Radioactive Decay. or N = N 0 e -λt. or A = A 0 e -λt 1

Transcription

1 Radioacive Decay Aciviy: Unis: he number of aoms ha decay per uni ime: (disineraions per second). Becquerel (Bq) = 1 dps Curie (Ci) [old uni] = 3.7 x Bq exacly (oriinally defined as he aciviy of 1.0 of radium Exponenial Decay: Aciviy (A) of a radioacive nuclide decreases exponenially wih ime. Le = # aoms presen d = - d The consan of proporionaliy,, has unis of sec -1. d d A = = Each radioacive nuclide has a unique decay consan. d = d d = d ln = - + c When = 0, 0 aoms are presen - implies ha ln 0 = c ln = - + ln 0 ln = 0 - = e - 0 or = 0 e - or A = A 0 e - 1

2 Half-Life ( 1/ or T) When = / = e o 0 1 e = 1 / - ln = - ½ = ½ = ½ 1 / = Imae removed due o copyrih resricions. Fi. 4.1 in Turner J. E. Aoms, Radiaion, and Radiaion Proecion, nd ed. ew York, Y: Wiley-Inerscience, 1995.

3 Specific Aciviy Specific Aciviy (SA) defined as aciviy per uni mass. Unis: Bq or Ci A = = # of aoms 3 aoms 6.0x10 = mole rams M mole = aoms A SA = = SA= 6.0x10 M 3 Example: Specific aciviy of radium M = 6 ½ = 1600 y = mole.693 ½ SA = 3 aoms 6.0x10 mole y 1d 1h 1m y 365d 4h 60 min 60 sec mole SA = x10 aoms sec = 3.66x10 10 Bq 1 Ci = 3.66 x dps 1 Ci ori. defined as aciviy associaed wih 1 of Radium. Ci is now defined as 3.7 x dps exacly. 3

4 Coun raes - vs half-life Example: Compound A: ½ = 45 min Compound B: ½ = 45 years Given aoms of each - find he aciviy (A) A = = ½ [ =.5 x 10-4 sec -1 ] A A = ( ) 60sec 45min min aoms A A =.56 x 10 6 Bq A B = ( 45y)( 365)( 4)( 60)( 60) [ = 4.8 x sec -1 ] A B = 4.8 Bq 39 Pu ½ = 4,065 y 35 U ½ = x 10 8 y 4

5 Serial Radioacive Decay 1 10 = # paren aoms presen a = 0. 0 = # dauher aoms presen a = 0. General Case d 1 = 11 A = A10 ( e e ) + A0e d 1 Secular equilibrium (T 1 >> T ) Simplifyin assumpions: A 0 = 0 - T 1 is lare, 1 is small; - 1 = e 1 1 General Case simplifies o A = A ( 1 e ) afer ~ seven half-lives (of dauher), e 0 A = A A 1 A = A 1 Aciviies A Secular Equilibrium T 1 >> T 0 ~7T Aciviy A of relaively shor-lived radionuclide dauher (T << T 1 ) as a funcion of ime wih iniial condiion A 0 = 0. Aciviy of dauher builds up o ha of he paren in above seven half-lives (~7T ). Thereafer, dauher decays a he same rae i is produced (A = A 1 ), and secular equilibrium is said o exis. 5 Fiure by MIT OCW.

6 Mass umber Radon Decay 6 Radium 160y Radon 3.8d Shor-lived radon dauhers 18 Polonium 3.05m (Radium A) 0.019% Asaine s Radon 0.035s 14 Lead 6.8m (Radium B) Bismuh 19.7m (Radium C) Polonium s (Radium C) 0.01% 10 Thallium 3.1m Lead Bismuh y 5d Polonium 138d % % 06 Mercury 8m Thallium 4m Lead Radon iself, due o is fairly shor half-life ( Rn) is no a major concern. Radon is also an iner as and is ypically exhaled afer breahin i in (alhouh some will dissolve in he blood). The concern is over he dauher producs of radon ha are pariculae (aached o aerosol paricles), -emiin, and decay wihin hours o 10 Pb (T 1/ = years). 6

7 Transien equilibrium (T 1 T ) General Case d 1 = 11 A = A10 ( e e ) + A0e d 1 Simplifyin assumpions: A 0 = 0 A = A 10 A = A 1 1 or e - 1 A A 1 = 1 e afer ~ 10½s << e 1 1 by definiion: A10 e = A1 - a equilibrium A 1 and A presen in a consan raio T 1 >~ T A 1 +A Aciviies A 10 A 1 Transien Equilibrium A A 1 +A A 0 A 1 Aciviies as funcions of ime when T 1 is somewha larer han T (T 1 >~ T ) and 0 = 0. Transien equilibrium is evenually reached, in which all aciviies decay wih he half-life T 1 of he paren. Fiure by MIT OCW. 7

8 o equilibrium (T 1 < T ) [no simplifyin assumpions possible] d 1 = 11 A = A10 ( e e ) + A0e d 1 A 10 T > T 1 Aciviies A 1 A 1 +A A 0 Aciviies as funcions of ime when T > T 1 and 0 = 0. o equilibrium condiions occur. Evenually, only he dauher aciviy remains. Fiure by MIT OCW. 8

9 The 99m Tc Generaor: Transien equilibrium in acion 99 Mo is adsorbed on an alumina column as ammonium molybdae (H 4 MoO 4 ) 99 Mo (T = 67 hrs) decays (by -decay) o 99m Tc (T = 6 hrs) 99 MoO 4 ion becomes he 99m TcO 4 (perechneae) ion (chemically differen) 99m TcO 4 has a much lower bindin affiniy for he alumina and can be selecively elued by passin physioloical saline hrouh he column. Imae removed due o copyrih resricions. 9

10 EDTA ehylenediamineeraaceae O O - O O - O - O O - O DTPA 10

11 Chelaor Kis Imae removed due o copyrih resricions. 11