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Abundance and Radioactivity of Unstable Isotopes

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Abundance and Radioactivity of Unstable Isotopes 5 RADIONUCLIDE DECAY AND PRODUCTION This section contains a brief review of relevant facts about radioactivity, i.e. the phenomenon of nuclear decay, and about nuclear reactions, the production of nuclides. For full details the reader is referred to textbooks on nuclear physics and radiochemistry, and on the application of radioactivity in the earth sciences (cited in the list of references). 5.1 NUCLEAR INSTABILITY If a nucleus contains too great an excess of neutrons or protons, it will sooner or later disintegrate to form a stable nucleus. The different modes of radioactive decay will be discussed briefly. The various changes that can take place in the nucleus are shown in Fig.5.1 In transforming into a more stable nucleus, the unstable nucleus looses potential energy, part of its binding energy. This energy Q is emitted as kinetic energy and is shared by the particles formed according to the laws of conservation of energy and momentum (see Sect.5.3). The energy released during nuclear decay can be calculated from the mass budget of the decay reaction, using the equivalence of mass and energy, discussed in Sect.2.4. The atomic mass determinations have been made very accurately and precisely by mass spectrometric measurement: 2 E = [Mparent Mdaughter] P mc (5.1) with 1 amu V 931.5 MeV (5.2) Disintegration of a parent nucleus produces a daughter nucleus which generally is in an excited state. After an extremely short time the daughter nucleus looses the excitation energy through the emittance of one or more (gamma) rays, electromagnetic radiation with a very short wavelength, similar to the emission of light (also electromagnetic radiation , but with a longer wavelength) by atoms which have been brought into an excited state. In some cases, however, ß decay is directly to the ground state of the daughter nucleus, without the emission of radiation. Fig.5.2 shows the various decay schemes of some familiar nuclides. 67 Chapter 5 5.2 NUCLEAR DECAY AND RADIATION In the now following sections the various types of spontaneous nuclear disintegration will be discussed. 5.2.1 NEGATRON ( ) DECAY The most abundant decay mode is ß decay, involving the emission of a negative electron, a negatron or (beta) particle because of a transformation inside the nucleus of a neutron into a proton: n J p+ + + + Q (5.3) This results in a daughter nucleus with equal A and a change in atomic number Z to Z+1, and the emission of an electron and an anti-neutrino. A (anti)neutrino is a particle with mainly a relativistic mass, i.e. mass because of its motion. (Neutrino's and negatrons have their spin anti-parallel to their direction of motion and anti-neutrino's and positrons parallel). The total reaction energy Q is shared between the particle and the (anti)neutrino. The consequence is that, although Q is a specific amount of energy, the energy spectrum of the ß particles is continuous from zero to a certain maximum energy at Eßmax = Q. The energy distribution is such that the maximum in this distribution is at an energy about one third of the maximum energy. As mentioned above, in some cases the resulting daughter nucleus is not in an excited state, so that no radiation is emitted. This happens to be the case with the two isotopes that are relevant in isotope hydrology, viz. 3H and 14C. 5.2.2 POSITRON (+) DECAY This type of nuclear transformation involves the emission of a positron or ß+ (beta plus) particle as the result of a transformation inside the nucleus of a proton into a neutron: p+ J n + e+ + + Q (5.4) and, because after slowing down the positron reacts fast with an electron anywhere present: e+ + e J 2 (5.5) Here two electron masses are transformed into energy. The process is called annihilation, the energy released annihilation energy. With the mass of the electron 4 me = 5.4858026P10 amu (5.6) 68 Nuclear Decay and Radiation EC p + n Z N Fig.5.1 Different modes of radioactive decay visualised on one spot of the chart of nuclides (cf. Fig. 1.2). N is the number of neutrons, Z the number of protons. the resulting energy is 1.022 MeV, which is represented by two oppositely directed particles of 511 keV each. This type of decay is, for instance, known from naturally occurring 40K (Fig.5.2). 5.2.3 ELECTRON CAPTURE (EC) The nucleus may pick up one electron from the atomic electrons circling the nucleus in consecutive shells. In that case the following reaction takes place: p+ + e J n + + Q (5.7) Depending on from which atomic shell the electron is caught by the nucleus, electron capture is called K capture, L capture, and so on. + decay and EC leave the mass number A of the nucleus unchanged, while Z becomes Z-1 (Fig.5.1). The atom is left in an excited state and returns to the ground state by emitting short-wave electromagnetic radiation, viz. low-energy rays or X rays. As in the previous decay modes, the excited state of the nucleus causes the emission of one or more rays. 5.2.4 ALPHA () DECAY (alpha) decay involves the emission of an particle (a 4He nucleus): A J A4 4 Z X Z2Y 2 He (5.8) 69 Chapter 5 14 C 5730 a 22Na 2.6 a + EC 2 Emax = 158 keV 2mc 1.275 MeV 14N 22Ne 40K 1.3P109 a EC 11% + 0.001% 88.8% 1.32 MeV 2 1.46 MeV 1.02 MeV EC 0.16% 1.51 MeV 40Ca 40Ar Fig.5.2 Decay schemes for some nuclides obeying , + or EC decay, the latter example of 40K in branching decay, and the consecutive radiation by the excited daughter nucleus as well as the formation of 2 by annihilation of an emitted + particle. This type of decay occurs primarily within the heavy elements such as in the uranium and thorium series. The emission of the heavy particle practically coincides with the emission of relatively large-energy rays. Because as in all cases the reaction energy Q is shared by the atoms Y and He according to the two conservation laws, the case of emission is special. As with a gun shot, where the rifleman feels a large momentum against his shoulder, the daughter nucleus receives a relatively large so-called recoil. This is particularly important where the recoil energy is large enough to loose the daughter nucleus from its chemical bond. This phenomenon is the basis for studying the natural abundance of the decay nuclides of uranium and thorium. In Sect.5.3 we will deal with recoil energy quantitatively. 70 Nuclear Decay and Radiation 5.2.5 SPONTANEOUS AND INDUCED FISSION, NEUTRON EMISSION Nuclides of the heavy elements have the possibility of breaking up into two relatively large daughter nuclei together with the emission of a number of neutrons. This decay may occur spontaneously as well as induced by the bombardment of the parent nucleus by a neutron from elsewhere, for instance from a neighbouring nucleus. This is the dominant process in nuclear reactors (Sect.5.4.2; Chapter 12). 5.3 RECOIL BY RADIOACTIVE DECAY In the preceding chapter we mentioned the phenomenon of the recoil momentum and energy which any decaying nucleus experiences. However, in the case of a heavy particle such as the particle leaving the nucleus, the effect is not negligibly small. We will now calculate the recoil energy by considering the classical mechanics of this process (Fig.5.3). V v M m Fig.5.3 After radioactive decay the daughter nucleus M and the smaller emitted particle m (for instance, an particle) move in opposite direction, together carrying the decay energy as the respective kinetic energies. The principle of conservation of momentum requires: MV + mv = 0 or M2V2 = m2v2 (5.9) while the principle of conservation of energy requires the decay energy to be equal to the sum of the two kinetic energies: 2 2 Edecay = ½ MV + ½ mv = EM + Em (5.10) From Eq.5.9 we have: 1 1 1 m E MV 2 M 2V 2 m2 v2 E (5.11) M 2 2M 2M M m 71 Chapter 5 With Eq.5.10: m . E 1 /E decay M 0 m so that the two particle energies are, respectively: M m E E and E E (5.12) m M m decay M M m decay In the case of the decay of 238U with a decay energy of about 4.2 MeV, the daughter nucleus, 234Th, receives a recoil energy of [4/(234+4)] P 4.2 MeV = 71 keV, more than enough to break the chemical bond between the Th atom and the surrounding atoms in the mineral (see Sect.12.14 and Volume 4 on Groundwater) for a discussion of the consequences. 5.4 NUCLEAR REACTIONS The overall principle of a nuclear reaction is that a nucleus is bombarded by a particle that is in the first instance taken up by the nucleus to form a compound nucleus. This does not result in a stable particle. Within an extremely short time the compound nucleus will loose the excess energy by the release of one or more particles, ultimately forming a new nuclide. The bombarding particles may be "man-made" and originate from a nuclear particle accelerator (electrically charged particles) or a nuclear reactor (high- or low-energy neutrons), or may be from natural origin. A few examples may serve to show the convention of writing nuclear reactions: 36Ar + n J p + 36Cl or 36Ar(n,p)36Cl 40Ca + n J + 37Ar or 40Ca(n.
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