Physics
Radioactive Decay
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha or beta particles, or gamma rays. This process results in the transformation of the original element into a different element or isotope. The rate of decay is characterized by the element's half-life, which is the time it takes for half of the radioactive atoms to decay.
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eBook - PDFIsotopes in Nanoparticles
Fundamentals and Applications
- Jordi Llop, Vanessa Gomez-Vallejo, Jordi Llop, Vanessa Gomez-Vallejo(Authors)
- 2016(Publication Date)
- Jenny Stanford Publishing(Publisher)
In the latter state, the nucleus has an excess of internal energy and tends to move to a more stable state. The process by which the atomic nucleus moves from an unstable to a more stable state is called Radioactive Decay. Radioactive Decay is spontaneous and is accompanied by the emission of particles and/or electromagnetic radiation. The unstable nucleus is called a radioactive atom or radionuclide. 145 During Radioactive Decay, the unstable atoms can become a different element via a process known as transmutation. This is the case in radioactive processes that result in the emission of alpha particles ( a , or 4 He 2+ ), electrons ( b – ), or positrons ( b + ). As an example, fluorine-18 ( 18 F) has nine protons and nine neutrons in its nucleus and is a positron emitter; on spontaneous decay a positron is emitted and, consequently, one of the protons becomes a neutron. The newly formed element, which has eight protons and ten neutrons, is oxygen-18 ( 18 O). Radioactive Decay can also occur via electron capture (when a nucleus captures an orbiting electron, thereby converting a proton into a neutron with consequent transmutation), by emission of gamma ( g ) rays, by emission of a neutron, or by ejection of an orbital electron due to interaction with an excited nucleus in a process called “internal transition”. In the latter three decay modalities, the atoms before and after Radioactive Decay correspond to the same element because the number of protons remains unchanged and transmutation does not occur. Radioactive atoms exist in nature (and indeed are continuously produced naturally) and can be found in air, water, soil, or even living organisms. They can also be produced artificially using different technologies. Over 1500 radionuclides, both natural and artificial, have been identified. 6.2.2 Radioactive Decay Equations Radioactive Decay is a stochastic process in which, according to quantum theory, it is impossible to predict when a specific atom will decay.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
______________________________ WORLD TECHNOLOGIES ______________________________ Chapter- 6 Radioactive Decay Alpha decay is one example type of Radioactive Decay, in which an atomic nucleus emits an alpha par-ticle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive Decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, Radioactive Decay happens due to a process confined to the nucleus of the unstable atom, but, on occasion (as with the different processes of electron capture and internal conversion), an inner electron of the radioactive atom is also necessary to the process. Radioactive Decay is a stochastic (i.e., random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides), the decay rate for the collection is predictable, via the Law of Large Numbers. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, ______________________________ WORLD TECHNOLOGIES ______________________________ and a gamma ray) and transforms to a nitrogen-14 atom (the daughter).
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 1 Radioactive Decay Alpha decay is one example type of Radioactive Decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive Decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, Radioactive Decay happens due to a proceses confined to the nucleus of the unstable atom, but occasionally (as with the different proceses of electron capture and internal conversion) an inner electron of the radioactive atom is also necessary to the process. Radioactive Decay is a stochastic (i.e. random) process on the level of single atoms, in that according to quantum theory it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides) the decay rate for the collection is predictable. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, and a gamma ray) and transforms to a nitrogen-14 atom (the daughter). By contrast, there exist two types of Radioactive Decay processes (gamma decay and internal conversion decay) that do not result in transmutation, but only
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter- 1 Radioactive Decay Alpha decay is one example type of Radioactive Decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive Decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, Radioactive Decay happens due to a proceses confined to the nucleus of the unstable atom, but occasionally (as with the different proceses of electron capture and internal conversion) an inner electron of the radioactive atom is also necessary to the process. Radioactive Decay is a stochastic (i.e. random) process on the level of single atoms, in that according to quantum theory it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides) the decay rate for the collection is predictable. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, and a gamma ray) and transforms to a nitrogen-14 atom (the daughter). By contrast, there exist two types of Radioactive Decay processes (gamma decay and internal conversion decay) that do not result in transmutation, but only
eBook - PDF- Walter D. Loveland, David J. Morrissey, Glenn T. Seaborg(Authors)
- 2017(Publication Date)
- Wiley(Publisher)
57 3 Radioactive Decay Kinetics The number of nuclei in a radioactive sample that disintegrate during a given time interval decreases exponentially with time. Because the nucleus is insu- lated by the surrounding cloud of electrons, this rate is essentially independent of pressure, temperature, the mass action law, or any other rate-limiting factors that commonly effect chemical and physical changes. 1 As a result, this decay rate serves as a very useful means of identifying a given nuclide. Since Radioactive Decay represents the transformation of an unstable radioactive nuclide into a more stable nuclide, which may also be radioactive, it is an irreversible event for each nuclide. The unstable nuclei in a radioactive sample do not all decay simultaneously. Instead the decay of a given nucleus is an entirely random event. Consequently, studies of Radioactive Decay events require the use of statistical methods. With these methods, one may observe a large number of radioactive nuclei and pre- dict with fair assurance that, after a given length of time, a definite fraction of them will have disintegrated but not which ones or when. 3.1 Basic Decay Equations Radioactive Decay is what chemists refer to as a first-order reaction; that is, the rate of Radioactive Decay is proportional to the number of each type of radioac- tive nuclei present in a given sample. So if we double the number of a given type of radioactive nuclei in a sample, we double the number of particles emitted by the sample per unit time. 2 1 In the case of electron capture and internal conversion, the chemical environment of the electrons involved may affect the decay rate. For L-electron capture in 7 Be (t 1∕2 = 53.3 days), the ratio of t BeF 2 1∕2 /t Be 1∕2 is 1.00084. Similarly, a fully stripped radioactive ion cannot undergo either EC or IC decay, a feature of interest in astrophysics.
eBook - PDF- Yuri A Berezhnoy(Author)
- 2005(Publication Date)
- WSPC(Publisher)
Chapter 4 Radioactivity of Atomic Nuclei 4.1 The Law of Radioactive Decay Human history records but a few great scientific discoveries made acciden-tally. The discovery of the radioactivity of atomic nuclei is one of them. Radioactivity is the process of spontaneous transmutation of an unstable nucleus into another one, which is accompanied by the emission of various particles and photons. Several elementary particles can undergo Radioactive Decay as well. In February 1896, the physics professor Becquerel was working at the Ecole Poly technique in Paris. He studied the abilities of various crystals under sunlight to emit a penetrating radiation similar to the X-rays that had been recently discovered by Roentgen. Becquerel supposed that crys-tals under the influence of light would emit rays that could register on the photographic plates covered by black paper. A screen made out of copper wires was placed between the crystal and the plate. Thus, after developing, the plate would be light-struck everywhere except the region covered by the copper wires. Among the crystals Becquerel was working with, by chance some ura-nium salts were stored, specifically uranium sodium bisulphate. Also by chance, the weather during the experiments was cloudy so that Becquerel put the plates into the box of the laboratory table together with the crystals of uranium salt. After a few days when the plates were developed, they appeared dark and demonstrated a very clear image of the screen, even though no sunlight had illuminated the uranium salt. Becquerel attributed the rays that registered on the plate to the ura-nium. Afterwards it was found that the same rays could be emitted by other elements as well. In 1898, Marie Sklodowska-Curie discovered that 89 90 The Quantum World of Nuclear Physics the same rays were emitted by thorium; she and her husband Pierre Curie subsequently discovered radium. The term radium originates from the Latin word radius, which means ray.
eBook - PDFBasic Physics Of Radiotracers
Volume II
- Earl W. Barnes(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
In time it was determined that there were three types of radiations that accounted for the phenomenon that was called radioactivity. The three types of radiations were named: 1. Alpha particles (cr) 2. Beta particles ( ß) 3. Gamma rays (y) The substances that emit one or more of these radiations are called radioactive nu clides. Investigations since the early years of this century have established that the three types of radiations originate in the nucleus of certain nuclides, and that (1) alpha par ticles (a) are, in actuality, helium nuclei (2He); (2) beta particles ( ß~ and ß +) are, in actuality, negative and positive electrons (e and e+); and (3) gamma rays (y) are high energy electromagnetic radiations (photons). Radioactive disintegration is a mechanism whereby an unstable nucleus can give up energy in order to achieve a configuration of greater stability. II. THE Radioactive Decay CURVE If N represents the number of radioactive nuclei in a certain sample at a certain time, then the rate at which the nuclei in the sample decay is given by -dN dt where the minus sign signifies that the number of nuclei in the sample decreases with time. The quantity — (dN/dt) is called the activity of the sample: -dN ACTIVITY = -------dt The activity of a radioactive substance is often measured in terms of the curie, which is defined as follows: Activity is sometimes measured in terms of the rutherford, which is defined as fol lows: disintegrations per second 39 1 rutherford (rd) = IO6 disintegrations per second (1 mrd = IO-3 rd = IO3 disintegrations per second) (1 ¡did = IO-6 rd = 1 disintegration per second) The disintegration of radioactive nuclei is a random process. However, when a large number of nuclei are considered it is found that the activity of a radioactive substance is directly proportional to the number of radioactive atoms present, i.e.: where À is a proportionality constant called the Radioactive Decay constant.
eBook - PDFPhysics of Nuclear Radiations
Concepts, Techniques and Applications
- Chary Rangacharyulu(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
2 Radioactivity 2.1 Introduction Nuclear radiations are ubiquitous. They are present in the atmosphere as cosmic rays originating in outer space, sources of which are yet un-known. They are also present in vegetation as carbon contains a small but finite radioactive isotope, 1 a fact used advantageously to determine the ages of archaeological samples. Most living beings including hu-mans contain calcium, which consists of a tiny amount of long-lived ra-dioactive potassium ( 40 K isotope). The list goes on. In the 20th century, we made significant progress in harnessing energy from nuclear fis-sion, employing nuclear techniques for non-destructive testing of ma-terials, medical diagnostics and therapy. Whether we handle radioac-tive materials for applications or we are concerned about health and safety, we need to have a good grasp of some basic terminology and be able to do simple calculations to make quantitative estimates of radi-ation phenomena. When one is concerned about radiation effects, one has to consider the species and energies of the radiations emitted and the activity levels and characteristic lifetimes of the radiation emitting sources. This chapter is devoted to radioactive levels and characteristic times. 2.1.1 Exponential Decay Law It has been found that in a sample of radioactive material, the intensity of emissions (number of emissions per unit time) decreases exponen-tially with time. Exponential growths and decays are very common in physical sciences. In the case of growth, we can specify a maximum 1 See Section 2.7. 21 22 Physics of Nuclear Radiations: Concepts, Techniques and Applications limit to which a sample, left to itself, will grow after an infinite amount of time. In the case of decay, a sample will vanish only after an infinite amount of time. 2 However, as we will see below, both growth and de-cay will be quite small after some finite time.
eBook - PDFRadiochemistry and Nuclear Chemistry
2nd Edition of Nuclear Chemistry, Theory and Applications
- Gregory Choppin, Jan-Olov Liljenzin, Jan Rydberg, JAN RYDBERG(Authors)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
The nonexistence in nature of elements with atomic numbers greater than 92 is explained by the fact that all the isotopes of these elements have life-times considerably shorter than the age of the earth. Radioactive Decay is a random process. Among the atoms in a sample undergoing decay it is not possible to identify which specific atom will be the next to decay. We denote the decay rate by A. It is a measure of the number of disintegrations per unit time: A = —dN/dt (4.39) The decay rate is proportional to the number of radioactive atoms, N, present: A oc N. If 10 5 atoms show a decay rate of 5 atoms per second then 10 6 atoms show a decay rate of 50 atoms per second. If the number of radioactive nuclei and the number of decays per unit time are sufficiently great to permit a statistical treatment, then — dN/dt = N (4.40a) where is the proportionality constant known as the decay constant. If the time of observation At during which AN atoms decay is very small compared to t i/2 (usually < 1 %), one may simply write A = AN/At = XN (4.40b) If the number of nuclei present atsome original time t = 0 is designated as N0, (4.40a) upon integration becomes the general equation for simple Radioactive Decay: N = N0 e _Xl (4.41a) In Figure 4.8 the ratio of the number of nuclei at any time t to the original number at time t = 0 (i.e. N/Nq) has been plotted on both a linear (left) and logarithmic (right) scale as a function of t. The linearity of the decay curve in the semi-logarithmic graph illustrates the exponential nature of Radioactive Decay. Since A oc N, the equation can be rewritten as A = A q e _Xi (4.41b) Commonly, log A is plotted asa function of t since it is simpler todetermine the disintegration rate than it is to determine the number of radioactive atoms in a sample. 80 Radiochemistry and Nuclear Chemistry TIME t IN NUMBER OF HALF-LIVES FIG. 4.8. Linear and logarithm plots of simple Radioactive Decay.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Thus these decays reveal that the laws for subatomic processes are statistical. For example, in a 1 mg sample of uranium metal, with 2.5 × 10 18 atoms of the very long-lived radionuclide 238 U, only about 12 of the nuclei will decay in a given second by emitting an alpha particle and transforming into a nucleus of 234 Th. However, 1294 CHAPTER 42 Nuclear Physics Taking the exponential of both sides (the exponential function is the antifunction of the natural logarithm) leads to N ___ N 0 = e −λt , or N = N 0 e –λt (Radioactive Decay), (42.3.5) in which N 0 is the number of radioactive nuclei in the sample at t = 0 and N is the number remaining at any subsequent time t. Note that lightbulbs (for one example) follow no such exponential decay law. If we life-test 1000 bulbs, we expect that they will all “decay” (that is, burn out) at more or less the same time. The decay of radionuclides follows quite a different law. We are often more interested in the decay rate R (= –dN/dt) than in N itself. Differentiating Eq. 42.3.5, we find R = − dN ___ dt = λN 0 e −λt , or R = R 0 e –λt (Radioactive Decay), (42.3.6) an alternative form of the law of Radioactive Decay (Eq. 42.3.5). Here R 0 is the decay rate at time t = 0 and R is the rate at any subsequent time t. We can now rewrite Eq. 42.3.1 in terms of the decay rate R of the sample as R = λN, (42.3.7) where R and the number of radioactive nuclei N that have not yet undergone decay must be evaluated at the same instant. The total decay rate R of a sample of one or more radionuclides is called the activity of that sample. The SI unit for activity is the becquerel, named for Henri Becquerel, the discoverer of radioactivity: 1 becquerel = 1 Bq = 1 decay per second. An older unit, the curie, is still in common use: 1 curie = 1 Ci = 3.7 × 10 10 Bq. Often a radioactive sample will be placed near a detector that does not record all the disintegrations that occur in the sample.
eBook - PDF- Michael F. L'Annunziata(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
1.1. The emission of gamma radia-tion often accompanies radionuclide decay processes that occur by alpha par-ticle emission. Gamma radiation is described in Section III. A of this chapter. The nuclei of daughter atoms of alpha particle-emitting nuclides are often unstable themselves and may also decay by further alpha particle emission. Thus, alpha particle-emitting nuclides may consist of a mixture of radionuclides, e ay he e of he re ati e ab da e i te itie of a ha arti e a d a a ra y e i io are e re ed i er e t be ide the radiatio e er y a e i e N N N all part of a decay chain, as illustrated in Fig. 1.32 further on in this chap-ter. Additional reading on radionuclide alpha decay is available from Das and Ferbel(1994). N o w consider what happens to an alpha particle that dissipates its kinetic energy by interaction with matter. Alpha particles possess a double positive charge due to the two protons present. This permits ionization to occur within a given substance (solid, liquid, or gas) by the formation of ion pairs due to coulombic attraction between a traversing alpha particle and atomic electrons of the atoms within the material the alpha particle traverses. The two neutrons of the alpha particle give it additional mass, which further facilitates ionization by coulombic interaction or even direct collision of the alpha particle with atomic electrons. The much greater mass of the alpha particle, 4 atomic mass units (u), in comparison with the electron (5 X 1 0 ~ 4 u) facilitates the ejection of atomic electrons of atoms through which it passes, either by direct collision with the electron or by passing close enough to it to cause its ejection by coulombic attraction. The ion pairs formed consist of the positively charged atoms and the negatively charged ejected electrons.
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