1 / 45

Kinetics of Radioactive Decays

Kinetics of Radioactive Decays. Kinetics of First Order Reactions. 2.1 First-Order Decay Expressions. 2.1 (a) Statistical Considerations (1905) Let: p = probability of a particular atom disintegrating in time interval t.

fala
Download Presentation

Kinetics of Radioactive Decays

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Kinetics of Radioactive Decays

  2. Kinetics of First Order Reactions

  3. 2.1 First-Order Decay Expressions • 2.1 (a) Statistical Considerations (1905) • Let: p = probability of a particular atom disintegrating in time interval t. Since this is a pure random event; that is, all decays are independent of past and present information; then each t gives the same probability again. Total time = t = n t

  4. 2.1 First-Order Decay Expressions • 2.1 (a) Statistical Considerations (1905) Note: typo “+”

  5. 2.1 First-Order Decay Expressions • 2.1 (b) Decay Expressions: • (i) N-Expression

  6. 2.1 First-Order Decay Expressions Excel Example

  7. 2.1 First-Order Decay Expressions • 2.1 (b) Decay Expressions: • (ii) A-Expression • Define: A = Activity (counts per second or disintegrations per second) For fixed geometry:

  8. 2.1 First-Order Decay Expressions • 2.1 (b) Decay Expressions: • (ii) A-Expression • Define: A = Activity (counts per second or disintegrations per second) A = c  N Where: c = detection coeff. N A

  9. 2.1 First-Order Decay Expressions • 2.1 (c) Lives • (i) Half-life: t1/2 • Defined as time taken for initial amount ( N or A ) to drop to half of original value.

  10. 2.1 First-Order Decay Expressions Note: What is N after x half lives?

  11. 2.1 First-Order Decay Expressions • 2.1 (c) Lives • (ii) Average/Mean Life:  (common usage in spectroscopy) • Can be found from sums of times of existence of all atoms divided by the total number.

  12. 2.1 First-Order Decay Expressions • 2.1 (c) (ii) Average/Mean Life:  (common usage in spectroscopy) 

  13. 2.1 First-Order Decay Expressions • 2.1 (c) Lives • (iii) Comparing half and average/mean life 1.44 t1/2 Why is  greater than t1/2 by factor of 1.44?  gives equal weighting to those atoms that survives a long time!

  14. 2.1 First-Order Decay Expressions • 2.1 (c) Lives (iii) Comparing half and average/mean life What is the value of N at t =  ? Excel Example

  15. 2.1 First-Order Decay Expressions • 2.1 (d) Decay/Growth Complications • Kinetics can get quite complicated mathematically if products are also radioactive (math/expressions next section) • Examples:

  16. 2.1 First-Order Decay Expressions • 2.1 (e) Units of Radioactivity • Refers to “Activity” • 1 Curie (Ci) = the amount of RA material which produces 3.700x1010 disintegrations per second. • SI unit => 1 Becquerel (Bq) = 1 disintegration per second • Example (1): Compare 1 mCi of 15O ( t1/2 = 2 min ) with 1 mCi of 238U ( t1/2 = 4.5x109 y ) • Use “Specific Activity” = Bq/g ( activity per g of RA material )

  17. 2.1 First-Order Decay Expressions • 2.1 (e) Units of Radioactivity • Rad = quantitative measure of radiation energy absorption (dose) • 1 dose of 1 rad deposits 100 erg/g of material • SI dose unit => gray (Gy) = 1 J/kg; 1 Gy = 100 rad • Roentgen (R) = unit of radiation exposure; • 1 R = 1.61x1012 ion pairs per gram of air. • More Later !

  18. 2.1 First-Order Decay Expressions • 2.1 (e) Units of Radioactivity: • Example (2): Calculate the weight (W) in g of 1.00 mCi of 3Hwith t1/2 = 12.26 y .

  19. 2.1 First-Order Decay Expressions • 2.1 (e) Units of Radioactivity: • Example (3): Calculate W of 1.00 mCi of 14C with t1/2 = 5730 y . • Example (4): Calculate W of 1.00 mCi of 238U with t1/2 = 4.15x109 y .

  20. 2.1 First-Order Decay Expressions • 2.1 (e) Units of Radioactivity:

  21. 2.2 Multi-Component Decays • 2.2 (a) Mixtures of Independently Decay Activities

  22. 2.2 Multi-Component Decays • 2.2 (a) Mixtures of Independently Decay Activities • Resolution of Decay Curves • (i) Binary Mixture ( unknowns 1 , 2 , initial A1 & A2 ) Excel plot

  23. 2.2 Multi-Component Decays • 2.2 (a) Mixtures of Independently Decay Activities • Resolution of Decay Curves • (ii) If 1 & 2 are known but 12(not very different) • (iii) Least Square Analysis ( if only At versus t ) [Multi-parameter fitting software]

  24. 2.2 Multi-Component Decays • 2.2 (b) Relationships Among Parent and RA Products • Consider general case of Parent(N1)/daughter(N2) in which daughter is also RA. • (i) If (2) is stable • (ii) If (2) is RA and (3) is stable

  25. 2.2 Multi-Component Decays • 2.2 (b) Relationships Among Parent and RA Products • N2equation (2.8) and its variations.

  26. 2.2 Multi-Component Decays • 2.2 (b) Relationships Among Parent and RA Products • N2equation (2.8) and its variations … cont.

  27. 2.2 Multi-Component Decays • 2.2 (c) Equilibrium Phenomena (Transient & Secular): Parent longer lived • Consider equation (2.8) • (1) Transient Equilibrium ( 1 < 2 ) • (i) When t is large:

  28. 2.2 Multi-Component Decays • 2.2 (c) Equilibrium Phenomena (Transient & Secular): Parent longer lived • Consider equation (2.8) • (1) Transient Equilibrium ( 1 < 2 ) • (ii) for activities Note: Main point is that for transient equilibrium, after some time, both species will decay with 1 .

  29. 2.2 Multi-Component Decays • 2.2 (c) Equilibrium Phenomena (Transient & Secular): Parent longer lived • Consider equation (2.8) • (1) Transient Equilibrium ( 1 < 2 ) • (iii) A1 + A2 (starting with pure 1) • Will go through a maximum before transient equilibrium is achieved.

  30. 2.2 Multi-Component Decays • 2.2 (c) Equilibrium Phenomena (Transient & Secular): Parent longer lived • Consider equation (2.8) • (1) Transient Equilibrium ( 1 < 2 ) • (iii) A1 + A2 (starting with pure 1) • Will go through a maximum before transient equilibrium is achieved.

  31. 2.2 Multi-Component Decays • 2.2 (c) Relationships Among Parent and RA Products • (2) Secular Equilibrium ( 1 << 2 )

  32. 2.2 Multi-Component Decays • 2.2 (c) Relationships Among Parent and RA Products • (2) Secular Equilibrium ( 1 << 2 ) … cont.

  33. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (i) If parent is shorter-lived than daughter ( 1 > 2 )

  34. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (i) If parent is shorter-lived than daughter ( 1 > 2 ) … cont. Note: If parent is made free of daughter at t=0, then daughter will rise, pass through a maximum ( dN2/dt=0 ), then decays at characteristic 2 .

  35. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (i) If parent is shorter-lived than daughter ( 1 > 2 ) … cont.

  36. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (ii) If parent is shorter-lived than daughter ( 1 >> 2 )

  37. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (ii) If parent is shorter-lived than daughter ( 1 >> 2 ) At large t, extrapolate back to t=0 to get c22N1o and slope=-2

  38. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (ii) If parent is shorter-lived than daughter ( 1 >> 2 ) … cont. • Useful Ratio:

  39. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (iii) Use of tm for both transit & non-equilibrium analysis Idea: Differentiate original N2 equation to get maximum ( with N2o = 0 )

  40. 2.2 Multi-Component Decays • 2.2 (d) Non-Equilibrium Cases • (iii) Use of tm for both transit & non-equilibrium analysis Idea: Differentiate original N2 equation to get maximum ( with N2o = 0 ) Note: tm =  for secular equilibrium .

  41. 2.2 Multi-Component Decays • 2.2 (e) Many Consecutive Decays: (note: previous N1 & N2 equations are still valid.) H. Bateman gives the solutions for n numbers for pure N1o at t=0. (i.e. N2o = N3o = Nno = 0) Can also be found for N2o , N3o , N4o … Nno 0 . But even more tedious!

  42. 2.2 Multi-Component Decays • 2.2 (f) Branching Decays • Nuclide decaying via more that one mode.

  43. 2.2 Multi-Component Decays • 2.2 (f) Branching Decays • Example: 130Cs has a t1/2 = 30.0 min and decays by + and - emissions. It is found that for every 2 atoms of 130Ba in the products there are 55 atoms of 130Xe. Calculate (t1/2)- and (t1/2)+ .

  44. 2.2 Multi-Component Decays • 2.2 (f) Branching Decays • Example: 130Cs has a t1/2 = 30.0 min and decays by + and - emissions. It is found that for every 2 atoms of 130Ba in the products there are 55 atoms of 130Xe. Calculate (t1/2)- and (t1/2)+ . (t1/2)-= 855 min (t1/2)+ = 31.1 min

  45. Kinetics of Radioactive Decays

More Related