DOCSLIB.ORG

CHAPTER 3 Radioactive Decay Equations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
CHAPTER 3 Radioactive Decay Equations 1 CHEMISTRY OF THE EARTH CHAPTER 3 Radioactive decay equations 3.1 The radioactive decay law As discussed in Chapter 2, the decay rate of a radioactive substance was found to decrease exponentially with time. Radioactive decay was found to follow a statistical law, that is, it is impossible to predict when any given atom will disintegrate. The rate at which a radioactive substance N1 decays is given by dN 1 = −λ N (3.1) dt 1 1 where N is the number of radioactive atoms and λ1 is called the decay constant , which represents the probability per unit time for one atom to decay. The fundamental assumption in the statistical law for radioactive decay is that this probability for decay is constant, that is, it does not depend on time or on the number of radioactive atoms present. Eq. 3.1 can be integrated with the boundary condition that the initial number of o radioactive atoms is N1 = N1 )0( . This leads to the exponential law of radioactive decay : o −λ1t N1 = N1 e (3.2) Denoting the daughter product of N1 as N2, and for the case in which N2 is a stable daughter product, the accumulation of N2 is simply given by N = N o + N o 1( − e−λ1t ) 2 2 1 (3.3) o λ1t N 2 = N 2 + N1 (e − )1 o where N 2 is the initial amount of N2 prior to the accumulation of radioactive decay products of N1. For measurement purposes, it is often convenient to express Eq. 3.2 in terms of the activity A of a radioactive substance, which is defined to be the number of decays per unit time or simply A= λ1N1. If we multiply both sides of Eq. 3.2 by λ1 , we find that dN − 1 = λ N = λ N oe−λ1t (3.4) dt 1 1 1 1 It follows that o −λt A1 = A1 e (3.5) o where A1 is the initial activity of the radioactive substance. The unit most commonly used in activity measurements is the curie (Ci), which is defined as 3.7×10 10 decays/s. The half-life of a radioactive substance is defined as the elapsed time over which the radioactive substance has decreased to half its original abundance. Thus, by letting o N1 = N1 2/ in Eq. 3.2, the half-life is given by ln 2 .0 69315 t = = (3.6) 5.0 λ λ The mean life, t , or the average amount of time a radioactive element lives, is given by Cin-Ty Lee 2 CHEMISTRY OF THE EARTH ∞ ∞ ∞ 1 1 −λ1t 1 t = − tdN = tλ1 N1dt =λ1 te dt = (3.7) ∫0 ∫0 ∫0 N o N o λ1 Thus, the mean life is simply the inverse of the decay constant. During the mean life, the abundance of a radioactive substance decreases by a factor of 1/e. 3.2 Branched decay 3.2.1 Basic equations In some cases, the parent N1 decays to two different products, a process termed branched decay . Calling these two decay modes a and b, we define the probability of each decay mode as (dN / dt ) λ = − 1 a a N 1 (3.8) (dN 1 / dt )b λb = − N1 The total decay rate of N1 is dN 1 dN 1 dN 1 − = − − = N1 ()λ ,1 a + λ ,1 b = N1λ ,1 total (3.9) dt total dt a dt b where (λ ,1 a + λ ,1 b )= λ ,1 total is the total decay constant. It follows that N1 decays according to the following law o −λ1total t N1 = N1 e (3.10) Thus, if we were to measure only the abundance or activity of the radioactive nuclide, N1, we would have no way of distinguishing between the two decay modes because we can only measure the total decay constant. However, if we were to monitor the evolution of the abundance or activity of the two daughter products of N1 as a function of time, we would be able to distinguish between the two decay modes. For example, we know that a fraction λ ,1 a / λ ,1 total of N1 decays by mode a and a fraction λ ,1 b / λ ,1 total decays by mode b. Denoting the two types of daughter products as N2,a and N2,b , the formulas describing the accumulation of each of the daughter products are N = N o + (λ / λ )N o 1( − e−λ ,1 total t ) ,2 a ,2 a ,1 a total 1 (3.11) o o −λ1total t N ,2 b = N ,2 b + ()λ ,1 b / λtotal N1 1( − e ) o o where N ,2 a and N ,2 b are the initial amounts of daughter product N2,a and N2,b present before the decay of N1. 3.2.2 Example: decay of 40 K to 40 Ar and 40 Ca An example of a branched decay is the decay of naturally occurring 40 K to stable 40 Ar and 40 Ca, the former by electron capture and the latter by β- emission (negatron emission). Electron capture decay to 40 Ar is favored by 11.2 % of 40 K atoms and beta decay to 40 Ca is favored by 88.8 %. Accordingly, the decay constants for each branching decay, λK,Ar and λK,Ca , are Cin-Ty Lee 3 CHEMISTRY OF THE EARTH λ = .0 581 ×10 −10 yr −1 K ,Ar (3.12) −10 −1 λK ,Ca = .4 962 ×10 yr -10 -1 and the total decay constant, λK,total = λK,Ar + λ K,Ca , is 5.543×10 y , corresponding to a half-life of 1.250 Gy. Referring back to Eq. 3.11, we find that the total number of 40 Ar atoms in a system with 40 K is given by 40 40 o 40 λK ,total t Ar = Ar +(λK,Ar / λK,total ) K(e −1) (3.13) where 40 Ar o is the initial number of 40 Ar atoms present prior to the decay of 40 K. Both the 40 K-40 Ar and 40 K-40 Ca isotopic systems have geologic applications. The K-Ar system, in particular, has been used extensively as a geochronometer. 3.3 Decay series 3.3.1 N1 → N 2 → N 3 In Section 3.1, we discussed the decay of a nuclide N1 to a stable daughter product N2. We now discuss the case in which N2 decays to N3. The decay rates of N1 and N2 are given by dN 1 = −λ N (3.14) dt 1 1 dN 2 = λ N − λ N (3.15) dt 1 1 2 2 where λ1 and λ2 are the decay constants of N1 and N2, respectively. Substituting Eq. 3.2 into 3.15 and rearranging yields dN 2 + λ N − λ N oe−λ1t = 0 (3.16) dt 2 2 1 1 The solution to Eq. 3.16 is λ1 o −λ1t −λ2t o −λ2t N 2 = N1 (e − e )+ N 2 e (3.17) λ2 − λ1 and can be verified by substitution into Eq. 3.16. In Eq. 3.17, the first term on the right reflects the production of N2 by decay of N1 and the loss of N2 by decay. The second term on the right represents the contribution from any initial N2 in the system. Note that if λ2 is zero, that is, N2 is a stable nuclide, then Eq. 3.17 is equivalent to Eq. 3.3. Cin-Ty Lee 4 CHEMISTRY OF THE EARTH A N1 N2 λ1N1 A N1 N2 λ2N2 N N 1 2 t B N1 N2 N3 N4 Secular equilibrium in a decay chain Figure 1. Secular Equilibrium. A better understanding of Eq. 3.17 can be had if we look at some examples. For example, let us assume that λ1 << λ2 , that is, N1 decays much slower than N2. It follows that for long times the quantity e −λ1t is much larger than e−λ2t , and therefore Eq. 3.17 simplifies approximately to λ1 o −λ1t N 2 ~ N1 e = λ1 N1 (3.18) λ2 or in other words λ1 N1 = λ2 N 2 (3.19) which essentially means that the activities (or decay rate) of N1 and N2 are equal. This asymptotic state is called secular equilibrium and is illustrated schematically in Figure X. Secular equilibrium is another way of saying a system has reached steady-state, that is, there is no longer a change in the decay rates of each nuclide. For example, let N2 represent the number of people in a restaurant. At 5 PM, the restaurant doors open. Initially, there are no people in the restaurant, but immediately after 5 PM, there is a steady stream of people entering the restaurant. Assuming each person finishes eating and leaves the restaurant in about 45 minutes, we would see that initially the number of people in the restaurant would increase, but after a while, a maximum number will be reached as people start to exit. At this point, the amount of people leaving the restaurant equals the amount entering. This situation is called steady state and is a form of secular equilibrium. At secular equilibrium , it can be shown that the stable daughter nuclide (in this case, N3) increases as o −λ1t N3 = N1 (1− e ) (3.20) Cin-Ty Lee 5 CHEMISTRY OF THE EARTH from which it can be seen that the growth of N3 depends only on the decay constant of N1. We leave the proof of Eq. 3.20 as an exercise for the student.
Load more

Recommended publications
  • Hetc-3Step Calculations of Proton Induced Nuclide Production Cross Sections at Incident Energies Between 20 Mev and 5 Gev
    JAERI-Research 96-040 JAERI-Research—96-040 JP9609132 JP9609132 HETC-3STEP CALCULATIONS OF PROTON INDUCED NUCLIDE PRODUCTION CROSS SECTIONS AT INCIDENT ENERGIES BETWEEN 20 MEV AND 5 GEV August 1996 Hiroshi TAKADA, Nobuaki YOSHIZAWA* and Kenji ISHIBASHI* Japan Atomic Energy Research Institute 2 G 1 0 1 (T319-11 l This report is issued irregularly. Inquiries about availability of the reports should be addressed to Research Information Division, Department of Intellectual Resources, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken, 319-11, Japan. © Japan Atomic Energy Research Institute, 1996 JAERI-Research 96-040 HETC-3STEP Calculations of Proton Induced Nuclide Production Cross Sections at Incident Energies between 20 MeV and 5 GeV Hiroshi TAKADA, Nobuaki YOSHIZAWA* and Kenji ISHIBASHP* Department of Reactor Engineering Tokai Research Establishment Japan Atomic Energy Research Institute Tokai-mura, Naka-gun, Ibaraki-ken (Received July 1, 1996) For the OECD/NEA code intercomparison, nuclide production cross sections of l60, 27A1, nalFe, 59Co, natZr and 197Au for the proton incidence with energies of 20 MeV to 5 GeV are calculated with the HETC-3STEP code based on the intranuclear cascade evaporation model including the preequilibrium and high energy fission processes. In the code, the level density parameter derived by Ignatyuk, the atomic mass table of Audi and Wapstra and the mass formula derived by Tachibana et al. are newly employed in the evaporation calculation part. The calculated results are compared with the experimental ones. It is confirmed that HETC-3STEP reproduces the production of the nuclides having the mass number close to that of the target nucleus with an accuracy of a factor of two to three at incident proton energies above 100 MeV for natZr and 197Au.
    [Show full text]
  • 1 11. Nuclear Chemistry 11.1 Stable and Unstable Nuclides Very Large
    11. Nuclear Chemistry Chemical reactions occur as a result of loosing/gaining and sharing electrons in the valance shell which is far away from the atomic nucleus as we described in previous chapters in chemical bonding. In chemical reactions identity of the elements (atomic) and the makeup of the nuclei (mass due to protons and neutrons) is preserved which is reflected in the Law of Conservation of mass. This idea of atomic nucleus is always stable was shattered as Henri Becquerel discovered radioactivity in uranium compound where uranium nuclei changes or undergo nuclear reactions where nuclei of an element is transformed into nuclei of different element(s) while emitting ionization radiation. Marie Curie also began a study of radioactivity in a different form of uranium ore called pitchblende and she discovered the existence of two more highly radioactive new elements radium and polonium formed as the products during the decay of unstable nuclide of uranium-235. Curie measure that the radiation emanated was proportional to the amount (moles or number of nuclides) of radioactive element present, and she proposed that radiation was a property nucleus of an unstable atom. The area of chemistry that focuses on the nuclear changes is called nuclear chemistry. What changes in a nuclide result from the loss of each of the following? a) An alpha particle. b) A gamma ray. c) An electron. d) A neutron. e) A proton. Answer: a), c), d), e) 11.1 Stable and Unstable Nuclides There are stable and unstable radioactive nuclides. Unstable nuclides emit subatomic particles, with alpha −α, beta −β, gamma −γ, proton-p, neutrons-n being the most common.
    [Show full text]
  • An Octad for Darmstadtium and Excitement for Copernicium
    SYNOPSIS An Octad for Darmstadtium and Excitement for Copernicium The discovery that copernicium can decay into a new isotope of darmstadtium and the observation of a previously unseen excited state of copernicium provide clues to the location of the “island of stability.” By Katherine Wright holy grail of nuclear physics is to understand the stability uncover its position. of the periodic table’s heaviest elements. The problem Ais, these elements only exist in the lab and are hard to The team made their discoveries while studying the decay of make. In an experiment at the GSI Helmholtz Center for Heavy isotopes of flerovium, which they created by hitting a plutonium Ion Research in Germany, researchers have now observed a target with calcium ions. In their experiments, flerovium-288 previously unseen isotope of the heavy element darmstadtium (Z = 114, N = 174) decayed first into copernicium-284 and measured the decay of an excited state of an isotope of (Z = 112, N = 172) and then into darmstadtium-280 (Z = 110, another heavy element, copernicium [1]. The results could N = 170), a previously unseen isotope. They also measured an provide “anchor points” for theories that predict the stability of excited state of copernicium-282, another isotope of these heavy elements, says Anton Såmark-Roth, of Lund copernicium. Copernicium-282 is interesting because it University in Sweden, who helped conduct the experiments. contains an even number of protons and neutrons, and researchers had not previously measured an excited state of a A nuclide’s stability depends on how many protons (Z) and superheavy even-even nucleus, Såmark-Roth says.
    [Show full text]
  • Compilation and Evaluation of Fission Yield Nuclear Data Iaea, Vienna, 2000 Iaea-Tecdoc-1168 Issn 1011–4289
    IAEA-TECDOC-1168 Compilation and evaluation of fission yield nuclear data Final report of a co-ordinated research project 1991–1996 December 2000 The originating Section of this publication in the IAEA was: Nuclear Data Section International Atomic Energy Agency Wagramer Strasse 5 P.O. Box 100 A-1400 Vienna, Austria COMPILATION AND EVALUATION OF FISSION YIELD NUCLEAR DATA IAEA, VIENNA, 2000 IAEA-TECDOC-1168 ISSN 1011–4289 © IAEA, 2000 Printed by the IAEA in Austria December 2000 FOREWORD Fission product yields are required at several stages of the nuclear fuel cycle and are therefore included in all large international data files for reactor calculations and related applications. Such files are maintained and disseminated by the Nuclear Data Section of the IAEA as a member of an international data centres network. Users of these data are from the fields of reactor design and operation, waste management and nuclear materials safeguards, all of which are essential parts of the IAEA programme. In the 1980s, the number of measured fission yields increased so drastically that the manpower available for evaluating them to meet specific user needs was insufficient. To cope with this task, it was concluded in several meetings on fission product nuclear data, some of them convened by the IAEA, that international co-operation was required, and an IAEA co-ordinated research project (CRP) was recommended. This recommendation was endorsed by the International Nuclear Data Committee, an advisory body for the nuclear data programme of the IAEA. As a consequence, the CRP on the Compilation and Evaluation of Fission Yield Nuclear Data was initiated in 1991, after its scope, objectives and tasks had been defined by a preparatory meeting.
    [Show full text]
  • Radioactive Decay
    North Berwick High School Department of Physics Higher Physics Unit 2 Particles and Waves Section 3 Fission and Fusion Section 3 Fission and Fusion Note Making Make a dictionary with the meanings of any new words. Einstein and nuclear energy 1. Write down Einstein’s famous equation along with units. 2. Explain the importance of this equation and its relevance to nuclear power. A basic model of the atom 1. Copy the components of the atom diagram and state the meanings of A and Z. 2. Copy the table on page 5 and state the difference between elements and isotopes. Radioactive decay 1. Explain what is meant by radioactive decay and copy the summary table for the three types of nuclear radiation. 2. Describe an alpha particle, including the reason for its short range and copy the panel showing Plutonium decay. 3. Describe a beta particle, including its range and copy the panel showing Tritium decay. 4. Describe a gamma ray, including its range. Fission: spontaneous decay and nuclear bombardment 1. Describe the differences between the two methods of decay and copy the equation on page 10. Nuclear fission and E = mc2 1. Explain what is meant by the terms ‘mass difference’ and ‘chain reaction’. 2. Copy the example showing the energy released during a fission reaction. 3. Briefly describe controlled fission in a nuclear reactor. Nuclear fusion: energy of the future? 1. Explain why nuclear fusion might be a preferred source of energy in the future. 2. Describe some of the difficulties associated with maintaining a controlled fusion reaction.
    [Show full text]
  • Arxiv:1901.01410V3 [Astro-Ph.HE] 1 Feb 2021 Mental Information Is Available, and One Has to Rely Strongly on Theoretical Predictions for Nuclear Properties
    Origin of the heaviest elements: The rapid neutron-capture process John J. Cowan∗ HLD Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK 73019, USA Christopher Snedeny Department of Astronomy, University of Texas, 2515 Speedway, Austin, TX 78712-1205, USA James E. Lawlerz Physics Department, University of Wisconsin-Madison, 1150 University Avenue, Madison, WI 53706-1390, USA Ani Aprahamianx and Michael Wiescher{ Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA Karlheinz Langanke∗∗ GSI Helmholtzzentrum f¨urSchwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany and Institut f¨urKernphysik (Theoriezentrum), Fachbereich Physik, Technische Universit¨atDarmstadt, Schlossgartenstraße 2, 64298 Darmstadt, Germany Gabriel Mart´ınez-Pinedoyy GSI Helmholtzzentrum f¨urSchwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany; Institut f¨urKernphysik (Theoriezentrum), Fachbereich Physik, Technische Universit¨atDarmstadt, Schlossgartenstraße 2, 64298 Darmstadt, Germany; and Helmholtz Forschungsakademie Hessen f¨urFAIR, GSI Helmholtzzentrum f¨urSchwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany Friedrich-Karl Thielemannzz Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland and GSI Helmholtzzentrum f¨urSchwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany (Dated: February 2, 2021) The production of about half of the heavy elements found in nature is assigned to a spe- cific astrophysical nucleosynthesis process: the rapid neutron capture process (r-process). Although this idea has been postulated more than six decades ago, the full understand- ing faces two types of uncertainties/open questions: (a) The nucleosynthesis path in the nuclear chart runs close to the neutron-drip line, where presently only limited experi- arXiv:1901.01410v3 [astro-ph.HE] 1 Feb 2021 mental information is available, and one has to rely strongly on theoretical predictions for nuclear properties.
    [Show full text]
  • Heavy Element Nucleosynthesis
    Heavy Element Nucleosynthesis A summary of the nucleosynthesis of light elements is as follows 4He Hydrogen burning 3He Incomplete PP chain (H burning) 2H, Li, Be, B Non-thermal processes (spallation) 14N, 13C, 15N, 17O CNO processing 12C, 16O Helium burning 18O, 22Ne α captures on 14N (He burning) 20Ne, Na, Mg, Al, 28Si Partly from carbon burning Mg, Al, Si, P, S Partly from oxygen burning Ar, Ca, Ti, Cr, Fe, Ni Partly from silicon burning Isotopes heavier than iron (as well as some intermediate weight iso- topes) are made through neutron captures. Recall that the prob- ability for a non-resonant reaction contained two components: an exponential reflective of the quantum tunneling needed to overcome electrostatic repulsion, and an inverse energy dependence arising from the de Broglie wavelength of the particles. For neutron cap- tures, there is no electrostatic repulsion, and, in complex nuclei, virtually all particle encounters involve resonances. As a result, neutron capture cross-sections are large, and are very nearly inde- pendent of energy. To appreciate how heavy elements can be built up, we must first consider the lifetime of an isotope against neutron capture. If the cross-section for neutron capture is independent of energy, then the lifetime of the species will be ( )1=2 1 1 1 µn τn = ≈ = Nnhσvi NnhσivT Nnhσi 2kT For a typical neutron cross-section of hσi ∼ 10−25 cm2 and a tem- 8 9 perature of 5 × 10 K, τn ∼ 10 =Nn years. Next consider the stability of a neutron rich isotope. If the ratio of of neutrons to protons in an atomic nucleus becomes too large, the nucleus becomes unstable to beta-decay, and a neutron is changed into a proton via − (Z; A+1) −! (Z+1;A+1) + e +ν ¯e (27:1) The timescale for this decay is typically on the order of hours, or ∼ 10−3 years (with a factor of ∼ 103 scatter).
    [Show full text]
  • A Guide to Naturally Occurring Radioactive Materials (NORM)
    ABOUT NORM SOME NORM NUCLIDES OF SPECIAL INTEREST A Guide to Naturally There are three types of NORM: Occurring Radioactive • Cosmogenic – NORM produced by cosmic rays interacting with the Earth’s Materials (NORM) Beryllium 7 atmosphere; the most important Developed by the 3 7 14 examples are H (tritium), Be, and C. 7Be is being continuously formed in the DHS Secondary Reachback Program • Primordial – Sufficiently long-lived atmosphere by cosmic rays. Jet engines can March 2010 NORM for some to have survived from accumulate enough 7Be to set off before the formation of the Earth; there radiological alarms when being cleaned. are 20 primordial NORM nuclides with As defined by the International Atomic the most important being 40K, 232Th, Energy Agency (IAEA), Naturally 235U, and 238U. Polonium 210 Occurring Radioactive Materials • Daughters – When 232Th, 235U and 238U In the 238U decay chain 210Po is a distant (NORM) include all natural radioactive decay 42 different radioactive nuclides daughter of 226Ra. 210Po gained notoriety in materials where human activities have are formed (see below) with the most the 1960s as a radioactive trace component increased the potential for exposure in important being 222Rn, 226Ra, 228Ra and in cigarette smoke. Heavy use of phosphate comparison with the unaltered natural 228 Ac. fertilizers (which have trace amounts of out here. fold Next situation. If processing has increased 226Ra) can triple the amount of 210Po found the concentrations of radionuclides in a When 232Th, 235U and 238U decay a in tobacco. material then it is Technologically radioactive “daughter” nuclide is formed, Enhanced NORM (TE-NORM).
    [Show full text]
  • Alpha-Decay Chains of Z=122 Superheavy Nuclei Using Cubic Plus Proximity Potential with Improved Transfer Matrix Method
    Indian Journal of Pure & Applied Physics Vol. 58, May 2020, pp. 397-403 Alpha-decay chains of Z=122 superheavy nuclei using cubic plus proximity potential with improved transfer matrix method G Naveyaa, S Santhosh Kumarb, S I A Philominrajc & A Stephena* aDepartment of Nuclear Physics, University of Madras, Guindy Campus, Chennai 600 025, India bDepartment of Physics, Kanchi Mamunivar Centre for Post Graduate Studies, Lawspet, Puducherry 605 008, India cDepartment of Physics, Madras Christian College, Chennai 600 059, India Received 4 May 2020 The alpha decay chain properties of Z = 122 isotope in the mass range 298 A 350, even-even nuclei, are studied using a fission-like model with an effective combination of the cubic plus proximity potential in the pre and post-scission regions, wherein the decay rates are calculated using improved transfer matrix method, and the results are in good agreement with other phenomenological formulae such as Universal decay law, Viola-Seaborg, Royer, etc. The nuclear ground-state masses are taken from WS4 mass model. The next minimum in the half-life curves of the decay chain obtained at N=186,178 & 164 suggest the shell closure at N=184, 176 & 162 which coincides well with the predictions of two-centre shell model approach. This study also unveils that the isotopes 298-300, 302, 304-306, 308-310, 312,314122 show 7, 5, 4, 3, 2 and 1 decay chain, respectively. All the other isotopes from A = 316 to 350 may undergo spontaneous fission since the obtained SF half -lives are comparatively less. The predictions in the present study may have an impact in the experimental synthesis and detection of the new isotopes in near future.
    [Show full text]
  • Isotopic Composition of Fission Gases in Lwr Fuel
    XA0056233 ISOTOPIC COMPOSITION OF FISSION GASES IN LWR FUEL T. JONSSON Studsvik Nuclear AB, Hot Cell Laboratory, Nykoping, Sweden Abstract Many fuel rods from power reactors and test reactors have been punctured during past years for determination of fission gas release. In many cases the released gas was also analysed by mass spectrometry. The isotopic composition shows systematic variations between different rods, which are much larger than the uncertainties in the analysis. This paper discusses some possibilities and problems with use of the isotopic composition to decide from which part of the fuel the gas was released. In high burnup fuel from thermal reactors loaded with uranium fuel a significant part of the fissions occur in plutonium isotopes. The ratio Xe/Kr generated in the fuel is strongly dependent on the fissioning species. In addition, the isotopic composition of Kr and Xe shows a well detectable difference between fissions in different fissile nuclides. 1. INTRODUCTION Most LWRs use low enriched uranium oxide as fuel. Thermal fissions in U-235 dominate during the earlier part of the irradiation. Due to the build-up of heavier actinides during the irradiation fissions in Pu-239 and Pu-241 increase in importance as the burnup of the fuel increases. The composition of the fission products varies with the composition of the fuel and the irradiation conditions. The isotopic composition of fission gases is often determined in connection with measurement of gases in the plenum of punctured fuel rods. It can be of interest to discuss how more information on the fuel behaviour can be obtained by use of information available from already performed determinations of gas compositions.
    [Show full text]
  • Production and Properties Towards the Island of Stability
    This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Leino, Matti Title: Production and properties towards the island of stability Year: 2016 Version: Please cite the original version: Leino, M. (2016). Production and properties towards the island of stability. In D. Rudolph (Ed.), Nobel Symposium NS 160 - Chemistry and Physics of Heavy and Superheavy Elements (Article 01002). EDP Sciences. EPJ Web of Conferences, 131. https://doi.org/10.1051/epjconf/201613101002 All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. EPJ Web of Conferences 131, 01002 (2016) DOI: 10.1051/epjconf/201613101002 Nobel Symposium NS160 – Chemistry and Physics of Heavy and Superheavy Elements Production and properties towards the island of stability Matti Leino Department of Physics, University of Jyväskylä, PO Box 35, 40014 University of Jyväskylä, Finland Abstract. The structure of the nuclei of the heaviest elements is discussed with emphasis on single-particle properties as determined by decay and in- beam spectroscopy. The basic features of production of these nuclei using fusion evaporation reactions will also be discussed. 1. Introduction In this short review, some examples of nuclear structure physics and experimental methods relevant for the study of the heaviest elements will be presented.
    [Show full text]
  • 1 Chapter 16 Stable and Radioactive Isotopes Jim Murray 5/7/01 Univ
    Chapter 16 Stable and Radioactive Isotopes Jim Murray 5/7/01 Univ. Washington Each atomic element (defined by its number of protons) comes in different flavors, depending on the number of neutrons. Most elements in the periodic table exist in more than one isotope. Some are stable and some are radioactive. Scientists have tallied more than 3600 isotopes, the majority are radioactive. The Isotopes Project at Lawrence Berkeley National Lab in California has a web site (http://ie.lbl.gov/toi.htm) that gives detailed information about all the isotopes. Stable and radioactive isotopes are the most useful class of tracers available to geochemists. In almost all cases the distributions of these isotopes have been used to study oceanographic processes controlling the distributions of the elements. Radioactive isotopes are especially useful because they provide a way to put time into geochemical models. The chemical characteristic of an element is determined by the number of protons in its nucleus. Different elements can have different numbers of neutrons and thus atomic weights (the sum of protons plus neutrons). The atomic weight is equal to the sum of protons plus neutrons. The chart of the nuclides (protons versus neutrons) for elements 1 (Hydrogen) through 12 (Magnesium) is shown in Fig. 16-1. The Valley of Stability represents nuclides stable relative to decay. Examples: Atomic Protons Neutrons % Abundance Weight (Atomic Number) Carbon 12C 6P 6N 98.89 13C 6P 7N 1.11 14C 6P 8N 10-10 Oxygen 16O 8P 8N 99.76 17O 8P 9N 0.024 18O 8P 10N 0.20 Several light elements such as H, C, N, O, and S have more than one stable isotope form, which show variable abundances in natural samples.
    [Show full text]