Radioactive Decay BSEN-625 ADVANCES IN FOOD ENGINEERING

Transcription

1 Radioacive Decay BSE-65 DVCES I FOOD EGIEERIG

2 civiy The rae of decay of a radionuclide I is he number of aoms ha decay per uni ime Unis Bacquarel (Bq): one desinegaion/second Bq s - Curie-(Ci): aciviy of g of Ra 6 Ci: Ci 3.7x0 0 Bq

3 Exponenial decay The aciviy of a pure radionuclide decreases exponenially wih ime /o

4 Exponenial radioacive decay law If # of aoms of a radionuclide in a a given ime: I. C.: o, 0; d d d d d d ln + c ln o 0 + c ln ln or o o + ln e o

5 Half-life, T Time required for he aciviy of a radionuclide drop by a facor of onehalf e o T e T ln ln ln T Decay consan

6 Exponenial decay in erm of T o o ln o o T / T e 0.63 / T ln T /o T o e 0.63 T T 3T

7 Example Calculae he aciviy of a 30-MBq source of a-4 afer.5 d. Wha is is decay consan Soluion T half-life 5 h (appendix D) h T 5 o 30MBq,.5d 4h / d 30e ( ).88MBq 60h

8 Mean life, τ The average of all he individual lifeimes ha aoms in a sample of he radionuclide experience The mean value of under he exponenial curve /o τ e

9 Mean life, τ I defines a recangle wih area equal o: τ τ > T e d e T τ 0 0 /o e τ

10 Specific civiy, S civiy per uni mass Bq/g For a pure radionuclide he S is deermined by is decay consan,, or half-life T, and by is aomic weigh M: S M MT 3 [ Bq / g] # of aoms per gram of nuclide In [s]

11 Example Wha is he S of Ra 6 in Bq/g T 600y( appendix M S MT S s ( ) g Bq / g

12 S (T,) S Ci 600 T [ Ci Bq / g] T is expressed in years

13 Serial radioaciviy decay sample in which one radionuclide produces one or more radioacive offspring in a chain Secular equilibrium Transien equilibrium o equilibrium

14 Secular equilibrium (T >>T ) any ime a Long-Lived paren () decays ino a Shor-Lived daugher (), which decays o a sable nuclide T >>T of he paren is consan (assuming shor inervals of ime compared o T ) any ime T +

15 Secular equilibrium (T >>T ) d u du d du u d d d d ; consan e e c C I c ) ( ln ) ln( ) ln( + +

16 Secular equilibrium civiy relaively shorlived radionuclide as funcion of ime I.C: 0 0 civiy of daugher builds up o ha of paren in abou 7 half-lives Daugher decays a he same rae i is produced () Secular equilibrium is said o exis Toal aciviy is () civiies secular equilibrium T>>T 0 ~7T

17 Secular equilibrium In erms of numbers of aoms chain of n shor-lived radionuclides can all be in secular equilibrium wih a long-lived paren The aciviy of each member of he chain aciviy of paren Toal aciviy (n+)( of original paren)

18 General Case If here is no resricion on he relaive magniudes of T and T: equilibrium)!!!(alsodescribesa secular 0 ) ( and e e C I d d >>

19 Transien equilibrium (T >T ) 0 0 T >T of he daugher iniially build-up seadily Wih ime, e - becomes negligible, since >

20 Transien equilibrium (T >T ) ) ( ) ( 0 ) ( >> e e e e

21 civiies as funcion of ime fer iniially increasing, he daugher aciviy goes hru a maximum and decreases a he same rae as he paren aciviy Thus, ransien equilibrium exis The oal aciviy also reaches a maximum, early han he daugher The ime ransien equilibrium is reached depends on T & T aciviies Transien equilibrium T > T

22 o Equilibrium (T < T ) When a daugher ( 0 0) has a longer T han he paren T is aciviy build ups a maximum and hen declines The paren evenually decays away (T is shorer) Thus, only he daugher is lef o equilibrium occurs

23 o Equilibrium (T < T ) civiies as funcion of ime when T > T and 0 0 on equilibrium occurs 0 aciviies T > T + Only he daugher aciviy remains 0

24 Example Saring wih a 0 GBq (0 0 Bq) sample of pure Sr 90 a ime 0, how long will i ake for he oal aciviy (Sr 90 + Y 90 ) o build up 7.5 GBq?

25 Soluion ppendix D 38 Sr 90 β - decays wih a T 9. y ino 39 Y 90, which β - decays ino sable 40 Zr 90 wih T 64 h T >> T Secular equilibrium is reached in abou 7T 7x64 448h he end of his ime, he Sr 90 aciviy has no diminished appreciably The Y 90 aciviy has increased o he level 0 GBq Toal aciviy T 0 GBq

26 Soluion Time a which Y 90 reaches 7.5 GBq The answer will be less han 448 h 0 ( e / T 7.5 0( e ) ) 0 e 0.008h ; 0GBq, 7.5GBq 8h

27 Example How many gram of Y 90 are in secular equilibrium wih mg of Sr 90?

28 Soluion The amoun of Y 90 will be ha having he same aciviy as mg of Sr 90 The S of Sr 90 of (T 9.y) is: S 38Ci / g g 38Ci / g 0.38Ci S m (secular equilibrium) 600y d y 64h 90 4 h 365 d 0.38Ci 0.5µ g Ci / g 5 Ci / g

29 Example sample conains mci of Os 9 a ime 0. The isoope decays by β- emission ino measable Ir 9m which hen decay by γ emission ino Ir m γ 9 77 Os Ir β 5.4d 4.94s Ir

30 Example (a) how many grams of Os 9 are presen a 0? (b) how many mci of Ir 9m are presen a 5 d? (c) how many aoms of Ir 9m decay beween 00s and 0s? (c) how many aoms of Ir 9m decay beween 30d and 40d?

31 Soluion Secular equilibrium is reached a 7X s Thus, a he equilibrium However, during he ime considered a (b) and (d) will have decayed appreciably (ransien equilibrium)

32 Soluion (a) Grams of Os S Ci 8 m.3 0 g Ci / g (b) 5d 4 Ci / g /5.4 e 0. 35mCi

33 Soluion (c) Beween 00s and 0 s secular equilibrium exiss wih he osmium source essenially sill a is original 00s mci during he nex s #aoms s s s

34 Soluion (d) Beween 30 and 40s and do no say consan Transien equilibrium exiss, so he # of aoms of Paren and Daugher ha decay are equal e / ( ) e