1 The Exponential Law of Decay
1.1 Phenomenological approach
The most fundamental quantity of radioactive decay is the activity A meaning the number of atoms decaying in the specimen per time.
Historical units of activity. The formerly used unit of radioactivity—the curie (Ci)—was introduced in 1930. One curie was originally defined as the disintegration rate of 1 gram of pure 226Ra. Radium was chosen as a reference because of its then importance among radioactive elements. However it was rather disturbing that the value of the unit had to be changed from time to time as more accurate data were obtained for the decay of radium. Finally the value of curie was fixed arbitrarily at 3.7 × 1010 disintegrations per second (1950). (During the thirties another unit: 106 disintegrations per second—called rutherford —was also suggested but it has never become widely known.)
SI unit of activity. Since 1975, the internationally recommended unit is the becquerel(Bq) defined as 1...
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Notes
- 1.
1 Some authors prefer to use the term no-carrier-added (n.c.a.) in more or less the same sense as carrier-free. (See, e.g., Chapters 3 and 7 in Volume 4.)
- 2.
2 Some authors use the term ‘specific radioactivity’ in the sense of molar activity, although according to IUPAP and IUPAC recommendations the adjective’ specific’ should be reserved for naming quantities that are divided by mass. (See, e.g., Chapter 5 in Volume 4.)
- 3.
3 Volume editor's note: The statistical nature of radioactive decay is a quantum effect and, as such, emerges from an intrinsic indefiniteness in the quantum mechanical state of each nucleus of a sample. Decay can thus be described as a time-dependent evolution of a single nucleus. However, quantum mechanics does not allow the existence of purely exponential decay. One can convince oneself of this statement by recognizing that (1) a pure exponential decay must have been started an infinitely long time ago and must last up to infinity; (2) in such a state the probability of finding the emitted particle in the vicinity of any point of space must decrease exponentially in time at the same rate. From proposal (2) it follows that such a state cannot be normalized, thus it cannot be a genuine quantum mechanical state. Nevertheless, one can introduce the exponential time dependence as an approximation in the Schrödinger equation, and end up with a generalized eigenvalue problem for the spatial factor of the wave function of the decaying state. This eigenfunction is called the Gamow wave function, and it turns out to be a good approximation to the exact time-dependent decaying state. The exact state departs from the exponential law at the time of its birth in a way that is specific to each nucleus and, again, towards the end of its life, i.e., after a great many half-lives have passed since its birth. These deviations from the decay law are, however, too delicate to have any practical consequences.
- 4.
4 Some authors prefer to use the term mother rather than parent.
- 5.
5Ehmann and Vance (1991) as well as several authors of this handbook refer to the result summarized by Eqs. (42)-(43) as the Bateman equation (Bateman 1910). Other authors refer to the whole series of equations shown in Eq. (40) as Bateman equations.
- 6.
6 We should mention here the double beta (2β) decay in which two beta particles and two neutrinos are emitted simultaneously. The typical half-life is in the order of 1020 a, therefore such primordial nuclides can be considered stable for any practical purpose. (Note that the estimated age of our Universe is only about 1.4 × 1010 a according to some recent measurements mentioned in Chapter 1 of Volume 2.)
- 7.
7 Volume editor's note: It may be mentioned that there exist decay modes in between α decay and fission, which are called (heavy-) cluster decay . The typical clusters emitted are 14C, 18O etc. These decay modes are regarded as types of radioactivity, like α decay, since, the cluster is emitted in its ground state and the residual nucleus is brought about either in its ground state or in some low-lying excited state. In fission the products are usually highly excited and de-excite partly via neutron emission. However, recently cold fission was also discovered; in that process the nucleus disintegrates into two nearly equal fragments with low excitation energies and hardly any particle emission. Cold fission is half-way between fission and cluster decay. All these exotic processes are extremely rare.
References to Kinetics of Radioactive Decay
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CHOPPIN, G.R., RYDBERG, J., 1980, Nuclear Chemistry—Theory and Applications (Oxford: Pergamon Press).
EHMANN, W.D., VANCE, D.E., 1991, Radiochemistry and Nuclear Methods of Analysis (New York: John Wiley & Sons).
FRIEDLANDER, G., KENNEDY, J.W., MACIAS, E.S., MILLER, J.M., 1981, Nuclear and Radiochemistry (New York: John Wiley & Sons).
LEFORT, M., 1968, Nuclear Chemistry (London: D. Van Nostrand Company).
RÉNYI, A., 1979, Wahrscheinlichkeitsrechnung. Mit einen Anhang über Informationstheorie, 6. Aufl. (Berlin: VEB Deutscher Verlag der Wissenschaften).
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VÉRTES, A., NAGY, S., SÜVEGH, K., 1998, Nuclear Methods in Mineralogy and Geology (New York: Plenum) Chapter 1.
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(2003). Kinetics of Radioactive Decay. In: Handbook of Nuclear Chemistry. Springer, Boston, MA. https://doi.org/10.1007/0-387-30682-X_5
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