A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 1 Lecture 3 Nuclear Fission

A. Dokhane, PHYS487, KSU, 2008

Chapter2- Nuclear Fission

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Lecture 3

Nuclear Fission



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1. Review

2. Neutron Reactions

3.3. Nuclear FissionNuclear Fission4. Thermal Neutrons

5. Nuclear Chain Reaction

6. Neutron Diffusion

7. Critical Equation



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• Fissionable Materials

• Mass distribution of fission products

• Energy distribution of fission fragments

• Energy release from fission

• Neutron yield and neutron production ratio

• Prompt and delayed neutrons

• Energy distribution (very short)

Lecture content:



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3.1 Introduction

Nuclear fissionNuclear fission has been observed to occur with many of the heavy nuclidesheavy nuclides when they are bombarded with neutrons, protons, deuterons, alpha-particles, and even electrons and gamma-rays.

U235

NeutronFission

Neutron fission of uranium and plotonium is the only type that has acquired practical importance.



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3.2 Fissionable Materials

QuestionQuestion: Why nuclear fission is an outstanding reaction?

AnswerAnswer: production of more than one neutron per fission on the average when a neutron interacts with certain heavy nuclei.

Importance ?

This net gain in free neutrons makes a nuclear chain reactionnuclear chain reaction possible.

U235

NeutronFission + 2 to 3

neutrons



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The only naturallynaturally occurring nuclide that can be fissioned with thermal neutrons is U235, which constitutes 0.71% of naturally occurring uranium.

The other artificiallyartificially produced nuclides that can be fissioned by thermal neutron are U233 and Pu239 produced from Th232 and U238, respectively.

Th232 and U238 are called Fertile MaterialsFertile Materials because they are convertible into nuclear fuels U233 and Pu239.

Reactions that convert fertile materials into fissionable materials are called Breeding Reactions. They are neutron capture process with subsequent

decay.

23992

10

23892 UnU

23993Np

23994 Pu

خصبة

تفاعالت التوالد



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most important material that undergo fission by fast neutron only is U238 of about 1 Mev.

23390

10

23290 ThnTh

23391Pa

23392U



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3.3 Mass distribution of fission products

Question: What is the mechanism of fission of U235 nucleus?

Answer: neutron and U235 combine compound nucleus U236 break into two nuclei P1 and P2 of intermediate mass numbers with simultaneous emission of one to several neutrons.

10021

21 nPP AA *23692

23592

10 UUn

0 number of emitted neutrons always an integral number



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See Table 5.1: page111

probability of a particular values of 0neutrons to be emitted in a thermal fission of U235 nucleus

Important: the average number of neutrons emitted per fission which is universally denoted by is an important quantity in nuclear reactor physics.



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Value of can be obtained from Table 5.1 by averaging:

)()(

0

00

n

n = 2.43 for U235

Question: what are properties of the fission fragments?

Answer: any nuclide with mass number from 70 to 170, See Figure 5.1

300 different nuclides can be produced after uranium fission



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1. Twin peaks in the mass distribution

2. Maximum yield number is 95 and 140

3. Rarity of symmetric fission (P1=P2): a. mass ratio of 3/2 occurs with 6% of all

fissionsb. only 0.01 is for symmetric fission

asymmetry of fission is a asymmetry of fission is a characteristic characteristic of Thermal neutron fissionof Thermal neutron fission..

4. Fast neutron symmetric fission is more probable with increasing neutron energy.

for high-energy neutron only one single peak appears.

symmetric fission is the most likely event for high-energy neutron fission



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All fission fragments are unstableunstable because of their excessive neutron/protonexcessive neutron/proton ratio: according general principles of nuclear stability, they should give rise to short radioactive series with beta and gamma radiations.

On average, 3 beta emissions are required for fragments to reach its stability.



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3.4 Energy Distribution of fission Fragments

Assymptions:

• Initially at rest fissioned nucleus.

• Mass of neutron is negligible as compared to those of the other fission products

The two fission fragments P1 and P2 must fly numerically equalequal but opposite momentaopposite momenta

2211 vmvm Ratio of their energies must be

1

2

2

1

222

211

2

1

2

12

1

m

m

v

v

vm

vm

E

E

Important: experimental determination of the fragment energies leads to information about the mass ratio of the fission fragments.



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Important: experimental determination of the fragment energies leads to information about the mass ratio of the fission fragments.

Such measurements on fission fragment energies give a clear evidence for the asymmetryasymmetry of the fission process. See Figure 5.3, page 114.



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Peaks are seen to occur for thermal neutron fission of U235

at energies of ~60 Mev and ~95 Mev,

This agree closely with the ratio of 3/2 as obtained from Figure 5.1.



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3.5 Energy Release from Fission

Estimate of the average amount of energy release per fission can be evaluated from the Binding Energy curve.

We have seen that the result of U235 fission is most likely two fragments that lie in the neighborhood of A=95 and A=140.

Average value for the B.E per nucleon in the region A=95 and A=140 is seen to be 8.5 Mev

B.E. per nucleon for U235 of 7.6 Mev

B. E. per nucleon differs by 0.9 Mev between U235 and the favored fission fragments.

Total B.E. difference for the 236 nucleons that participate in the fission process amounts to 236 X 0.9 = 210 Mev.



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A similar estimate can be obtained from masses of U235 and interacting neutron from one side and those of the two fission fragments.

Let us assume that the compound nucleus U236 splits into two neutrons and Mo98 and Xe136 as end product of this fission chain.

The combined isotopic masses before and after fission are:

1

01

0136

54136

53136

52

9842

9841

9840*236

92235

921

0nnXeITe

MoCbZrUUn

U235=235.124 amu, n1= 1.009 amu 133.236im amu

Mo98=97.936 amu, Xe136= 135.951 amu, 2n1=2.018 amu 905.235fm amu



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By adding the energies of the several beta- emissions then it raises to 215 Mev.

228.0fi mm amu=210 Mev

A convenient value to use in numerical calculations is 200 Mev per fission which is closer to the experimental value.

Distribution of energy in fission:

1. Kinetic energy of fission fragment: 168 Mev

2. Kinetic energy of Neutrons 5 Mev

3. Energy associated with beta- decays: 16 Mev

4. Energy emitted as gamma rays: 10 Mev

TOTAL: 199 Mev



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Example 5.1

Calculate the fission rate for U235 required to produce 1 watt and the amount of energy that is released in the complete fissioning of 1Kg of U235?



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3.6 Neutron Yield and Neutron Production Ratio

accurate knowledge of the average number of neutrons emitted per fission is of great importance to the nuclear engineer or scientist. SEE TABLE 5.2.

Important: must distinguish between : number of neutrons released per fission

and number of fission neutrons released per absorption



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3.6 Neutron Yield and Neutron Production Ratio

Since not all thermal neutrons that are absorbed cause a fission hence is smaller that

in the same ratio as is fission cross section f to the absorption cross section a

1fc

f

a

f

f

c

See Table 5.2 Values of for thermal neutrons



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3.7 Prompt and delayed neutrons

Except for a very small fraction, all fission neutrons are emitted instantaneously: the time delay is less than 10-12 sec.

In the case of U235, about 0.64% of all fission neutrons are emitted with a time delay of several seconds to more than a minute after fission.

Prompt neutrons

delayed neutrons

Question: where delayed neutrons come from???

Answer: from radioactive decay of fission product nucleus.



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When the excitation energy of the daughter nucleus after beta- emission

is greater than the neutron separation energy Sn, the subsequent de-excitation

occurs in the form of a neutron emission with a half-life practically identical with that of the preceding beta- decay.



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Existence of 6 distinct groups6 distinct groups of delayed neutrons, each group with its own characteristic half-life and decay rate.

Question: importance of delayed neutrons??

Answer: They are very important because of the decisive part they play in the control of nuclear reactors. Although they are only a small fraction of the total neutron yield, yet their influence on the time dependent behavior of the thermal reactors is pronounced so that they furnish a ready means of control. It makes the reactor controllable from 10-12 sec to seconds or even minutes



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3.8 Energy Distribution of Fission Neutrons



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Homework

• Problems: 1, 2, 5, 8 of Chapter 5 in Text Book, Pages 131-132

• To be submitted next week

Documents

A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 1 Lecture 3 Nuclear Fission