Genetically dependent nuclides

Transcription

1 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 ( y)

2 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.

3 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)

4 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 N 2 - N 1,0 e - t =0

5 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 = 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 -

6 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 = 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

7 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

8 Genetic independence T ½ (1)<<T ½ (2) total

9 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

10 Genetically dependent nucl i des T ½ (1)<<T ½ (2) Total Daughter nuclide Mother nuclide

11 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.

12 T ½ (1)>T ½ (2), transient equilibrium Total activity Daughter ingrowth Short, separate daughter Also applicable as isotope generator.

13 "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.

14 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 )