Chapter 16

Nuclear Reaction

Chapter 16

Nuclear Reaction

Chapter Outline :

16.1 Nuclear Reaction16.2 Nuclear Fission16.3 Nuclear Fusion

Conceptual MapConceptual MapConceptual MapConceptual Map

-- the original nuclei are converted into the nuclei of other elements.

Must obey

Nuclear Reaction Nuclear Reaction

The Principle of Conservation of …

Energy

Linear momentum

angular momentum

Total Charge ( Z )

Mass Number ( A )

Equation for Nuclear ReactionEquation for Nuclear Reaction

a + X → Y + b + Qa + X → Y + b + Q@ compact form :

X ( a , b ) YX ( a , b ) Y

Reaction energy , QReaction energy , Q

Q = [ ( Q = [ ( ΣΣm )m )before reactionbefore reaction – ( – ( ΣΣm ) m ) after reactionafter reaction ]c ]c22

Q > 0Q > 0 : exothermic ; exothermic ; Q < 0Q < 0 : endothermicendothermic

Nuclear FissionNuclear Fission Nuclear FusionNuclear Fusion

-- occurs when a heavy nucleus splits into two smaller nuclei

-- 2 light nuclei combinecombine to form a heavier nucleus.

Chain reactionChain reaction Controlled – nuclear reactor

UnUnControlled – atomic bomb

At the end of this topic, student should be able to :At the end of this topic, student should be able to :

1. Understand the conservation of charge ( Z ) and nucleon number ( A ) in a nuclear reaction.

2. Write and complete the equation for nuclear reaction.

3. Understand the principle of conservation of energy and calculate the energy liberated in the process of nuclear reaction.

4. Understand nuclear fission and fusion5. Understand the occurrence of fission and

fusion from the aspect of binding energy per nucleon.

6. State the condition for chain reaction7. Decribe the process of nuclear fusion in the

sun.

16.1 Nuclear Reaction 16.1 Nuclear Reaction

In nuclear reactions, the original nuclei are converted into the nuclei of other elements.

- Approximately 400 stable nuclei- Hundreds of other nuclei have been observed

but they are unstable- Light nuclei are most stable if they contain an

equal number of proton & neutrons ( N = Z )- Heavy nuclei are more stable if the number of

neutrons exceeds the number of protons –

above Z = 20.- Z > 82, do not have stable nuclei – all are

unstable.

2 type of nuclear reaction :2 type of nuclear reaction :

1. Nuclear FissionNuclear Fission-- occurs when a heavy nucleus splits into

two smaller nuclei-- the combined mass of the daughter nuclei is less that the mass of the parent nucleus.-- energy is released

2. Nuclear FusionNuclear Fusion-- 2 light nuclei combinecombine to form a heavier

nucleus.-- the final nuclei is less than the combined

masses of the original nuclei.-- loss of mass accompanied by a release of

energy.

The Principle of conservation for nuclear reaction

1. Conservation of energy -- ∑ relativistic energy before reaction = ∑ relativistic energy after reaction

2. Conservation of Linear Momentum -- ∑ linear momentum before reaction = ∑ linear momentum after reaction

3. Conservation of angular momentum -- ∑ angular momentum before reaction = ∑ angular momentum after reaction

4. Conservation of Total Charge ( Z ) -- ∑ atom number, Z before reaction = ∑ atom number, Z after reaction

5. Conservation of Mass Number, A -- ∑ mass number, A before reaction = ∑ mass

number , A after reaction

Example :Example :Consider the reaction which has a Q value of 8.124 MeV.

OpF16

),(19

HeOFH2

4

8

16

9

19

1

1

The total number of nucleons before the reaction ( 1 + 19 = 20 ) is equal equal to total number after the reaction ( 16 + 4 = 20 ).

Total charge ( Z = 10 ) is same before & after the reaction.

Equation for nuclear reactionEquation for nuclear reaction

A target nucleus X is bombarded by a particle a resulting in a daughter nucleus Y and a particle b :

a + X a + X → Y + b + Q→ Y + b + Q

@ written in the more compact form :X ( a , b ) YX ( a , b ) Y

where X & Y : nucleia & b : particlesQ : reaction energy ( being absorbed

/ released )

Example :Example :An alpha particle colliding with a nitrogen nucleus produces a proton & nucleus is artificially transmuted into an oxygen nucleus

HONHe1

1

8

17

7

14

2

4

@ in a shorthand notation :

OpN17

),(14

Reaction Energy , QReaction Energy , Q

Q Q = [ ( = [ ( ΣΣm )m )before reactionbefore reaction – ( – ( ΣΣm ) m ) after reactionafter reaction ]c ]c22

= [ ( m = [ ( m aa + m + m XX ) – ( m ) – ( m YY + m + m bb ) ] c ) ] c22

= [ m = [ m aa + m + m XX – m – m YY – m – m bb ] c ] c22

Q > 0Q > 0 : reaction is exothermicexothermic ( exoergic ) -- some mass converted into energy (

mass of reactants > mass of products ) -- energy is released

Q < 0Q < 0 : reaction is endothermicendothermic ( endoergic ) -- some kinetic energy converted into

mass )

Example :Example :Calculate the Q value for the following reaction :(i)

(ii)

CpnN6

14),(

7

14

PnAl15

30),(

13

27

Solution :Solution :Nuclear reaction equation :

HONHe1

1

8

17

7

14

2

4

Given :Given :

mass of = 14.11543 u

mass of = 1.00867 u

mass of = 14.11627 u

mass of = 1.007276 u

N7

14

n0

1

C6

14

p1

1

Σ mass before reaction = 14.11543 + 1.00867 = 15.1241 u

Σ mass after reaction = 14.11627 + 1.00728 = 15.12355 u

Reaction energy , Q : Q Q = [ ( = [ ( ΣΣm )m )before reactionbefore reaction – ( – ( ΣΣm ) m ) after reactionafter reaction ]c ]c22

= [15.1241u – 15.12355 u] ( 3x10 = [15.1241u – 15.12355 u] ( 3x10 8 8 ) ) 22

= 0.00055u ( 1.66x10= 0.00055u ( 1.66x10-27-27)(3x10)(3x1088) ) 22

= 8.217x10= 8.217x10-14-14 J / 1.6 x 10 J / 1.6 x 10 -19-19 = + 0.514 M eV= + 0.514 M eV ( > 0 : exothermic )( > 0 : exothermic )

(ii) Nuclear reaction equation :

nPHeAl0

1

15

30

2

4

13

27

Given :Given :

mass of = 27.21645 u

mass of = 4.03298 u

mass of = 30.24735 u

mass of = 1.00867 u

Al13

27

He2

4

P15

30

n0

1

Σ mass before reaction = 27.21645 + 4.03298= 31.24943 u

Σ mass after reaction = 30.24735 + 1.00867 = 31.25602 u

Reaction energy , Q :

Q Q = [ ( = [ ( ΣΣm )m )before reactionbefore reaction – ( – ( ΣΣm ) m ) after reactionafter reaction ]c ]c22

= [31.24943u – 31.25602u] ( 3x10 = [31.24943u – 31.25602u] ( 3x10 8 8 ) ) 22

= -0.00659u ( 1.66x10= -0.00659u ( 1.66x10-27-27)(3x10)(3x1088))22

= - 6.153 M eV = - 6.153 M eV

Q < 0 – endothermic Q < 0 – endothermic

16.2 Nuclear Fission16.2 Nuclear Fission 16.2 Nuclear Fission16.2 Nuclear Fission

-- occurs when a heavy nucleus splits into two smaller nuclei-- the combined mass of the daughter nuclei is less that the mass of the parent nucleus.-- energy is released-- divided into 2 :

(a) spontaneousspontaneous fission – at a very slow rates – take a very long time.(b) induced induced fission – heavy nucleus is bombarded with particles such as proton, alpha particle , thermal neutron

Example of nuclear fission :Example of nuclear fission :

When a nucleus absorbs a neutron, it may

fission into 2 nuclei through the following

nuclear reaction :

U92

235

QnKrBaUnU )0

1(3

36

90

56

143*

92

235

0

1

92

235

QnSrXeUnU )0

1(2

38

94

54

140*

92

235

0

1

92

235

QnMoSnUnU )0

1(3

42

101

92

132*

92

235

0

1

92

235

-- most of the daughter nuclei have mass number ( 90-100 ) & ( 135 – 145 )

-- The energy released is approximately ≈ 234 MeV

Chain Reaction :Chain Reaction :

-- the neutrons that result from 1 fission event can initiate other fission reactions which in turn initiate further fission reactions and so on.

ex : fission of uranium-235 in nuclear reactors.

To achieve chain reaction :To achieve chain reaction :

(1) Slow neutrons are better at causing fission

– so uranium are mixed with a material

that does not absorb neutrons but slows

them down.

(2) the fission material must more than a

critical size.

-- uncontrolled chain reactions are used in nuclear weapons – atomic bomb

-- controlled chain reactions take place in nuclear reactors & release energy at a steady rate.

16.3 Nuclear Fusion16.3 Nuclear Fusion In a nuclear fusion reaction, two or more

small light nuclei come together, or fuse to form a more massive nucleus, releasing energy in the process, Q > 0

Energy, Q was released : Ebounding per nucleon

for the bigger nucleus > E bounding per nucleon for the smaller

nucleus.

To achieve fusion reaction, the two nucleus must hit each other with a high velocity.

It can be achieve by heated the deuterium to around 108 K.

It is also known as a Thermonuclear Reaction.

Example:

21H + 2

1H 32H + 1

0n + Q

product of reaction (mHe + mn) < 2mD,

mc2 was released as a kinetic energy 32He,

10n and Q.

Fusion appears to be an ideal energy Fusion appears to be an ideal energy source for the future.source for the future.

Why?Why?

Enough deuterium exists in the oceans, in the form of heavy water, to supply our needs for centuries.

Fusion does not depend on a chain reaction - less danger of the release of radioactive material.

Fusion products tend to have relatively short half- lives.

-- However there are many unresolved technical problems to be solved before controlled fusion can be commercially to produce electric energy.

-- Primary problem : very high temperature are needed to initiate fusion reactions.

Process of nuclear fusion in the sun & Process of nuclear fusion in the sun & star.star.

The sun surface’s has a lot of hydrogen gases and the temperature are very high - the fusion reaction always happen there.

The reaction can be summarized as:

vHeH 21

02

2

4

1

14

According to the Coulomb energy potentials, 1.1x10-14J of kinetic energy are needed for every deuteron to fusion between one another to become helium.

Average kinetic energy for every proton E = 3/2 kT where k = Boltzman constant, T= temperature in Kelvin.

Temperature for Thermonuclear, T= 2E/3k

= 2(1.1x10-14J)/3(1.38x10-23JK-1) = 5.8x108K

Every 1g of sun mass contented 4.5x1023 proton ; equal to 4.5x1023 x 24.69 MeV = 1.1x1025 MeV = 130 Mwatthour.

If all proton are change to helium, sun will take 5x109 years to finish 1/5 of it proton.

Comparison between fission and fusion Comparison between fission and fusion reaction.reaction.

The differenceThe difference Fission Fission FusionFusion

Heavy to light nucleus Light to heavy nucleus

Target is bombarded by a High temperature

Particles such as neutron

Chain reaction Not a chain reaction

Produce more than 1 nucleus Produce 1 nucleus

Easy to handle & controlled Difficult to handle

The equalization between Fusion & Fission

1. Releasing big energy, Q

2. Deducting mass after reaction

3. Produce new nucleus.

That`s all for chapter 16That`s all for chapter 16