# a. dokhane, phys487, ksu, 2008 chapter2- nuclear fission 1 lecture 3 nuclear fission

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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 1 Lecture 3 Nuclear Fission
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 2 1.Review 2.Neutron Reactions 3.Nuclear Fission 4.Thermal Neutrons 5.Nuclear Chain Reaction 6.Neutron Diffusion 7.Critical Equation
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 3 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 4 3.1 Introduction Nuclear fissionheavy nuclides Nuclear fission has been observed to occur with many of the heavy nuclides when they are bombarded with neutrons, protons, deuterons, alpha-particles, and even electrons and gamma-rays. U 235 Neutron Fission Neutron fission of uranium and plotonium is the only type that has acquired practical importance.
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 5 3.2 Fissionable Materials Question Question: Why nuclear fission is an outstanding reaction? Answer Answer: production of more than one neutron per fission on the average when a neutron interacts with certain heavy nuclei. Importance ? nuclear chain reaction This net gain in free neutrons makes a nuclear chain reaction possible. U 235 Neutron Fission + 2 to 3 neutrons
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 6 3.2 Fissionable Materials naturally The only naturally occurring nuclide that can be fissioned with thermal neutrons is U 235, which constitutes 0.71% of naturally occurring uranium. artificially The other artificially produced nuclides that can be fissioned by thermal neutron are U 233 and Pu 239 produced from Th 232 and U 238, respectively. Fertile Materials Th 232 and U 238 are called Fertile Materials because they are convertible into nuclear fuels U 233 and Pu 239. Reactions that convert fertile materials into fissionable materials are called Breeding Reactions. They are neutron capture process with subsequent decay.
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 7 3.2 Fissionable Materials most important material that undergo fission by fast neutron only is U 238 of about 1 Mev.
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 8 3.3 Mass distribution of fission products Question : What is the mechanism of fission of U 235 nucleus? Answer : neutron and U 235 combine compound nucleus U 236 break into two nuclei P1 and P2 of intermediate mass numbers with simultaneous emission of one to several neutrons. number of emitted neutronsalways an integral number
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 9 3.3 Mass distribution of fission products See Table 5.1: page111 probability of a particular values of neutrons to be emitted in a thermal fission of U 235 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 10 3.3 Mass distribution of fission products Value of can be obtained from Table 5.1 by averaging: = 2.43 for U 235 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 11 3.3 Mass distribution of fission products 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 fissions b. only 0.01 is for symmetric fission asymmetry of fission is a characteristic of 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 12 3.3 Mass distribution of fission products
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 13 3.3 Mass distribution of fission products unstableexcessive neutron/proton All fission fragments are unstable because of their excessive 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 14 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 equalopposite momenta The two fission fragments P1 and P2 must fly numerically equal but opposite momenta Ratio of their energies must be Important : experimental determination of the fragment energies leads to information about the mass ratio of the fission fragments.
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 15 3.4 Energy Distribution of fission Fragments 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 asymmetry for the asymmetry of the fission process. See Figure 5.3, page 114.
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 16 3.4 Energy Distribution of fission Fragments Peaks are seen to occur for thermal neutron fission of U 235 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 17 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 U 235 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 U 235 of 7.6 Mev B. E. per nucleon differs by 0.9 Mev between U 235 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. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 18 3.5 Energy Release from Fission A similar estimate can be obtained from masses of U 235 and interacting neutron from one side and those of the two fission fragments. Let us assume that the compound nucleus U 236 splits into two neutrons and Mo 98 and Xe 136 as end product of this fission chain. The combined isotopic masses before and after fission are: U 235 =235.124 amu, n 1 = 1.009 amu amu Mo 98 =97.936 amu, Xe 136 = 135.951 amu, 2n 1 =2.018 amu amu
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 19 3.5 Energy Release from Fission By adding the energies of the several beta- emissions then it raises to 215 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 20 3.5 Energy Release from Fission Example 5.1 Calculate the fission rate for U 235 required to produce 1 watt and the amount of energy that is released in the complete fissioning of 1Kg of U 235 ?
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 21 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 22 3.6 Neutron Yield and Neutron Production Ratio See Table 5.2
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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 23 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 U 235, 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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- A. Dokhane, PHYS487, KSU, 2008 Chapter2- Nuclear Fission 24 3.7 Prompt and delayed neutrons When the excitation energy of the daughter nucleus after beta- emission is greater than the neutron separation energy S n, the subsequent de-excitation occurs in the form of a neutron emission with

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