is defined as a physical
process in which there is a
change in identity of an
atomic nucleus.
CHAPTER 30:
Nuclear reaction
(2 Hours)
1
Four types of
nuclear reaction:
L.O: At the end of this topic, students should be able to:



State the conservation of charge (Z) and nucleon number
(A) in a nuclear reaction.
Write and complete the equation of nuclear reaction.
Calculate the energy liberated in the process of nuclear
reaction
2
27.1 Nuclear Reaction
Definition
A nuclear reaction is defined as a physical process in
which there is a change in identity of an atomic nucleus.
Example
6
3
Li + H  2 H e
2
1
4
2
Figure 27.1
3
27.1.1 Conservation of nuclear reaction
In any nuclear reaction, several conservation laws must be
obeyed, primarily conservation of charge and conservation of
nucleons.
– Conservation of charge (atomic number Z):

atomic number
before reaction
Z

atomic number
after reaction
Z
– Conservation of mass number A (nucleon)

mass number A
before reaction

mass number
after reaction
A
4
27.1.2 Reaction Energy, Q
Reaction energy is the energy released (liberated) in a
nuclear reaction in the form of kinetic energy of the particle
emitted, the kinetic energy of the daughter nucleus and the
energy of the gamma-ray photon that may accompany the
reaction.
Reaction energy , Q  Δmc
M ass d ifferen ce

Δm 

2
mass of nucleus
before
reaction

mass of nucleus
product
after reaction
m  mi  mf
5
Note:
Δm = mi - mf
a) If Δm or Q > 0 (positive value)
- exothermic (exoergic) reaction.
- energy is released.
b) If Δm or Q < 0 (negative value)
- endothermic (endoergic) reaction.
- energy is required/absorbed in the form of kinetic
energy of the bombardment particle.
Other reference : Δm = mf – mi
Δm →negative (energy is released)
Δm →positive (energy is absorbed)
6
27.1.3 Radioactive Decay



is defined as the phenomenon in which an unstable
nucleus disintegrates to acquire a more stable nucleus
without absorb an external energy.
The disintegration is spontaneous and most commonly
4
involves the emission of an alpha particle ( OR 2 He ),
0
0
a beta particle ( OR 1 e ) and gamma-ray ( OR 0 γ ).
It also release an energy Q known as disintegration
energy.
Example:
212
84
Po 
66
28
208
82
Pb  2 He  Q
Ni 
4
66
29
X
0
1
eQ

Ti 
208
81
Ti  γ
208
81
7
27.1.4 Bombardment with energetic particles


is defined as an induced nuclear reaction that does not
occur spontaneously; it is caused by a collision between
a nucleus and an energetic particles such as proton,
neutron, alpha particle or photon.
Consider a bombardment reaction in which a target
nucleus X is bombarded by a particle x, resulting in a
daughter nucleus Y, an emitted particle y and reaction
energy Q: X  x  y  Y  Q
sometimes this reaction is written in the more compact
form:
X  x, y Y
daughter
target (parent)
nucleus
nucleus
emitted
bombarding
particle
particle
8
Example:
14
7
N  2 He  8 O  1 H  Q
4
7
1
Li

3
1H
10
5
17
1
 2 2 He  Q OR
4
14
7
OR
N  , p  8 O
17
p ,  42 He
10
7


B
n
,

5
3 Li
7
3 Li
1
7
4
B  0 n  3 Li  2 He  Q OR
9
Example 27.1
1.
Complete the following radioactive decay equations :
Be  2 He  
4
a. 8

4
b. 240 Po  97 Sr  139 Ba 
94
38
56
c. 236 U  131 I  3
92
53
 n  
1
0
d. 29 Na  0 e  
11
1
40
19
K  20 Ca  
40



e. 47 Sc   47 Sc  
21
21
f.



10
Example 27.2
When lithium 7Li is bombarded by a proton, two alpha 4He
particles are produced. Calculate the reaction energy.
Given
1
1
H mass  1.007825
u
7
3
Li mass  7.016003
u
4
2
He mass  4.002603
u
Solution:
11
12
Example 27.3
A deuterium bombards a
nuclide.
13
6
14
C nuclide and produces 7 N
a) Write an equation for the nuclear reaction.
b) Calculate the kinetic energy (in MeV) that is
released in the reaction.
Given
:
13
6
2
1
14
7
C mass  13.00335
H mass  2.01410
N mass  14.00307
1
0
n mass  1.00867
u
u
u
u
13
Solution
14
EXERCISE
1.
Calculate the energy released in the alpha decay below:
238
92
2.
U
234
90
Th  2 He  Q
(Given mass of U-238 is 238.050786 u ; mass of Th-234 is
234.043583 u and mass of  particle is 4.002603 u)
ANS. : 6.871013 J
The following nuclear reaction is obtained :
14
1
14
1
N

n

C

H  0 . 55 MeV
7
0
6
1
14
6
3.
4
Determine the mass of C in atomic mass unit (u).
(Given the mass of nitrogen nucleus is 14.003074 u)
ANS. :14.003872 u
7
4
A nuclear reaction can be written as 3 Li  p ,  2 He .
Calculate the energy involved in the reaction and state whether it
is absorbed or released. (Given mass of Helium is 4.002602u,
mass of Lithium is 7.016003u and mass of proton is 1.006024u).
ANS. :15.67MeV 15
L.O: At the end of this topic, students should be able to:




Distinguish the processes of nuclear fission and fusion.
Explain the occurrence of fission and fusion using the
graph of binding energy per nucleon.
Explain chain reaction in nuclear fission of a nuclear
reactor.
Describe the process of nuclear fusion in the sun.
16
27.2.1 Nuclear Fission
Definition
Nuclear fission is the process by which heavy nuclei are split
into two lighter nuclei.
235
92
U  0 n
1
236
92

U  35 Br 
85
148
57
La  3 0 n  Q
1
 Energy is released by the process because the average
binding energy per nucleon of the fission products is
greater than that of the parent.
 The energy released is in the form of increased kinetic
energy of the product particles (neutrons) and any
radiation emitted (gamma ray).
17
 Nuclear fission can be divided into two ways of processes :
i) spontaneous fission
very rarely occur (take very long time)
ii) induced fission
heavy nucleus is bombarded by a particle :
proton, alpha particle and neutron (slow neutrons or
thermal neutrons of low energy (about 10-2 eV).
18

For example, consider the bombardment of 235
by
92 U
slow neutrons. One of the possible reaction is
235
92
U0n
1
236
92

U  35 Br 
85
148
57
La  3 0 n  Q
1
Nucleus in the excited state.
The reaction can also be represented by the diagram
in Figure 27.2
85
35
1
0
Br
n
235
92
U
236
92
U

148
57
Figure 27.2
1
0
n
1
0
n
1
0
n
La
Other possible reactions are:
235
92
U0n
1
235
92
236
92

U  36 Kr 
U0n
1
89
236
92

144
56 Ba
U  38 Sr 
94
30 n  Q
1
139
54 Xe
 30 n  Q
1
19

Most of the fission fragments (daughter nuclei) of the
uranium-235 have mass numbers from 90 to 100 and from
135 to 145 as shown in Figure 27.3.
Figure 27.3
20
21
Binding energy per nucleon as a function of mass number,A
Figure 27.4
Binding energy per
nucleon (MeV/nucleon)
Greatest stability
daughter
nuclei
parent
nuclei
fission
Moving toward more stable nuclei
Mass number A
22
Explanation of Figure 27.4
 An estimate of the energy released in a fission reaction can
be obtained by considering the graph in Figure 27.4.
 From the figure, the binding energy per nucleon for uranium is
about 7.6 MeV/nucleon, but for fission fragment (Z~100), the
average binding energy per nucleon is about 8.5
MeV/nucleon.
 Since the fission fragments are tightly bound, they have less
mass.
 The difference in mass (or energy) between the original
uranium nucleus and the fission fragments is about 8.5 -7.6 =
0.9 MeV per nucleon. Since there are 236 nucleons involved
in each fission, the total energy released is
0.9 MeV
nucleon
x 236 nucleons
  200
MeV
23
Example 27.4
Calculate the energy released (MeV) in the following fission
reaction :
235
1
148
85
1
U

n

La

Br

3
nQ
92
0
57
35
0
Given :
235
92
U mass  235.1 u
1
0
n mass  1.01 u
85
35
148
57
Br mass  84.9 u
La mass  148.0 u
Solution:
24
Example 27.5
Calculate the energy released when 10 kg of uranium235 undergoes fission according to
235
92
U  0 n
1
141
56
Ba  36 Kr  3 0 n  Q
92
1
(Given mass of U-235 is 235.04u, mass of Ba-141 is
140.91u, mass of Kr-92 is 91.91u, mass of neutron is
1.01u and NA=6.02x1023mol-1)
Solution:
25
26
27.2.2 Chain Reaction
Figure 27.5
Figure 27.6
27
Definition
Chain reaction is a series of nuclear fissions whereby
some of the neutrons produced by each fission cause
additional fissions.
Condition to achieve chain reaction in a nuclear reactor
a) Slow neutrons are better at causing fission.
b) The fissile/fission material must more than a critical
size/mass (a few kg).
Note:
The critical size/mass is defined as the minimum
mass of fissile/fission material required to
produce a sustained chain reaction.
28
Nuclear Reactor

A nuclear reactor is a device in which energy is
generated by a controlled fission chain reaction.
(The uncontrolled chain reactions are used in nuclear
weapons – atomic bomb )
 Apart from being used to obtain energy from the
reaction of fission, a reactor is widely applied, for
example to generate :
- radioactive elements,
- new fissile materials, such as 233U or 239Pu,
- neutrons for scientific research.
29
A nuclear reactor
Figure 27.7
30
Figure 27.8
31
• A nuclear reactor consists of fuel rods (fission
material), movable control rods and a moderator
(water).
• Fission reactors use a combination of 235U and
238U (3-5% 235 U).
• The 235U will fission, while the 238U(more stable)
merely absorbs neutrons (slow neutrons).
• Firstly, neutron is bombarded to the 235U and other
neutrons are emitted during fission.
• Then the emitting neutrons with high energy are
slowed down by collisions with nuclei in the
surrounding material, called moderator, so that they
can cause further fissions and produce more energy.
32
• In order to release energy at a steady rate, the rate
of the reaction is controlled by inserting or
withdrawing control rods made of elements (often
cadmium) whose nuclei absorb neutrons without
undergoing any additional reaction.
• To have a self-sustaining chain reaction, the mass of
fission material must be sufficiently large (> critical
mass) so that on the average at least one neutron
produced in each fission must go on to produce
another fission.
33
27.2.3 Nuclear Fusion
Definition
Nuclear fusion is the process in which nuclei of light
element combine to form nuclei of heavier elements.
Examples
2
2
3
H

H

1
1
2 He
0n  Q
1
Deuterium
2
1
H
2
2
3
1
H

H

H

1
1
1
1H
Tritium
3
1
H
Fusion
reaction
Alpha 4 He
2
particle
Q
2
3
4
H

H

1
1
2
He  0 n  Q
1
Neutron
1
0
Figure 27.9
n
34

The energy released in this reaction is called
thermonuclear energy.
 The amount of energy released by this process can be
estimated by using the binding energy per nucleon curve
(Figure 27.10).
 From Figure 27.10, the binding energy per nucleon for the
lighter nuclei (2H) is small compared to the heavier nuclei.
The energy released per nucleon in the fusion process is
given by the difference between two values of binding
energy per nucleon.
 And it is found that the energy released per nucleon by
this process is greater than the energy released per
nucleon by fission process.
35
Binding energy per nucleon as a function of mass number,A
Figure 27.10
Binding energy per
nucleon (MeV/nucleon)
Greatest stability
Moving toward more stable nuclei
fusion
Mass number A
36
Figure 27.11
37
 For two nuclei to undergo fusion, as both nuclei are
positively charged there is a strong repulsive force between
them, which can only be overcome if the reacting nuclei
have very high kinetic energies.
 These high kinetic energies imply temperatures of the order
of 108 K.
 At these elevated temperatures, however fusion reactions
are self sustaining and the reactants are in form of a
plasma (i.e. nuclei and free electron) with the nuclei
possessing sufficient energy to overcome electrostatic
repulsion forces.
 The nuclear fusion reaction can occur in fusion bomb and
in the core of a star.
38
Example 27.6
A fusion reaction is represented by the equation below:
2
2
3
1
H

H

H

1
1
1
1H
Calculate
a. the energy in MeV released from this fusion reaction,
b. the energy released from fusion of 1.0 kg deuterium,
(Given mass of proton =1.007825 u, mass of tritium
=3.016049 u and mass of deuterium =2.014102 u)
Solution :
39
40
27.2.4 Nuclear Fusion in the sun




The sun is a small star which generates energy on its
own by means of nuclear fusion in its interior.
The fuel of fusion reaction comes from the protons
available in the sun.
The protons undergo a set of fusion reactions, producing
isotopes of hydrogen and also isotopes of helium.
However, the helium nuclei themselves undergo nuclear
reactions which produce protons again. This means that
the protons go through a cycle which is then repeated.
Because of this proton-proton cycle, nuclear fusion in the
sun can be self sustaining.
The set of fusion reactions in the proton-proton cycle can
be illustrated by Figure 27.12.
41
positron (beta plus)
neutrino
1
1
2
0
H

H

H

1
1
1
1e
vQ
2
1
3
1 H  1 H  2 He
3
2 He
 Q
 2 He  2 He  1 H  1 H  Q
3
4
1
1
Figure 27.12

The amount of energy released per cycle is about 25 MeV.
 Nuclear fusion occurs in the interior of the sun because the
temperature of the sun is very high (approximately 1.5  107 K).
42
27.2.5 Comparison between nuclear
Fission and nuclear Fusion
Differences
Fission
Heavy to light nucleus
Fusion
Light to heavy nucleus
Neutron to bombard
High temperature
Produce more than 1 nucleus Produce 1 nucleus
Easy to handle & control
Difficult to handle & control
Similarities
 new product is produced.
 energy is released.
 mass is reduced after reaction.
43
Figure 27.13
Binding energy per
nucleon (MeV/nucleon)
Greatest stability
Fission
The falling part of the binding energy curve
shows that very heavy elements such as
uranium can produce energy by fission of their
nuclei to nuclei of smaller mass number.
Fusion
The rising part of the binding energy curve
shows that elements with low mass number
can produce energy by fusion.
Mass number A
44
45