dr.
Department of physics, Addis Ababa University,
Ethiopia, East Africa.
P.O.Box 80359 (personal), 1176 (Institutional)
E-mail: [email protected]; [email protected].
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.
African Virtual University 111
XIX. 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.