désintégrations radioactives

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1 désintégrations radioactives
Radioactivité - 1 désintégrations radioactives Now let’s discuss radioactive decay, including important terms and concepts Jour 1 – Leçon 4

2 Objectif Discuter les principes de désintégration radioactive et certains termes pertinents Définir les unités de mesure de la désintégration radioactive

3 Contenu Activité Loi de décroissance radioactive
Période radioactive ou demi-vie La vie moyenne Constante de décroissance radioactive Unités This lesson includes activity and how it relates to number of atoms of a radioactive isotope, the equation for radioactive decay (including terms), half-life and how it relates to the decay constant, definition of mean life and how it relates to half-life, and important units used to measure radioactive decay.

4 La Radioactivité La radioactivité est la propriété de certains atomes qui se transforment spontanément en dégageant de l’énergie sous forme de rayonnements divers Les atomes radioactifs émettent des rayonnements ionisants lorsqu’ils se désintègrent The Becquerel is a fundamental unit of activity and is also expressed as decays or nuclear transformations per second.

5 Les éléments d'origine naturelle
Dans la nature il existe environ 300 nuclides La majorité des éléments d’origine naturelle sont sables Mais Certains ayant un poids atomique élevé, à partir du Polonium (Z = 84) suivi du Radium (88), du Thorium (90), de l‘Uranium (92) sont entièrement constitués de nucléides instables Les substances instables subissent des transformations spontanées, la désintégration radioactive ou la décroissance radioactive à des taux précis. The Becquerel is a fundamental unit of activity and is also expressed as decays or nuclear transformations per second.

6 L’Activité La quantité présente d’un radionucléide
Unité SI est le Becquerel (Bq) The Becquerel is a fundamental unit of activity and is also expressed as decays or nuclear transformations per second. 1 Bq = 1 désintégration par seconde

7 Multiples & Préfixes (Activité)
Multiple Préfixe Abréviation Bq Méga (M) MBq Giga (G) GBq Téra (T) TBq 1 x 1015 Péta (P) PBq These are common prefixes used to express activity.

8 Unités 1 Curie (Ci) = 3,7 x 1010 dps 1 Becquerel (Bq) = 1 dps
1 Ci = 3,7 x 1010 Bq ou 1Ci = 37 GBq In some countries, particularly the United States, the so-called “Special Units” of Curie are still used to express activity. This slide shows the relationship between the special unit and the SI units of Bq.

9 Unités Unités Ancienne unité Unités SI Conversion
Activité curie (Ci) becquerel (Bq) 1 Ci=3,7 x 1010Bq Dose Absorbée rad gray (Gy) 1 rad = 0.01 Gy Dose Equivalente rem sievert (Sv) 1 rem = 0.01 Sv This slide further shows the relationship between the Old (Special) Units and the SI units.

10 Constante de décroissance radioactive
La constante de décroissance est notée  1 temps NOTE: Unités de  en Typiquement ou sec-1 ou “par seconde” The decay constant is unique for each different radionuclide. It is a constant and can not be changed or altered by any known processes. 1 sec

11 Activité A = N Où “A = activité” son unité est la désintégration par seconde (dps ou Bq) If we have a collection of N atoms of a given radioisotope and the radioisotope has a known decay constant, the activity of this sample is given by the simple product of the number of atoms and the decay constant.

12 0.693* T½ =  Demi-vie et la Constante de décroissance
La relation entre la demi-vie (ou période) et la constant e  est: T½ = 0.693*  The half-life is the time required for an amount of any radionuclide to decay to one-half of its initial value. The half-life is related to the decay constant by this simple equation where is simply the natural logarithm of 2 (Ln2) . * Avec 0,693 = Ln 2

13 Demi-vie ou période This slide shows how the amount of a radionuclide decays with time and how the initial amount is related to number of elapsed half-lives. If the same plot is drawn using semi-log paper (i.e., the vertical axis is logarithmic) the line is straight instead of curved.

14 Demi-vie ou période Radionucléide Demi-vie Phosphor-32 14,3 jours
Iridium jours Cobalt-60 5,25 années Césium années Carbone années Uranium-238 4,5 x 109 années This slide simply shows a comparison of the half-lives of selected important radionuclides. As can be seen in this slide, half-lives of the radioisotopes vary greatly.

15 Exemple: Exercice Un accident de criticité se produit dans une installation de traitement de l'uranium fissions se produisent sur ​​une période de 17 heures. Etant donné que le rendement de fission pour 131I est de 0,03 et sa demi-vie est de 8 jours, calculer l'activité de l'iode-131 à la fin de l'accident. On néglige la désintégration de 131I lors de l'accident. This example problem will give us practice in calculating activity, using the equation based on decay constant and number of atoms present. The number of atoms of I-131 is calculated from the total number of U-235 fissions and the fission yield for I To keep the problem simple, we neglect I-131 decay during the criticality accident. This will result in very, very small error.

16 Solution Activité = N = x x ( 1019 x 0,03) = 3 x 1011 Bq de 131I
0,693 8 jrs 1 86,400 sec. jr-1 3 x 1011 Bq 3,7 x 1010 Bq/Ci = 8.1 Ci 131I A relatively large amount of I-131 is created in this example criticality accident. Of course, the concern here is people inhaling the I-131 with subsequent dose to the thyroid.

17 Equation Différentielle de décroissance Radioactive
Le taux de décroissance à un certain temps est directement proportionnel au nombre d'atomes radioactifs présents à ce moment-là = -N(t) dN dt This slide shows the differential equation for radioactive decay. The amount of a radioactive nuclide is changing (decreasing ) with time, since it is always decaying. The instantaneous rate of change is given by the negative of the activity. N is the number of radioactive atoms present at time t.

18 Equation de décroissance Radioactive
N(t) = No e -t Integration of the differential equation on the previous slide is shown above. This is the well-known equation for radioactive decay. No is the initial number of radioactive atoms present at time t=0; N is the number of radioactive atoms present at any subsequent time t; t is the time and  is the decay constant.

19 Equation de décroissance Radioactive
Exprimant l’équation en termes d’activité:  N(t) =  No e-t A(t) = Ao e- t ou The previous equation is expressed in terms of atoms. Let’s derive an equation in terms of activity. Multiplying both sides of the previous equation by the decay constant will not change the value of the equation. This will express the equation in terms of activity, which we will call “A”. It can be seen that the radioactive decay equation has the same general form, whether it is expressed in terms of activity or in terms of numbers of atoms. Où A(t) = l’activité à un temps t et Ao = l’activité initiale au temps t = 0

20 A(t) 1 - Ao Décroissance Radioactive
L’activité qui a décrue après “n” demi-vies est donnée par: A(t) Ao 1 - From the decay equation in terms of activity we can calculate how much of an isotope has decayed away after “n” half-lives or how much remains. “A” represents the activity which exists at time t so that A/Ao represents the fraction of the initial activity that still exists at time t. One minus this fraction represents the fraction that has decayed away.

21 A 1 = Ao 2n* Décroissance Radioactive
L’activité “A” qui reste après “n” demi-vie est donnée par A Ao 1 2n* = This slide shows how much of any radionuclide remains after “n” half-lives. * Avec n = t / T1/2

22 La vie moyenne Pour certaines applications, comme dans le cas de la dosimétrie interne, il est commode d'utiliser la durée de vie moyenne du radio-isotope TM = T1/2 The mean life is simply related to the half-life by this equation where 1.44 is simply 1/Ln2 or 1/0.693. Let’s discuss how we can derive this expression for the mean life.

23 Exemple Un radionucléide a une demi-vie de 10 jrs. Quelle est sa vie moyenne? This example problem will give us practice in how to calculate the mean life of a radionuclide.

24 Solution de l’exercice
Vie moyenne = T1/2 = x 10 jrs = jrs We use the equation we derived to calculate the mean life, given the half-life of 10 days. Although the mean life does not represent an actual time, it is very useful to determine the total number of disintegrations which will be important for calculating internal dose. It can also be applied to calculating external dose from sources if we know the initial dose rate. Multiplying by the Mean Life yields the total dose delivered by the source until the time when all the atoms have decayed.

25 Où obtenir plus d'informations
Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009) International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)