Radioactive decay, kinetics and equilibrium

Radioactive decay, kinetics and equilibrium

1. RASHTRASANT TUKADOJI MAHARAJ NAGPUR UNIVERSITY DEPARTMENT OF CHEMISTRY RADIOACTIVE DECAY, KINETICS, EQUILIBRIUM PRESENTED BY: BIJI SARO VARGHESE M.Sc. II Sem III 4/10/2018 1

2. CONTENTS 1.RADIOACTIVE DECAY 2.RADIOACTIVE KINETICS 3.RADIOACTIVE EQUILIBRIUM 2

3. Radioactive Decay Radioactive decay is a spontaneous phenomenon of emission of particles or electromagnetic radiation from an atomic nucleus. The phenomenon of radioactivity was discovered by Henri Becquerel in 1896 and the radiations emitted were called as Becquerel rays or Uranic rays . Pierre and Marie Curie introduced the term Radioactivity for this phenomenon 3

4. Radioactive decay results in the emission of either: an alpha particle ( α ), a beta particle ( β ), a gamma ray ( γ ) or fission fragments 4

5. A nucleus undergoing alpha decay emits an alpha particle [ ] +2 which is helium nucleus with two protons and two neutrons. Atomic and mass no. of the product nucleus are reduced by 2and 4 units respectively. Alpha Decay 5 2 He 4

6. Y A - 4 Z - 2 + He +E α 4 2 unstable atom more stable atom alpha particle 2 32 U 92 90 2 28 Th + 4 He +E α 2 6 X A Z

7. Beta decay In beta decay the charge of the resulting product nucleus differs from the starting nucleus by one unit and there is no change in mass number. Beta decay comprises of three processes: Negatron decay( β - ) 7 132 I 53 54 132 Xe + β - + ν + E β

8. 10 172 Lu 71 70 172 Yb + ν 8 ii. Positron decay( β + ) 2 2 Na 11 2 2 Ne + β + + ν + E β iii. Electron capture(EC)

9. Gamma deexcitation Alpha and beta decay quite often leave the daughter product nucleus in excited states. When an excited state of a nucleus undergoes deexcitation ,electromagnetic radiation, known as gamma rays, is emitted. 9

10. 60 Co * 29 30 60 Ni * + β - + ν 60 Ni * 30 30 60 Ni + γ 10

11. Spontaneous fission Spontaneous fission is a decay process in which a nucleus undergoes division into two fragments along with emission of 2-3 neutrons. This is prevalent in isotopes of heavy elements. 11 252 Cf 92 F 1 + F 2 +3.76 neutrons

12. RADIOACTIVE KINETICS The rate of decay of a radioisotope is proportional to the number of atoms of that isotope present at that instant. Radioactive decay follows the first order kinetics. - = λ N ………(1) where, N=no. of atoms at any time t λ =disintegration constant (time - )   12

13. On integration of eqn.(1) N=N e - λ t ……….(2) Where, N =no. of atoms at the initial time Radioisotopes are estimated by measuring radioactivity or simply activity (A),i.e. the product of decay constant ( λ ) and the no. of atoms present (N) rather than N alone A=N λ ………….(3) Activity has unit of disintegration per unit time The units of radioactivity are: 1 Becquerel(Bq)=1dps 1Curie(Ci)=3.7 x 10 10 dps 13

14. Combining equation 2 and 3, a relation for activity as a function of time is obtained. A=A e - λ t ………..(4) 14 Fig no.1 Decay scheme of 32 P on a linear plot

15. Half life The time required for the decay of half of the parent atoms to daughter products is defined as the half-life(t 1/2 ) of the parent nuclide. Thus , t=t 1/2 when N=N /2 Substituting in equation 2 and simplifying we get, = …………….(5) And t 1/2 = ……………(6)   15 1/2

16. Half life of the radioisotope is determined from the activity profile(fig 1). Taking log of equation no.4 log A=logA - λ t ………….(7) A straight line is obtained when logA is plotted as a function of time on a semi log paper. Half – life is a unique characteristic of each isotope. 16

17. Fig no.2 Log of activity as a function of time 17

18. Mean life The life time of radioactive isotope varies from 0 to∞ The average time that an atom of a radioisotope can survive is called mean life( τ ) which is obtained by dividing sum of the life times of all the atoms by the initial number of atoms. The mean life is given by τ = - ………….(8)   18

19. = = ………..(9) By partial integration of equation no. 9 we get, …………..(10)   19

20. Branching decay The total decay constant ( λ ) of the nuclide is given by the sum of the partial decay constants; λ = λ 1 + λ 2 + …. Let the nuclide X decays to two daughter products Y and Z, having corresponding decay constants as λ 1 and λ 2 respectively. λ 1 Y X λ 2 Z λ = λ 1 + λ 2 20

21. Rate of decay of X is ………..(11) Total half-life of X is related to partial half-lives as Thus the total half-life of X is shorter than any of the individual partial half-lives.   21 X X Z X Y

22. RADIOACTIVE EQUILIBIUM The condition of constant ratio of parent and daughter activity is called equilibrium. Half life of daughter< half life of parent But, if Half life of daughter> half life of parent Then, no equilibrium 22

23. TRANSIENT EQUILIBRIUM In the cases where decay constants λ 1 (parent) and λ 2 (daughter) are in the ratio of 0.1, the equilibrium is called transient equilibrium. A typical example is 23 99 Mo 99m Tc 99 Tc β - IT 6.01 h 65.94 h

24. Fig no.3 Activity profile in a transient equilibrium case Curve a: total activity of the parent and daughter Curve b: represents the decay of pure parent Curve c: represents growth of daughter product Curve d: extrapolation of c, represents activity of daughter Curve e: (curve c - curve d) represents the decay of pure daughter fraction 24

25. SECULAR EQUILIBRIUM If the half life of the parent isotope is much longer than the half life of the daughter isotope( λ 2 >> λ 1 ), then the equilibrium is called secular equilibrium. In this condition, the total activity of the parent and daughter reaches the maximum and does not decrease appreciably for several half-lives of the daughter product. Decay of 144 Ce is an example of secular equilibrium. 25 β - 17.28 min β - 284.893 d 144 Ce 144 Pr 144 Nd

26. Fig no.4 Activity profile in a secular equilibrium case Curve a: total activity of the parent and daughter Curve b: represents activity due to parent which is equal to daughter activity Curve c: represents growth of daughter activity in pure fraction Curve d: represents decay of the daughter product 26

27. NO EQUILIBRIUM If the decay constant of parent is larger than that of the daughter i.e. λ 1 > λ 2 ,then the parent decays faster than the growth of the daughter product. This does not satisfy the equilibrium condition of constant activity ratio at any point of time after preparing the pure parent sample and therefore represents a no equilibrium case. For example, 138 Xe is short lived compared to its daughter product 138 Cs. 27 β - 14.08 min 33.41 min β - 138 Xe 138 Cs 138 Ba

28. Fig no.5 Activity profile in a no equilibrium case Curve a: total activity of the parent and daughter Curve b: represents the decay of pure parent Curve c: represents growth of daughter product Curve d: extrapolation of c, represents decay of pure daughter 28

29. 29 1. D.D.Sood , A.V.R.Reddy and N.Ramamoorthy , Fundamentals of radiochemistry , IANCAS publication, 2007 2. H.J.Arnikar , Essentials of nuclear chemistry, New age international publishers,2014,Fifth edition

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