Genetically dependent nuclides!when a radioactive nuclide disintegrates to a nucløide which in turn also is radioactive, we say that the two are genetically dependent!there can be many consecutive nuclides in a genetic series, for instance: in the disintegration of 238 U, the nucleus ends in 206 Pb after 14 disintegrations. Important example: 99 Mo (66h) 99m Tc (6.0h) 99 Tc (213 000 y)
Genetic dependence Decay 1 Decay 2 Decay 3 Nuclide 1 Nuclide 2 Nuclide 3 Nuclide 4 For genetically dependent nuclides it is important to remember that the same atom changees all the time, and goes through different stages before ending up as stable.
Genetically dependent nuclides ctd. Other important examples: 210 Pb (22.3y) 210 Bi (5.0d) 210 Po (138 d) 206 Pb (stab.) 49 Cr (42m) 49 V (330d) 49 Ti (stable) 90 Sr (29y ) 90 Y (2.7d) 90 Zr (stable ) 137 Cs (30y ) 137m Ba (2.6m) 137 Ba (stable)
Mother/daughter relations!we have two genetically connected radionuclides, 1 and 2!Nuclide 1 nuclide 2 stable We want an expression of disintegration rates as function of time and start-conditions. Assume that nuclide 1 is the first. Then we have: N 1 = N 1,0 e - t in the time interval, the increase in N2 is: dn 2 = ( N 1-2 N 2 ) or: dn 2 + 2 N 2 - N 1,0 e - t =0
Mother/daughter relations Solve this differential equation: dn N2 uv, 2 du = v + u v du + u Demand: dv u( dv Gives: v = e - 2 t dv + 2 uv - N 1,0 e - t = 0 + 2 v ) = 0 du e - 2 t - N 1,0 e - t = 0 or du = 1 N 1,0 e -( - 2 )t INTEGRATE u= N 1,0 e -( - 2 )t + C 2 -
Mother/daughter relations. N 2 = uv = N 2,0 = N 1,0 e - t + Ce - 2 t 2 - C must be determined N 1,0 + C 2 - N1,0 C= N 2,0-2 - N = N e - 2 1,0 1 t - N e -,0 2 t + N e - 2,0 2 t 2-2 - = N 1,0 (e - t -e - 2 t )+ N 2,0 e - 2 t 2 - = N 1,0 e - t (1-e -( 2 - )t )+ N 2,0 e - 2 t 2 - = N 1 (1-e -( 2 - )t )+ N 2,0 e - 2 t 2 - D 2 = 2 N 2 = 2 D 1,0 e - t (1-e -( 2 - )t )+ D 2,0 e - 2 t 2 - D 1
Mother/daughter relations. Frequently,N 2,0 and D 2,0 are 0: N 2 = N 1 (1-e -( 2 - )t ) 2-2 D 2 = D 1 (1-e -( 2 - )t ) 2 - Saturation factor If << 2 : N 1 = N 1 (1-e - 2 t 2 ) 2 D 2 = D 1 (1-e - 2 t )!Saturation factor: 0,999 after 10 daughter nuclide halflives Then N 1 = 2 N 2 og D 1 = D 2!With more steps in the chain and T ½ (1)>>T ½ (2): N 1 = 2 N 2 =... n N n1 and D 1 = D 2...= D n
Genetic independence T ½ (1)<<T ½ (2) total
Mother/daughter relations, three cases! Short mother, long daughter ( >> 2 ), T ½ (1)<<T ½ (2) No equilibrium! Long mother, shorter daughter ( < 2 ), T ½ (1)>T ½ (2) Transient equilibrium may occur! Very long mother,short daughter ( << 2 ), T ½ (1)>>T ½ (2) Secular equilibrium may occur
Genetically dependent nucl i des T ½ (1)<<T ½ (2) Total Daughter nuclide Mother nuclide
T ½ (1) >> T ½ (2) Total activity Daughter growth Short, separated daughter!equilibrium after approx.10 T ½!The daughter nuclide may be chemically isolated, and reappears.
T ½ (1)>T ½ (2), transient equilibrium Total activity Daughter ingrowth Short, separate daughter Also applicable as isotope generator.
"Isotope generator! An isotope generator is a system where a short-lived daughter nuclide (or a nuclide further sown in the sequence) is allowed to grow in, whereafter it is separated from the mother activity utilising differences in chemical properties:! Some useful examples 99 Mo/ 99m Tc 68 Ge/ 68 Ga 228 Th/.../ 212 Pb 227 Ac/ 227 Th/ 223 Ra 238 U/.../ 226 Ra/ 222 Rn! The latter is a natural isotope generator used by Marie and Pierre Curie to obtain Ra from uraniumcontaining minerals.
99m Tc-generator Generator for elution of 99m Tc (as water soluble 99m TcO 4 - ) from unsoluble 99 Mo 2 O 3 (adsorbed on Al 2 O 3 )