Introduction to

Introduction to Nuclear
Physics
CHAPTER 2

Contents
 1- Introduction
 4- a) Alpha , b) Beta and c) Gamma Decay
 2- Some Nucleus Properties
 3- Radioactive Decay
 5- Natural radioactive decay series
 6- Induced Nuclear reactions
(nuclear fission and nuclear fusion)
 7- Radioactive Dating
 8- Measuring Radiation Dosage

1/ INTRODUCTION:
 By accident, becquerel discovered that uranium salts
spontaneously emit a penetrating radiation that can be
registered on a photographic plate.
 Rutherford showed that the radiation had three types:
Alpha, Beta and Gamma
1896

1/ INTRODUCTION:
 Rutherford fired a beam of alpha particles at foil of
gold leaf
 The results of the experiment are :
1) Most of alpha particles
Passed without deflection.
2) some of alpha particles are
deflected at small angles.
3) few of alpha particles are
deflected at large angles.
1911 Rutherford scattering experiment

1/ INTRODUCTION:
 The conclusions of the experiment are :
1) Most of the space inside the atom is empty
2) The positive charge of the atom occupies very little
space
3) That all the positive charge and mass of the atom
were concentrated in a very small volume within
the atom

1/ INTRODUCTION:
 Rutherford's Nuclear Model Of Atom :
1) There is a positively charged Centre in an atom
called the nucleus. Nearly all the mass of an atom
resides in the nucleus.
2) The electrons revolve around the nucleus in well-
defined orbits.
3) The size of the nucleus is very small as compared
to the size of the atom.
 Nucleus of an atom is positively charged ,very dense
, hard and very small

2/ Some Nuclear Properties
The materials are made of atoms
The atom is composed of a nucleus and electrons orbiting
around the nucleus.
The nucleus is a very small dense object made up of two
kinds of nucleons [Protons (p), Neutrons (n)].
Atom
Nucleus
Protons
Neutrons
Electrons

𝑚𝑝 ≅ 𝑚𝑛
𝑚𝑝 ≅ 1840 𝑚𝑒
Number of protons is equal to the number of the electrons
in the neutral atom.

Numbers that characterize the nucleus Z, N and A
Z = Atomic number
N = Neutron number
Number of nucleons in the
nucleus.
Number of protons in the nucleus.
The number of neutrons in the
nucleus.
A = Mass number
𝐴 = 𝑁 + 𝑍
a) Nuclear Terminology

Example
Find the number of protons, neutrons and electrons
Representation of a nucleus

Examples
1) Isotopes
The atoms of an element which have the same number of
protons (𝑍1 = 𝑍2) and different number of neutrons are
called Isotopes.

Example
2) Isobars
The atoms which have the same mass number (𝐴1 = 𝐴2)
but different atomic numbers are called isobars.

Example
3) Isotones
Atoms which have different atomic number (𝑍1 ≠ 𝑍2) and
different atomic masses (𝐴1 ≠ 𝐴2) but the same number of
neutrons 𝑁1 = 𝑁2 are called Isotones.

Isotopes
Isotones
Isobars
𝑍1 = 𝑍2
𝑁1 = 𝑁2
𝐴1 = 𝐴2

2) The Volume (V) of the nucleus is given by the
formula :
Most nuclei are spherical
b) Nucleus Radius and Volume
1) The Average radius is given by the formula :
𝑟 = 𝑟0 𝐴1/3
; 𝑟0 = 1.2 𝑋 10−15
m
The unit used for measuring distance on the scale of
nuclei is femtometer : 1 𝑓𝑚 = 10−15
𝑚
V =
4
3
𝜋(𝑟0 𝐴
1
3)3
V = 7.24 𝑋 10−45
(A) 𝑚3

Radius depends on 𝐴1/3
Volume depends on 𝐴

The Mass can also be expressed in 𝑀𝑒𝑉/𝑐2
The SI-unit of mass is Kg but in subatomic particles It is
convenient to use atomic mass units ( 𝑢 ) to express
masses.
c) Atomic Mass
Based on definition that the mass of one atom of C is
exactly 12 𝑢
1 𝑢 = 1.660 539 x 10−27
kg
𝑚𝑝 = 1.0073 𝑢 , 𝑚𝑁 = 1.0087 𝑢 , 𝑚𝑒 = 5.486 ∗ 10−4
𝑢
𝑚𝑝 = 938.25 𝑀𝑒𝑉/𝑐2 , 𝑚𝑁 = 939.57𝑀𝑒𝑉/𝑐2
, 𝑚𝑒= 0.511𝑀𝑒𝑉/𝑐2
1 𝑢 = 931.494 𝑀𝑒𝑉/𝑐2

ρ =
𝑚
𝑉
=
𝑍∗𝑚𝑝+𝑁∗𝑚𝑁
4
3
𝜋(𝑟0 𝐴
1
3)3
(𝑚𝑝≅ 𝑚𝑛)
≅
𝐴∗𝑚𝑝
4
3
𝜋(𝑟0 𝐴
1
3)3
=
𝐴∗𝑚𝑝
4
3
𝜋 𝑟0
3 𝐴
=
1.673∗10−27
7.238∗10−45 ≅ 2.3 ∗ 1017 Τ
𝐾𝑔 𝑚3
d) Nucleus Density
That’s mean all nuclei have the same Density

2) Electrical force: smaller in magnitude, but they
become progressively more important as the number of
protons in the nucleus increases.
1) Nuclear force: the force responsible of nuclei stability,
which overcome the electrical force (repulsion between
protons).
e) Forces in the nucleus
Properties of Nuclear force: strong, short range and
attraction between nucleons.

p-p: electric repulsion and nuclear attraction.
e) Forces in the nucleus
p-n: nuclear attraction.
n-n: nuclear attraction

3/ Radioactive Decay
Radioactivity : is the spontaneous emission of radiation.
Radioactivity : is the result of the decay, or disintegration,
of unstable nuclei.
Radioactive nuclei can emit 3 types of radiation in the
process:
a) Definitions

 Alpha particles (𝛼): consists of 2 protons and 2 neutrons,
and they are positively charged (+2e), have low speed and
short range in matter. [2
4
𝐻𝑒]
 Beta particles (𝛽): they could be 𝛽−
(electrons) or 𝛽+
(positrons) , have high speed (near speed of light) and
longer range in matter. [positrons are positively charged electrons]
 Gamma ray (𝛾): It is electromagnetic wave (photon)
carrying a high energy away from the nucleus, has speed
of light and it is the most penetrating radiation . [have no
mass or charge]

The number of particles that decay in a given time is
proportional to the total number of particles in a
radioactive sample.
b) The Decay Constant
λ is called the decay constant and determines the
probability of decay per nucleus per second.
𝑑𝑁
𝑑𝑡
= −𝜆𝑁 𝑔𝑖𝑣𝑒𝑠 𝑁 = 𝑁0𝑒−𝜆𝑡
N is the number of undecayed radioactive nuclei present.
No is the number of undecayed nuclei at time t = 0
(original number of nuclei).

The decay rate R of a sample is defined as the number of
decays per second.
c) The Decay Rate
𝑅0 = 𝜆𝑁0 is the decay rate at t = 0.
R =
𝑑𝑁
𝑑𝑡
= 𝜆𝑁 = 𝜆𝑁0𝑒−𝜆𝑡
= 𝑅0𝑒−𝜆𝑡
The decay rate is often referred to as the activity of the
sample.

The decay curve follows the equation:
d) Decay Curve and Half-Life
𝑁 = 𝑁0𝑒−𝜆𝑡
Half life 𝑇1/2 is defined as the time required for half the
nuclei present to decay.
𝑇1/2 =
𝐿𝑛2
𝜆
=
0.693
𝜆

c) Decay Curve and Half-Life
t N
0 𝑁0
T 𝑁0/2
2T 𝑁0/4
3T 𝑁0/8
nT 𝑁0/(2𝑛)

Activity (R) in term of decay constant (λ)
e) Activity (R) of a given mass
𝑁𝐴 = 6.023 𝑋1023
𝑚𝑜𝑙−1
is Avogadro’s Number
𝑛 =
𝑚𝑎𝑠𝑠
𝐴
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 ; 𝐴 is Mass number
𝑅 = 𝜆𝑛𝑁𝐴
𝑅 = 𝜆
𝑚𝑎𝑠𝑠
𝐴
𝑁𝐴

Activity (R) in term of Half life T
e) Activity (R) of a given mass
𝑅 =
0.693
𝑇
𝑛𝑁𝐴
Remark
Activity R must have a unit Bq ( Becquerel)
Half life T must have a unit s ( Second)
Constant decay λ must have a unit 𝑠−1

The SI unit of activity is the becquerel (Bq)
f) Activity Units
1 Bq = 1 disintegration/s
Remark
The curie (Ci) is another unit of activity,
1 Ci = 3.7 X 1010
disintegration/s
1 Ci = 3.7 X 1010
Bq

4/a Alpha Decay
𝑍
𝐴
𝑋 → 𝑍−2
𝐴−4
𝑌 + 2
4
𝐻𝑒
or
𝑍
𝐴
𝑋 → 𝑍−2
𝐴−4
𝑌 + 2
4
𝛼
X is called the parent nucleus
Y is called the daughter nucleus
Example : 92
238
𝑈 → 90
234
𝑇ℎ + 2
4
𝐻𝑒
84
234
𝑃𝑜 → 82
230
𝑃𝑏 + 2
4
𝛼
Alpha particle ( 2
4
𝐻𝑒 , 2
4
𝛼 ) is emitted leaving behind a
residual nucleus that has lost 2 protons and 2 neutrons; 𝛼-
decay is usually observed in heavier unstable nuclei (𝑍
> 82).

4/a Alpha Decay
Alpha particle (2
4
𝐻𝑒) is emitted leaving behind a residual
nucleus that has lost 2 protons and 2 neutrons; 𝛼-decay is
usually observed in heavier unstable nuclei (𝑍 > 82).

4/b Beta Decay
In Beta decay, an electron (𝑒−
) or a positron (𝑒+
) is emitted
by nucleus
 When a nucleus emits an electron, the nucleus
loses a neutron and gains a proton.
 When a nucleus emits an positron, the nucleus
loses a proton and gains a neutron.

4/b Beta Decay
9
18
𝐹 → 8
18
𝑂 + 1
0
𝑒 + 𝜈
6
14
𝐶 → 7
14
𝑁 + 𝛽−
+ ҧ
𝜈
6
14
𝐶 → 7
14
𝑁 + −1
0
𝑒 + ҧ
𝜈
9
18
𝐹 → 8
18
𝑂 + 𝛽+
+ 𝜈

4/c Gamma Decay
 Gamma rays are given off when an excited nucleus
decays to a lower energy state.
 The decay occurs by emitting a high energy photon
called gamma-ray photons
Example:
18
40
𝐴𝑟∗ → 18
40
𝐴𝑟 + 𝛾
The 𝑿∗
indicates a nucleus in an excited state.

5/ Natural radioactive decay series
 Decay series : The sequence of radioactive daughter nuclides that are formed
by the radioactive decay of a parent nuclide to a final stable daughter nuclide.
 There are three natural decay series that include the heavy elements
1) Thorium series : begins with 90
232
𝑇ℎ and end with 82
208
𝑃𝑏 ( its emits 6 𝛼 and 4
𝛽− in decay prosses)
90
232
𝑇ℎ → 82
208
𝑃𝑏 + 6 2
4
𝐻𝑒 + 4 −1
0
𝑒 + 4ഥ
𝜈
2) Uranium series : begins with 92
238
𝑈 and end with 82
206
92
238
𝑈 → 82
206
𝑃𝑏 + 8 2
4
𝐻𝑒 + 6 −1
0
𝑒 + 6 ҧ
𝜈
3) Actinium series : begins with 92
235
𝑈 and end with 82
207
92
235
𝑈 → 82
207
𝑃𝑏 + 7 2
4
𝐻𝑒 + 4 −1
0
𝑒 + 4 ҧ
𝜈
Each of the three series ends with an isotope of lead

5/ Natural radioactive decay series
Thorium series Uranium series Actinium series

6/ Induced Nuclear reactions
1) Nuclear fusion : is a reaction in which two or more light
nuclei are combined to form one or more heavy nuclei
and subatomic particles (neutrons or protons).
The fusion process releases a large amount of energy
(Nuclear fusion occur inside the center of stars)

6/ Induced Nuclear reactions
2) Nuclear Fission : is a reaction in which the heavy nucleus
splits into two or more smaller nuclei.
The fission process often produces gamma photons, and
releases a very large amount of energy

7/ Radioactive dating
Carbon-14 has half-life of 5730 years ; the production of
C-14 is explained by the next nuclear equation:
7
14
𝑁 + 0
1
𝑛 → 6
14
𝐶 + 1
1
𝑝
Neutrons are produced in upper atmosphere by interaction
of cosmic-ray with atomic nuclei
Once an organism dies, the input of radiocarbon stops and
the ratio of radiocarbon to ordinary carbon 6
12
𝐶 decreases
steadily as the 6
14
𝐶 decays. Thus the quantity of 6
14
𝐶
remaining indicates the date of death
6
14
𝐶 → 7
14
𝑁 + −1
0
𝛽 + ҧ
𝜈
The decay of C-14 is explained by the next nuclear equation:

8/ Measuring Radiation Dosage
a) major categories of radiation
1. Positive ions (protons and alpha particles)
2. Electrons and Positrons (beta particles)
3. Photons (gamma rays and X-rays)
4. Neutrons

b) Absorbed dose
This is a measure of radiation dose (as energy per unit
mass) actually absorbed by a specific object, such as
patient’s hand or chest.
SI unit: gray (Gy).
Other unit: rad,
1Gy =100 rad.
1Gy = 1 J/Kg

c) Dose Equivalent
Although different types of radiation (gamma ray and
neutrons…) may deliver the same amount of energy to
the body, they do not have the same biological effect.
The dose equivalent allows us to express the biological
effect
SI unit: Sievert (Sv)
 Other unit: rem
1 Sv = 100 rem

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