CP3 Chapter 12

1

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

CP3 Chapter 12

2

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)

CP3 Chapter 12

3

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

CP3 Chapter 12

4

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)

CP3 Chapter 12

5

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 )

CP3 Chapter 12

6

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.

CP3 Chapter 12

7

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.

CP3 Chapter 12

8

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

CP3 Chapter 12

9

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

CP3 Chapter 12

10

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).

CP3 Chapter 12

11

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.