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CHAPTER 27: Nuclear reaction (3 Hours)

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NUCLEAR REACTION

CHAPTER 27: Nuclear reaction(3 Hours)

27.1 Nuclear reaction

27.2 Nuclear fission and fusion

27.1Nuclear 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

Examples:

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 ,

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)

Example 27.1

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

Natural/decaying

Fusion

Fission

Example 27.2

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

Given

c2

or

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

a)

b)

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.

emitted

particle

new nucleus

(daughter

nucleus)

Target nucleus

(parent nucleus)

bombarding

particle

Learning Outcome:

27.2Nuclear 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.

(unstable)

(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.

Figure X

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

fission

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

Given:

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

Chain Reaction

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).

B

A

n

n

n

n

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.

A nuclear reactor

movable

Moderator

(water)

- 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.

- 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

fusion

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 27.7

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

a)

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

b)

Energy released per helium nucleus obtained,

Q = 3.88 x10-12 J

c)

Total energy produced,

Q= Δmc2 =(0.013)(3x108)2 =1.17x1015 J

- For two nuclei to undergo fusion, they must come
- together to within the range of the nuclear force,
- typically of the order of 2 x 10-15 m.

- 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).

- The lower border of the fusion temperature is 107 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.

- The sequence of fusion reactions are shown below ;

neutrino

i)

Positron (beta plus)

ii)

Gamma-ray

iii)

- 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.

Comparison between nuclear Fission and nuclear Fusion

Differences

Similarities

- new product is produced.
- energy is released.
- mass is reduced after reaction.