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NUCLEAR REACTION. CHAPTER 27: Nuclear reaction (3 Hours). 27.1 Nuclear reaction 27.2 Nuclear fission and fusion. Learning Outcome:. 27.1 Nuclear reaction ( 1 hour). At the end of this chapter, students should be able to:

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CHAPTER 27: Nuclear reaction(3 Hours)

27.1 Nuclear reaction

27.2 Nuclear fission and fusion

Learning outcome
Learning Outcome:

27.1 Nuclear reaction (1 hour)

At the end of this chapter, students should be able to:

  • Statethe conservation of charge (Z) and nucleon number (A) in a nuclear reaction.

  • Write and completethe equation of nuclear reaction.

  • Calculatethe energy liberated in the process of nuclear reaction

a) Radioactive decay.

c) Nuclear fission.

d) Nuclear fusion.

27.1 Nuclear reaction


b) Induced nuclear reaction

(particle bombardment).

27.1 Nuclear reaction

  • In any nuclear reaction, several conservation laws

  • must be obeyed, primaryly conservation of

  • charge and conservation of nucleons.

Conservation of charge (atomic number Z)

Conservation of mass number A (nucleon)

Reaction energy Q

  • Reaction energy is the energy released (absorbed)

  • 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 ,


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)

Example 27.1

Complete and state the type of reaction in the following nuclear reactions.




Example 27.2

When lithium 7Li is bombarded by a proton, two alpha 4He particles are produced. Calculate the reaction energy.




Example 27.3

A deuterium bombards a 136C nuclide and produces 147 N nuclide.

a) Write an equation for the nuclear reaction.

b) Calculate the kinetic energy (in MeV) that is

released in the reaction.

Solution 27.3



Kinetic energy is released

Example 27.4

Q= 15.67 MeV

A nuclear reaction can be written as .

Calculate the energy involved in the reaction and state whether it is absorbed or released.



new nucleus



Target nucleus

(parent nucleus)



Learning Outcome:

27.2 Nuclear fission and fusion (2 hour)

At the end of this chapter, students should be able to:

  • Distinguishthe processes of nuclear fission and fusion.

  • Explainthe occurrence of fission and fusion using the graph of binding energy per nucleon.

  • Explainchain reaction in nuclear fission of a nuclear reactor.

  • Describethe process of nuclear fusion in the sun.

27.2 Nuclear fission and fusion

  • Nuclear fission is the process by which heavy

  • nuclei are split 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).

27.2 Nuclear fission and fusion

  • Nuclear fission can be divided into two ways

  • of processes :

  • 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).

27.2 Nuclear fission and fusion

  • Example : is bombarded by a slow neutron.

Nucleus in the excited state.


(10-12 s)

27.2 Nuclear fission and fusion

  • Other possible reactions are:

  • Figure X is a graph of the distribution of fission

  • fragments (daughter nuclei) from the fission of

  • uranium-235 versus mass number A.

  • Most of the fission fragments (daughter nuclei)

  • of the uranium-235 have mass numbers from 90

  • to 100 and from 135 to 145.

Greatest stability

Binding energy per nucleon (MeV/nucleon)

Mass number A

Binding energy per nucleon as a function of mass number,A

daughter nuclei

parent nuclei


Moving toward more stable nuclei

Figure Y

  • An estimate of the energy released in a fission

  • reaction can be obtained by considering the graph in

  • Figure Y.

  • From the Figure Y, 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

Example 27.5

Calculate the energy released (MeV) in the following fission reaction :

Example 27.6

Calculate the energy released when 10 kg of uranium-235 undergoes fission according to


Solution 27.6

The energy released for one atom.

Solution 27.6

235x10-3 kg of 235U contains 6.02 x 1023 atoms.

10 kg of urainum-235 contains ;

The energy released for 10 kg 235U ,

Chain Reaction in nuclear fission of a nuclear reactor.

  • Chain reaction is a series of nuclear fissions

  • whereby some of the neutrons produced by

  • each fission cause additional fissions.

  • Conditions 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).

  • The critical size/mass is defined as the minimum

  • mass of fissile/fission material required to

  • produce a sustained chain reaction.

  • B






    A : If the amount of uranium is less than critical mass, most neutrons escape before additional fissions occur, and the chain reaction is not sustained.

    B : If the amount of uranium exceeds the critical mass, a sustained chain reaction is possible.

    Chain Reaction in nuclear fission of a nuclear reactor.

    • A nuclear reactor is a device in which energy is

    • generated by a controlled fission chain reaction.

    • 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.




    • 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.

    • 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.

    Nuclear Fusion

    • Nuclear fusion is the process in which nuclei of

    • light elements combine to form nuclei of heavier

    • elements.

    • The energy released in this reaction is called

    • thermonuclear energy.

    • Examples ;

    • The amount of energy released by this process

    • can be estimated by using the binding energy per

    • nucleon curve (Figure Y).

    Greatest stability

    Binding energy per nucleon (MeV/nucleon)

    Mass number A

    Binding energy per nucleon as a function of mass number,A

    Moving toward more stable nuclei


    Figure Y

    • From Figure Y, 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 27.8

    A fusion reaction occur as follows :

    • If 2 kg 2H is used, determine

    • Total mass loss after fusion

    • Energy released per helium nucleus obtained.

    • Total energy produced.

    • Given : mass of 21H = 2.014 u,

    • mass of 42 He = 4.002 u

    Solution 27.8

    Δm = mbefore –mafter

    Δm = 2(2.014)-4.002

    Δm = 0.026 u


    The mass loss after fusion for 2 2H nuclei is 0.026 u.

    Number of nucleus for 2 kg 2H is,

    Total mass loss after fusion

    Solution 27.8


    Energy released per helium nucleus obtained,

    Q = 3.88 x10-12 J


    Total energy produced,

    Q= Δmc2 =(0.013)(3x108)2 =1.17x1015 J

    • To do this, they must overcome the electrical

    • repulsion of their positive charges.

    • For two protons at this distance, the corresponding

    • potential energy is about 1.2 x 10-13 J or 0.7 MeV;

    • this represents the total initial kinetic energy that

    • the fusion nuclei must have, for example, 0.6 x 10-13J

    • each in head-on collision.

    • Atoms have this much energy only at extremely

    • high temperature (108 K).

    • Reactions that required such extremely high

    • temperature are called thermonuclear reactions.

    • The most important thermonuclear reactions

    • occurs in stars, such as our own sun.

    Nuclear Fusion in the Sun

    • Nuclear fusion occurs in the interior of the sun

    • because the temperature of the sun is very high

    • (approximately 1.5 x 107K).

    • The energy radiated by the sun comes from deep

    • within its core, where the temperature is high

    • enough to initiate the fusion process.

    • One group of reactions thought to occur in the sun is

    • the proton-proton cycle, which is a series of

    • reactions whereby 6 protons form one helium

    • nucleus, 2 positrons, 2 gamma-rays, 2 protons

    • and 2 neutrinos.



    Positron (beta plus)




    • The net result is the combination of 4 protons

    • to form a helium nucleus, two positrons and

    • two neutrinos. (consumes 6 protons but gives two

    • back)

    • The energy released by the proton-proton cycle is

    • about 26.7 MeV.


    • new product is produced.

    • energy is released.

    • mass is reduced after reaction.