CP3 Chapter 12
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Chapter 12: Nuclear Reaction
12.1 Nuclear Reaction
L.O 12.1.1 State the conservation of charge (Z) and nucleon number (A) in a nuclear
reaction
A nuclear reaction is defined as a physical process in which there is a change in identity of an
atomic nucleus.
Several conservation laws should be obeyed by every nuclear reaction but primarily
conservation of atomic number and of mass number.
Conservation of charge (atomic number Z):
reaction after reaction before ZZ
Conservation of mass number A (nucleon):
reaction after reaction before AA
L.O 12.1.2 Write and complete the equation of nuclear reaction
L.O 12.1.3 Calculate the energy released in nuclear reaction
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.
The reaction energy Q is the energy equivalent to the mass defect m of the reaction, thus
2 cmQ
reaction after nucleus of mass -reaction before nucleus of massdefect Mass m
Δm or Q > 0 (positive value) Δm or Q < 0 (negative value)
exothermic (exoergic) reaction
energy is released
endothermic (endoergic) reaction
energy is required/absorbed in
the form of kinetic energy of the
bombardment particle
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Radioactive Decay
Radioactive decay is defined as the phenomenon in which an unstable nucleus disintegrates to
acquire a more stable nucleus without absorbs an external energy.
The disintegration is spontaneous and most commonly involves the emission of an alpha
particle ( OR He4
2 ), a beta particle ( OR e0
1 ) and gamma-ray ( OR 0
0 ). It also releases
an energy Q known as disintegration energy.
Example:
decay: QHePbPo 4
2
208
82
212
84
decay: QeXNi
0
1
66
29
66
28
decay: TiTi 208
81
*208
81
Bombardment with energetic particle
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 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:
QyYxX
Sometimes this reaction is written in the more compact form:
YyxX ,
Example:
QHOHeN 1
1
17
8
4
2
14
7 OR OpN 17
8
14
7 ,
QHeHLi 4
2
1
1
7
3 2 OR HepLi 4
2
7
3 ,
QHeLinB 4
2
7
3
1
0
10
5 OR LinB 7
3
10
5 ,
Target (parent)
nucleus
Bombarding
particle
Emitted
particle
Daughter
nucleus
Excited state (unstable)
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Example
Question Solution
Radium nucleus decays by alpha emission to
radon nucleus can be represented by equation
below :
QHeRnRa 4
2
222
86
226
88
Calculate
a. the energy Q released in this decay.
b. the wavelength of the gamma-ray produced.
(Given mass of Ra-226, mRa = 226.0254 u; mass
of Rn-222, mRn = 222.0175 u and mass of
particle , m = 4.0026 u)
When lithium 7Li is bombarded by a proton, two
alpha 4He particles are produced. Calculate the
reaction energy.
Given u 007825.1mass 1
1 H
u 016003.7mass 7
3 Li
u 002603.4mass 4
2 He
Exercise
Question
A thorium-234 nucleus Th234
90 decays to a new nucleus by emitting a beta particle.
a. Write an equation represents the nuclear reaction.
b. Calculate the energy released in MeV if the mass of the thorium-234 nucleus is 234.0441
u and the mass of new nucleus is 234.0433 u.
(Given 1 u =931.5 MeV c-2
; 1 u =1.66 x 10-27
kg, mB = 5 x 10-4
u)
Answer: 0.745 MeV
The following nuclear reaction is obtained :
MeV 55.01
1
14
6
1
0
14
7 HCnN
Determine the mass of C14
6 in atomic mass unit (u).
(Given the mass of nitrogen nucleus is 14.003074 u)
Answer: 14.003872 u
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12.2 Nuclear Fission and Fusion
L.O 12.2.1 Explain the occurrence of fission and fusion using the graph of binding
energy per nucleon
L.O 12.2.2 Distinguish the processes of nuclear fission and fusion
L.O 12.2.3 Explain the chain reaction in nuclear fission of a nuclear reactor
L.O 12.2.4 Describe the process of nuclear fusion in the sun
Nuclear Fission
Nuclear fission is defined as a nuclear reaction in which a heavy nucleus splits into
two lighter nuclei.
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).
It can be divided into two types :
Spontaneous fission – very rarely occur (take very long time)
Induced fission – bombarding a heavy nucleus with slow neutrons or thermal
neutrons of low energy (about 10-2
eV). This fission is the important process in energy
production
Example:
U235
92 is bombarded by a slow neutron:
QnLaBrUnU 1
0
148
57
85
35
*236
92
1
0
235
92 3
Other possible reactions are: QnBaKrUnU 1
0
144
56
89
36
*236
92
1
0
235
92 3
QnXeSrUnU 1
0
139
54
94
38
*236
92
1
0
235
92 3
Excited state (unstable)
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The graph of binding energy per nucleon against nucleon number is shown below.
Explanation:
• An estimate of the energy released in a fission reaction can be obtained by considering
the graph in Figure above.
• From the Figure above, 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
MeV 200nucleons 236nucleon 1
MeV 9.0
Example
Question Solution
Calculate the energy released when 10 kg of
uranium-235 undergoes fission according to
QnLaBrnU 1
0
148
57
85
35
1
0
235
92 3
(Given: u 1.235mass 235
92 U , u 01.1mass 1
0 n ,
u 9.84massr 85
35 B , u 0.148mass a148
57 L )
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Chain Reaction
Chain reaction is defined as a nuclear reaction that is self-sustaining as a result of the
products of one fission reaction initiating a subsequent fission reaction.
• From figure, one neutron initially causes one fission of a uranium-235 nucleus, the two or
three neutrons released can go on to cause additional fissions, so the process multiples.
• Conditions to achieve chain reaction in a nuclear reactor :
• Slow neutrons are better at causing fission.
• The fissile material must more than a critical size.
(The critical size/mass is defined as the minimum mass of fissile/fission material required to
produce a sustained chain reaction.)
• The uncontrolled chain reactions are used in nuclear weapons – atomic bomb.
• The controlled chain reactions take place in nuclear reactors and release energy at a
steady rate.
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Nuclear Reactor
• A nuclear reactor consists of fuel rods (fission material, eg U-235), movable control
rods and a moderator (water).
• Nuclear reactors use a combination of U-235 and U-238 (3-5% 235
U). The U-235 will
undergo the fission reaction, while the U-238 (more stable) merely absorbs neutrons (slow
neutrons).
• In a nuclear reactor, the chain reaction is controlled so that only one of the secondary
neutrons from the fission of a U-235 nucleus is allowed to continue the fission reaction.
In this manner, energy is released at a constant rate.
• Firstly, neutron is bombarded to the 235
U 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.
• 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.
• Water circulating in the core of the reactor acts as coolant. The heated water flows to a
heat exchanger where steam is produced. The steam then rotates a turbine that
generates electricity.
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Nuclear Fusion
Nuclear fusion is defined as a type of nuclear reaction in which two light nuclei fuse to form
a heavier nucleus with the release of large amounts of energy.
The energy released in this reaction is called thermonuclear energy.
Example:
• QnHeHH 1
0
3
2
2
1
2
1
• QHHHH 1
1
3
1
2
1
2
1
The amount of energy released by this process can be estimated by using the binding energy
per nucleon curve
QnHeHH 1
0
4
2
3
1
2
1
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Explanation:
• From figure above, 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.
Example
Question Solution
A fusion reaction is represented by the equation
below:
QHHHH 1
1
3
1
2
1
2
1
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)
Exercise
Question
How many times is the energy per nucleon in the reaction is fusion
QHeLiH 4
2
6
3
2
1 2
greater than the energy per nucleon in the reaction is fission
QnSrBanPu 1
0
96
38
138
56
1
0
236
94 3
Given mH = 2.014 u; mHe = 4.002 u; mLi = 7.016 u; mPu = 236.046 u; mBa = 137.905 u;
mSr = 95.921 u; mn = 1.009 u
Answer: Approximately 3.4 ~ 3.6
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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 are given
• 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 x 107 K).
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Comparison between fission and fusion
Table below shows the differences between fission and fusion reaction.
Fission Fusion
Heavy to light nucleus 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
The similarity between the fission and fusion reactions is:
• Both reactions produce energy.
• Mass is reduced after reaction.
• New product is produced.