Radioactive Decay Activity: the number of atoms that decay per unit time: (disintegrations persecond). Units: Becquerel (Bq) = 1 dps Curie (Ci) [old unit] = 3.7 x 1010 Bq exactly (originally defined as the activity of 1.0 g of radium Exponential Decay: Activity (A) of a radioactive nuclide decreases exponentially with time. Let N = # atoms present dN = -λN dt The constant of proportionality, λ, has units of sec-1. -dN A = λN dt Each radioactive nuclide has a unique decay constant λ. dN dN = λN ∫ = -λ∫dt N N ln N = -λt + c When t = 0, N0 atoms are present - implies that ln N0 = c ln N = - λt + ln N0 N N In = -λt = e-λt or N = N0 e -λt N0 N0 or A = A0 e -λt Half-Life (t1/2 or T)  - ln 2 = - λt? 0.693 = λt? 0.693 0.693 λ = t ? = t ? λ  Specific Activity Specific Activity (SA) defined as activity per unit mass. Bq Ci Units : or g g A = λN N = # of atoms  A λN 6.02 x 1023 SA = = SA= λ g g M Example: Specific activity of radium g .693 M = 226 t? = 1600y λ= mole t?  3.66x1010 atoms 3.66x1010 Bq SA = = g ? sec g 1 Ci = 3.66 x 1010 dps 1 Ci orig. defined as activity associated with 1 g of Radium. Ci is now defined as 3.7 x 1010 dps exactly. Count rates - vs half-life Example: Compound A: t? = 45 min Compound B: t? = 45 years Given 1010 atoms of each - find the activity (A) 0.693 A=λN λ= [λ = 2.5 x 10-4 sce-1] t ?  AA= 2.56 x 106 Bq 0.693 AB= 1010 [λ = 4.8 x 10-10 sec-1] (45y)(365)(24)(60)(60) AB = 4.8 Bq 239Pu t? = 24,065 y 235U t? = 7.038 x 108 y Serial Radioactive Decay N1 → N2 N10 = # parent atoms present at t = 0. N20 = # daughter atoms present at t = 0. General Case  Secular equilibrium (T1 >> T2) Simplifying assumptions: A20 = 0 T1 is large, ∴ λ1 is small; λ2 -λ1 = λ2 e-λ1t ? 1 General Case simplifies to A2 = A10 (1-e-λ2t) after ~ seven half-lives (of N2 daughter), e-λ2t ≈ 0 A2 = A10  Radon Decay Mass Number  ? Radon itself, due to its fairly short half-life (222Rn) is not a major concern. ? Radon is also an inert gas and is typically exhaled after breathing it in (although some will dissolve in the blood). ? The concern is over the daughter products of radon that are particulate (attached to aerosol particles), α-emitting, and decay within hours to 210Pb (T1/2 = 22 years). Transient equilibrium (T1 ≧ T2) General Case  Simplifying assumptions: A20 = 0 after ~ 10t?s e-λ2t << e-λ1t λ2 A2 =A10 e-λ1t by definition: A10 e-λ1t = A1 λ2 -λ1 λ2 A2 λ2 A2 =A1 or = - at equilibrium A1 and A2 present in a λ2 –λ2 A1 λ2 –λ1 constant ratio  No equilibrium (T1 < T2) [no simplifying assumptions possible]   The 99mTc Generator: Transient equilibrium in action ? 99Mo is adsorbed on an alumina column as ammonium molybdate (NH4MoO4) ? 99Mo (T = 67 hrs) decays (by β -decay) to 99mTc (T = 6 hrs) ? 99MoO4 ion becomes the 99mTcO4 (pertechnetate) ion (chemically different) ? 99mTcO4 has a much lower binding affinity for the alumina and can be selectively eluted by passing physiological saline through the column.   EDTA ethylenediaminetetraacetate  DTPA  Chelator Kits