CHAPTER

Fission and fusion

This chapter looks at typical nuclear fission and fusion reactions, the forces that act
within the nucleus, energy transfer and important transformation phenomena in
stars and in the production of nuclear energy. It also examines the benefits and risks
of using nuclear power as an energy source for society.

Science as a Human Endeavour

Qualitative and quantitative analyses of relative risk are used to inform community
debates about the use of radioactive materials and nuclear reactions for a range of
applications and purposes, including:
• A fission chain reaction is a self-sustaining process that may be controlled to
produce thermal energy, or uncontrolled to release energy explosively if its critical
mass is exceeded. (Newtan)

• nuclear power stations employ a variety of safety mechanisms to prevent Kinetic

↓
Nz nuclear accidents, including shielding, moderators, cooling systems, and
E mc + mm
radiation monitors =
0(() +

A
·
O • the management of nuclear waste is based on the knowledge of the behaviour
C : speed of light
of radiation.

+
Science Understanding 0
• neutron-induced nuclear fission is a reaction in which a heavy nuclide captures a
↓ neutron and then splits into smaller radioactive nuclides with the release of energy
N + z • Einstein’s mass/energy relationship relates the binding energy of a nucleus to its

mass defect Binding

[mutEmp-michu
This includes applying the relationship
ΔE = Δmc2 =
• Einstein’s mass/energy relationship also applies to all energy changes and
enables the energy released in nuclear reactions to be determined from the mass
A + B > C+ D
change in the reaction + E
-

This includes applying the relationship

ΔE = Δmc2 DE (ma mp mc-mp)ch
=
+
-

• nuclear fusion is a reaction in which light nuclides combine to form a heavier

nuclide, with the release of energy
• more energy is released per nucleon in nuclear fusion than in nuclear fission
because a greater percentage of the mass is transformed into energy

WACE Physics ATAR Course Year 11 Syllabus © School Curriculum and Standards Authority,
Government of Western Australia, 2014; reproduced by permission
 4.1 Nuclear fission and energy
Muel
=
In 1905, Albert Einstein theorised that mass, m, and energy, E, are equivalent
through the equation E = mc2. This led to the realisation that vast amounts of energy
lie unharnessed within the nuclei of atoms. The ramifications of Einstein’s work and
the discovery of nuclear fission were realised in 1945 with the explosion of the first
atomic bomb in the desert near Alamogordo in New Mexico, USA (Figure 4.1.1).
In this section, nuclear fission and the energy that it can unleash will be explored.

INSIDE THE NUCLEUS

The current understanding of the basic properties and structure of the nucleus is
the result of intense scientific investigation in the early part of the twentieth century.
Physicists such as Becquerel, Rutherford, Chadwick, Geiger, Marsden and Harkins
were instrumental in the development of the model of the nucleus that exists today.
These renowned scientists are shown in Figure 4.1.2.
Recall from Chapter 3 that there is a strong nuclear force that acts within the
FIGURE 4.1.1 An atomic bomb explosion and its nucleus to overcome the electrostatic repulsion of the protons. This force holds
associated mushroom cloud.
the nucleus together.

a b c

*+
X Noe
-

H =

(Bq)-

(5)
FS FEM FEM FT d e f

C Fem
A

Fruclear
B

↓ FIGURE 4.1.2 (a) Henri Becquerel, (b) Ernest Rutherford, (c) James Chadwick, (d) Hans Geiger,
(e) Ernest Marsden and (f) William Harkins.
Fem
An example of how the electrostatic and strong nuclear forces act in a nucleus is
shown in Figure 4.1.3. In this example, proton A both attracts and repels proton B,
neutron proton
but, at short distances, the attraction due to the strong nuclear force is much greater
than the repulsion due to the electrostatic force. Proton A also both attracts and
-

FIGURE 4.1.3 The interaction between the repels proton C, but because of the greater distance between them, the force of
electrostatic and strong nuclear forces acting in

Vackand
repulsion is larger. However, proton A and proton C do not fly apart due to the
a nucleus.

y
strong attractive forces exerted on them by adjacent neutrons.

88 I
AREA OF STUDY 2 | IONISING RADIATION AND NUCLEAR REACTIONS
NUCLEAR FISSION
The discovery of the neutron by James Chadwick in 1932 enabled scientists to explore
the behaviour of larger atomic nuclei. Up until then, physicists such as Enrico Fermi PHYSICSFILE
had been firing alpha-particles at target nuclei and analysing the results. Chadwick Strong nuclear force
found that with larger target nuclei, the positive alpha-particles were too strongly
The existence of the strong nuclear
repelled from the positively charged nuclei and collisions did not occur.
force was first proposed by Japanese
The advantage of a neutron is that it is neutral and so is not repelled by any target theoretical physicist Hideki Yukawa
nucleus. The bombarding neutrons can be absorbed into the nucleus of the target in 1935. However, the properties of
atom, as shown in Figure 4.1.4. This makes neutrons very useful as a form of radiation. this force are so complex that it took
They are used in many experiments to artificially transmutate different isotopes. until 1975 for physicists to develop
a mathematical model that could
a successfully describe it.

"He Z
2

α2+
z = 2
&

1
0 n

FIGURE 4.1.4 (a) Charged α-particles are repelled by a nucleus. (b) Uncharged neutrons are able to
smash into a nucleus.

Nuclear fission occurs when an atomic nucleus splits into two or more pieces.
This is usually triggered or induced by the absorption of a neutron, as shown in
Figure 4.1.5. Nuclides that are capable of undergoing nuclear fission after absorbing
a neutron are said to be fissile. Fissile nuclides are all elements with high atomic
numbers, very few of which exist in nature.

incident
neutron
fission
fragments
Small E >
-

fissile
fissile released
nucleus neutrons

F of
nergy
-

FIGURE 4.1.5 Nuclear fission is the splitting of a nucleus.

239
235 Pu incident n
Uranium-235 and plutonium-239 are fissile and can be made to split when
bombarded by a slow-moving neutron. Uranium-238 and thorium-232 require a matters
very high-energy neutron to induce fission, so they are regarded as fissionable, but
-
requireslarge E >
-

fissionable
non-fissile.
-

CHAPTER 4 | FISSION AND FUSION 89

 Uranium is one of the heaviest naturally occurring elements, has several isotopes
and is found in most rocks. It is thought to have formed in supernovas around
6.6 billion years ago. Its isotopes have very long half-lives and the energy generated
from their radioactive decay is thought to be the main source of heat to the Earth’s
core, resulting in convection currents and continental drift.

RELEASE OF NEUTRONS DURING FISSION

Uranium-235 and plutonium-239 are the fissile nuclides most commonly used in
232 nuclear reactors and nuclear weapons. They are more fissile than uranium-238 and
Th thorium-232.
When a uranium-235 or plutonium-239 nucleus absorbs either a slow- or
fast-moving neutron, it becomes unstable and spontaneously undergoes fission.
However, fission is more likely to be induced by a slow-moving neutron because it
is more easily captured by the target nucleus. better
= >

A uranium-235 nucleus may split in many different ways. When a uranium-235

nucleus undergoes fission, it splits into two smaller nuclei plus neutrons. A wide
variety of pairs of smaller nuclei are produced, due to the completely random
way in which the nucleus splits. Many of the products are themselves radioactive.
Figure 4.1.6 shows one outcome but many others are possible. In this example
three neutrons are released, along with krypton-91 and barium-142 nuclides.
Usually either two or three neutrons are released. For uranium-235, an average of
2.47 neutrons per fission has been determined.
91
Kr

1
0 n

235
U three
neutrons

142
Ba
FIGURE 4.1.6 One possible outcome for the neutron-induced fission of uranium-235.

The equation for this reaction is:

1 235 236 91 142 1
0 n + 92 U → 92 U → 36 Kr+ 56 Ba + 30 n + energy

Krypton-91 and barium-142 are known as fission fragments or daughter nuclei.

Three neutrons are freed from this uranium nucleus when it splits. Note that in the
same way as for radioactive decay, both the atomic number, Z, and mass number,
A, are conserved in these nuclear reactions. For the reaction equation shown, the
atomic numbers on either side of the arrows add up to 92 and the mass numbers
add up to 236.
In the end, the decay products of the nuclear fission process form a lethal cocktail
of radioactive isotopes. It is these radioactive fission fragments that comprise the
bulk of the high-level waste produced by nuclear reactors.
239 Plutonium-239 will also undergo fission in a variety of ways. It releases an
in + pu average of 2.89 neutrons per fission, slightly more than uranium-235, but it does
not undergo fission as easily.

fissile
Co
90 AREA OF STUDY 2 | IONISING RADIATION AND NUCLEAR REACTIONS
HOW TO MEASURE ENERGY IN ELECTRONVOLTS
The energy of moving objects such as cars and tennis balls is measured in joules.
However, nuclei, subatomic particles and radioactive emissions have such small
195
-

amounts of energy that the joule is inappropriate. 1 eV = 1 6x10

.

The energy of subatomic particles and radiation is usually given in electronvolts

(eV). One electronvolt is an extremely small amount of energy and is equivalent to

+
1.60 × 10−19 J.

An electronvolt is the energy that an electron would gain if it were accelerated

by a voltage of 1 volt and is equal to 1.6 × 10−19 J.
To convert from eV to joules: multiply by 1.6 × 10−19 J.
To convert from joules to eV: divide by 1.6 × 10−19 J.

ENERGY RELEASED DURING NUCLEAR REACTIONS

It is well established that the mass of any nucleus is always less than the mass of
its individual nucleons. Two separate protons and two separate neutrons will have
slightly more total mass than a helium nucleus.
Albert Einstein, pictured in Figure 4.1.7, provided the explanation of the
origins of this missing mass. He showed that mass and energy were not completely
independent quantities. Indeed, mass can be converted into energy and energy can
be converted into mass.
If you wanted to separate a helium nucleus into four free nucleons, you would
need to add energy to the nucleus. This energy is the binding energy of the nucleus.
The free nucleons will have more energy and so, according to Einstein, will have
greater mass.
The energy released as a result of a mass defect (mass decrease) is given by
Einstein’s famous equation:

ΔE = Δmc2 GE omch =

where ΔE is energy (J)

Δm is the mass defect (the decrease in mass, in kg)
c is the speed of light = 3.0 × 108 m s−1 FIGURE 4.1.7 Albert Einstein.

The chemical reactions that you have probably performed at school typically
release only a few electronvolts of energy. Compared with this, an enormous amount
of energy is released during nuclear reactions. This has made nuclear energy a major
a decay 5- :

focus of scientific research over the past century.

10 ev
During radioactive decay millions of electronvolts of energy can be released.
Alpha particle decay usually involves the release of 5–10 MeV (5–10 million
electronvolts) of energy. Nuclear fission involves much more energy again,
1 MeV=
typically around 200 MeV. This energy is mainly in the form of the kinetic energy
of the fission fragments and neutrons, as well as the emission of energy as gamma
radiation. fission : ~200Mer
During any fission reaction, the combined mass of the incident neutron and
the target nucleus is always slightly greater than the combined mass of the fission
fragments and the released neutrons. For example, in Figure 4.1.8 on page 92,
the mass of the incident neutron and the uranium-235 nucleus is greater than the
combined masses of the fission products—barium-142, krypton-91 and the three
neutrons. This missing mass is converted into energy according to the equation
ΔE = Δmc2. In this case- 200 MeV of energy is released.
Only a very small proportion of the original mass of the nuclei is available
as usable energy—typically around 0.1%. If you had a 1.000 kg block of pure
uranium-235 that underwent fission completely, at the end you would have a block
of radioactive fission fragments with a mass of around 0.999 kg.

CHAPTER 4 | FISSION AND FUSION 91

 a 91Kr

three
1
0 n neutrons

235U

142Ba

fission fragments energ released

235 U

FIGURE 4.1.8 The mass of fission products is less than the mass of the incident neutron and
target atom.

Worked example 4.1.1

FISSION
Plutonium-239 is a fissile material. When a plutonium-239 nucleus is struck by and
absorbs a neutron, it can split in many different ways. Consider the example of a
nucleus that splits into barium-145 and strontium-93 and releases some neutrons.
240 138 + 2
The nuclear equation for this is: A : = a
= a =

1 239 145 93
0 n + 94 Pu → 56 Ba + 38Sr + a10n + energy

a How many neutrons are released during this fission process, i.e. what is the
value of a?

Om = 3 .
07 X 10-28kg Thinking Working

Analyse the mass numbers (A). 1 + 239 = 145 + 93 + (a × 1)

a = (1 + 239) − (145 + 93)
=2
2 neutrons are released during this
fission.

3 07 x 10
-
28
(3x10832 = 2 76x10k5
-E = 0mc2 x
.

= .

=
- --
v

92 AREA OF STUDY 2 | IONISING RADIATION AND NUCLEAR REACTIONS = 1 .

73x108eV
 = 173 MeV

b During this single fission reaction, there is a loss of mass (a mass defect)
of 3.07 Δ 10ff28 kg. Calculate the amount of energy that is released during−the
fission of a single plutonium-239 nucleus. Answer in both MeV and joules.

Thinking Working

The energy released during the fission αE = αmc2

of this plutonium nucleus can be = (3.07 Δ 10ff28) Δ (3.00 Δ 108)2
found by using E = mc2.
= 2.76 Δ 10ff11 J

To convert J into eV, divide by 2.76 × 10−11

1.6 Δ 10×19. E=
1.6 × 10−19
Remember that 1 MeV = 106 eV.
= 1.73 Δ 108 eV

2me
= 173 MeV

c The combined mass of the plutonium nucleus and bombarding neutron is

3.99 Δ 10ff25 kg. What percentage of this initial mass is converted into the energy
produced during the fission process?

Thinking Working
= 7 . 69x/54
Use the relationship percentage percentage of initial mass converted
of initial mass converted into
into energy =
mass defect 100
×
=
0 0769
. %
mass defect 100 initial mass 1
energy = ×
initial mass 1 3.07 × 10−28 100
= ×
3.99 × 10−25 1
= 0.0769%
This is a very small percentage loss
in mass.

Worked example: Try yourself 4.1.1

FISSION
Plutonium-239 is a fissile material. When a plutonium-239 nucleus is struck by
and absorbs a neutron, it can split in many di erent ways. Consider the example
of a nucleus that splits into lanthanum-143 and rubidium-94 and releases
some neutrons.
The nuclear equation for this is:
1 239 143 94 1
0 n + 94 Pu → 57La + 37Rb + a0n + energy

a How many neutrons are released during this fission process, i.e. what is the
value of a?

b During this single fission reaction, there is a loss of mass (a mass defect) of
4.58 Δ 10ff28 kg. Calculate the amount of energy that is released during fission
of a single plutonium-239 nucleus. Give your answer in both MeV and joules to
two significant figures.

c The combined mass of the plutonium nucleus and bombarding neutron

is 2.86 Δ 10ff25 kg. What percentage of this initial mass is converted into the
energy produced during the fission process?

CHAPTER 4 | FISSION AND FUSION 93

 PHYSICS IN ACTION

Enrico Fermi, Lise Meitner and nuclear fission

Enrico Fermi, pictured in Figure 4.1.9, was born in Italy If barium (Z = 56) was one of the products, then krypton
in 1901. He completed his doctorate and post-doctorate (Z = 36) must be another. This was found to be the case.
work in physics at the University of Pisa and in Germany. It was Frisch who coined the term ‘fission’ and Meitner
Fermi had emigrated to the USA by the time the nuclear who proposed that energy would be released during this
age dawned in the 1930s. The neutron had just been process.
discovered in 1932, which enabled scientists to fire neutral After the start of World War II, Enrico Fermi was
particles at atomic nuclei for the first time. Fermi was at commissioned by President Roosevelt to design and build
the forefront of this research. a device that would sustain the fission process in the form
Fermi bombarded uranium-238 atoms with neutrons of a chain reaction. In 1942, Fermi succeeded in this task.
and found that uranium-238 nuclei absorbed the A squash court at the University of Chicago was used as
neutrons and formed a radioactive isotope of uranium. the site for the world’s first nuclear reactor. It produced less
This isotope then decayed by emitting a beta-minus than 1 W of power—not even enough to power a small light
particle to become neptunium, which then emitted globe! This sounds like a bit of a failure, but in fact, achieving
another beta-minus particle to become plutonium, two fission for the first time was a very important breakthrough.
completely undiscovered elements. Fermi had successfully The reactor was later modified to produce about 200 W.
produced the world’s first artificial and transuranic (i.e. Fermi died of cancer in 1954. One year after his death, the
after uranium) elements. The nuclear reactions for this element with atomic number 100 was artificially produced
process are: and named fermium, Fm, in his honour.
1 238 239
0 n + 92 U → 92 U

239 238 0
92 U → 93Np + −1β

239
93Np → 239 0
94 Pu + −1β

In 1938, following on from Fermi’s work, two German

scientists, Otto Hahn and Fritz Strassmann, were also
bombarding uranium (Z = 92) in an attempt to produce
some transuranic elements (Z > 92). They found that, rather
than producing larger elements, they were getting isotopes
of barium (Z = 56). Hahn wrote to his colleague Lise
Meitner, pictured in Figure 4.1.10, about this unexpected
result. She then discussed this with her nephew Otto Frisch,
a nuclear physicist, and realised that the bombarding
FIGURE 4.1.9 Enrico Fermi. FIGURE 4.1.10 Lise Meitner.
neutrons were causing the uranium nuclei to split.

94 AREA OF STUDY 2 | IONISING RADIATION AND NUCLEAR REACTIONS