Physics
Disintegration Energy
Disintegration energy refers to the energy released when a nucleus undergoes radioactive decay. It is the difference in mass-energy before and after the decay process. This energy is often released in the form of gamma rays, alpha particles, or beta particles, and is a fundamental concept in understanding the behavior of radioactive materials.
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5 Key excerpts on "Disintegration Energy"
- John R. Fanchi, John R. Fanchi, (Authors)
- 2013(Publication Date)
- Academic Press(Publisher)
The amount of energy released in a nuclear decay process is called the Disintegration Energy Q . If Disintegration Energy Q is positive, the decay process releases energy as kinetic energy of the decay products. Unstable nuclei can decay in a variety of ways. The three most common decay processes are α decay, β decay, and γ decay. The α decay process is the emission of an α particle (helium nucleus) in the general process A Z X N → A − 4 Z − 2 Y N − 2 + 4 2 He 2 (11.2.8) The parent nucleus is A Z X N and the daughter nucleus is A − 4 Z − 2 Y N − 2 . The Disintegration Energy for α decay is Q = ( m X − m Y − m α ) c 2 (11.2.9) where m X is the mass of the parent nucleus, m Y is the mass of the daughter nucleus, and m α is the mass of the α particle. The α particle escapes the nucleus by quantum mechanical tunneling. An example of α decay is the decay of uranium-238 to produce thorium-234 and a helium nucleus: 238 92 U 146 → 234 90 Th 144 + 4 2 He 2 (11.2.10) The β decay process is the emission of a β particle (an electron) in the general process A Z X N → A Z + 1 Y N − 1 + e − + ¯ ν (11.2.11) where ¯ ν is an antineutrino that was created as a result of conservation of mass-energy. In the β decay process, a neutron in the nucleus decays to a 328 Energy: Technology and Directions for the Future proton and releases an electron and antineutrino. The Disintegration Energy for β decay is Q = ( m X − m Y − m e − m ¯ ν ) c 2 (11.2.12) where m X is the mass of the parent nucleus, m Y is the mass of the daughter nucleus, and m e is the mass of the β particle (an electron). The mass of the antineutrino m ¯ ν has traditionally been ignored because people believed neutrinos and antineutrinos were massless. Equation (11.2.12) allows for the possibility that neutrinos and antineutrinos have mass.
eBook - PDF- Richard Dunlap(Author)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 174 CHAPTER 6: Energy from Nuclear Fission nuclear fission reactors and provides some insight into the reasons for the history of the nuclear power industry, as well as its future. 6.2 The Fission of Uranium When a decay or an exothermic nuclear reaction occurs, the decrease in the total mass of the constituents involved is converted into energy. This energy is manifested as kinetic energy of the progeny nucleus and emitted particles, and it can, in principle, be converted into useful energy. This decrease in mass is associated with an increase in binding energy [equation (5.3)]. Because these processes conserve the total number of nucleons (i.e., number of neutrons plus number of protons), the average binding energy per nucleon is a good measure of the kinetic energy that can be liberated. In Figure 6.1, the average binding energy per nucleon is plotted as a function of the number of nucleons in the nucleus. Except for a few anomalous peaks, the figure shows that, as the number of nucleons increases, the average binding energy per nucleon increases sharply for light nuclei, followed by a broad maximum and then a slow decrease for heavy nuclei. This behavior allows substantial amounts of energy to be obtained from certain types of nuclear reactions. Consider, for example, a 238 U nucleus. This nucleus has a binding energy of 7.57 MeV per nucleon or a total binding energy for the 238 nucleons of about 1800 MeV. If, for some reason, this nucleus were to split in half, forming two nuclei containing 119 nucleons each, then, according to the figure, each of those nuclei would have an average binding energy per nucleon of 8.50 MeV for a total binding energy of the two smaller nuclei of about 2020 MeV. This difference in binding ener-gies, about 220 MeV, would be given up to the smaller nuclei as kinetic energy.
eBook - PDF- R. Peierls(Author)
- 2013(Publication Date)
- North Holland(Publisher)
comparable to the division of such a drop into two droplets, it is evidently necessary, however, that, the quasi-thermal distribution of energy be largely converted into some special mode of vibration of the compound nucleus involving a considerable deformation of the nuclear surface. In both cases, the course of the disintegration may thus be said to result from a fluctuation in the statistical distribution of the energy between the various degrees of freedom of the system, the prob- ability of occurrence of which is essentially deter- mined by the amount of energy to be concentrated on the particular type of motion considered and by the ‘temperature’ corresponding to the nuclear excitation. Since the effective cross-sections for the fission phenomcno, for neutrons of different velocities seem to be of about the same order of magnitude as the cross-sections for ordinary nuclear reactions, we may therefore conclude that, for the heaviest nuclei the deformation energy sufficient for the fission is of [342] the same order of magnitude as the energy necessary for the escape of a single nuclear particle. For some- what lighter nuclei, however, where only evaporation- like disintegrations have so far been observed, the former energy should be considerably larger than the binding energy of a particle. These circumstances find their straightforward explanation in the fact, stressed by Meitner and Frisch, that the mutual repulsion between the electric charges in a nucleus will for highly charged nuclei counteract to a large extent the effect of the short-range forces between the nuclear particles in opposing a deformation of the nucleus. The nuclear problem concerned reminds us indeed in several ways of the’ question of the stability of a charged liquid drop, and in particular, any deformation of a nucleus, sufficiently large for its fission, may be treated approximately as
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Consider a reaction in which a target nucleus X is bombarded by a particle a, resulting in a daughter nucleus Y and an outgoing particle b: a 1 X S Y 1 b (43.29) Nuclear reaction Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 43.7 Nuclear Reactions 1201 Sometimes this reaction is written in the more compact form X(a, b)Y In Section 43.5, the Q value, or Disintegration Energy, of a radioactive decay was defined as the rest energy transformed to kinetic energy as a result of the decay process. Likewise, we define the reaction energy Q associated with a nuclear reac- tion as the difference between the initial and final rest energies resulting from the reaction: Q 5 ( M a 1 M X 2 M Y 2 M b ) c 2 (43.30) As with nuclear decay, the appropriate reduction of Equation 8.2 for nuclear reac- tions is Equation 43.13. As an example, consider the reaction 7 Li(p, a) 4 He. The notation p indicates a proton, which is a hydrogen nucleus. Therefore, we can write this reaction in the expanded form 1 1 H 1 7 3 Li S 4 2 He 1 4 2 He The Q value for this reaction is Q 5 2DE R 5 17.3 MeV. A reaction such as this one, for which Q is positive, is called exothermic. A reaction for which Q is negative is called endothermic. To satisfy conservation of momentum for the isolated sys- tem, an endothermic reaction does not occur unless the bombarding particle has a kinetic energy greater than Q. (See Problem 54.) The minimum energy necessary for such a reaction to occur is called the threshold energy.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
43.1.1 cancels one of the two neutrons on the right of that equation. The mass difference for the reaction of Eq. 43.1.7 is Δm = (139.9054 u + 93.9063 u + 1.008 66 u) − (235.0439 u) = −0.223 54 u, and the corresponding Disintegration Energy is Q = −Δm c 2 = −(−0.223 54 u)(931.494 013 MeV/u) = 208 MeV, (Answer) which is in good agreement with our estimate of Eq. 43.1.6. If the fission event takes place in a bulk solid, most of this Disintegration Energy, which first goes into kinetic energy of the decay products, appears eventually as an increase in the internal energy of that body, revealing itself as a rise in temperature. Five or six percent or so of the disin- tegration energy, however, is associated with neutrinos that are emitted during the beta decay of the primary fission frag- ments. This energy is carried out of the system and is lost. Instructional video is available at the website www.wiley.com 1322 CHAPTER 43 Energy from the Nucleus After reading this module, you should be able to . . . 43.2.1 Define chain reaction. 43.2.2 Explain the neutron leakage problem, the neutron energy problem, and the neutron capture problem. 43.2.3 Identify the multiplication factor and apply it to relate the number of neutrons and power output after a given number of cycles to the initial number of neutrons and power output. 43.2.4 Distinguish subcritical, critical, and supercritical. 43.2.5 Describe the control over the response time. 43.2.6 Give a general description of a complete generation. 43.2 THE NUCLEAR REACTOR KEY IDEA 1. A nuclear reactor uses a controlled chain reaction of fission events to generate electrical power. LEARNING OBJECTIVES The Nuclear Reactor For large-scale energy release due to fission, one fission event must trigger others, so that the process spreads throughout the nuclear fuel like flame through a log.
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