Radioactive Decay

1. Radioactive Decay Professor Jasmina Vujic Lecture 3 Nuclear Engineering 162 Department of Nuclear Engineering University of California, Berkeley

2. Spontaneous Nuclear Transformation - Radioactivity • Only certain combinations of protons and neutrons form a stable nucleus • Unstable nuclei undergo spontaneous nuclear transformations, with a formation of new elements and emission of charges and/or neutral particles • These unstable isotopes are called radioactive isotopes, and the spontaneous nuclear transformation is called radioactivity.

3. Types of Radioactive Decay • The type of radioactive decay depends on the particular type of nuclear instability (whether the neutron to proton ratio is either too high or too low) and on the mass-energy relationship among the parent nucleus, daughter nuclear, and emitted particle.

4. Types of Radioactive Decay • Usually, radioactive decays are classified by types of particles that are emitted during the decay: • Alpha decay • Beta decay • Gamma decay • Electron capture (EC) • Internal conversion (IC) • Spontaneous fission • Isomeric transition (IT) • Neutron emission

6. Four types of radioactive decay 1) alpha (a) decay - 4He nucleus (2p + 2n) ejected 2) beta () decay - change of nucleus charge, conserves mass 3) gamma (g) decay - photon emission, no change in A or Z 4) spontaneous fission - for Z=92 and above, generates two smaller nuclei

7. Induced Nuclear Transformations - Nuclear Reactions • An event in which, because of interaction with a particle or radiation (a projectile), a nucleus (target) is changed in mass, charge or energy state, and particles or radiation is emitted.

8. The Conservation Laws in Nuclear Transformations (NT) • Conservation of Charge - the number of elementary positive and negative charges must be equal before and after NT • Conservation of the number of nuclides - A is the same before and after NT • Conservation of mass/energy - the total energy (rest mass energy plus kinetic energy) is the same before and after NT • Conservation of linear momentum • Conservation of angular momentum

9. Alpha Decay • Heavy nuclei with mass numbers higher than 150 can disintegrate by emission of an ALPHA PARTICLE. • Alpha particle is a nucleus of helium containing two neutrons and two protons: • Example

10. a decay - involves strong and coloumbic forces - alpha particle and daughter nucleus have equal and opposite momentums (i.e. daughter experiences “recoil”)

11. Alpha Decay

12. Beta Decay • Beta minus decay: • Neutron →proton (p+) + electron (e-) + antineutrino • Beta plus decay: • Proton (p+) → neutron + positron (e+) + neutrino

13.  decay - two types 1) - decay - converts one neutron into a proton and electron - no change of A, but different element - release of anti-neutrino (no charge, no mass) 2) + decay - converts one proton into a neutron and a positron - no change of A, but different element - release of neutrino

14. Beta Decay

15. Gamma Decay • Sometimes the newly formed isotopes (after alpha or beta decay) appear in the excited state (with a surplus of energy). Excited nuclides have tendency to release the excess of energy by emission of gamma rays (Photons) and return to their ground state.

16. Beta-EC-Gamma Decay

17. Beta-Gamma Decay

18. Beta-Gamma Decay

19. Orbital Electron Capture (EC) • In addition, an X-ray characteristic of the daughter element is emitted as an electron from an outer shell falls into K-shell. Internal Conversion (IC) • Is an alternative mechanism in which an excited nucleus may rid itself of the excitation energy from the nucleus by ejecting a tightly bound electron (K or L shell).

20. Electron Capture

22. Spontaneous Fission • This is another type of decay that heavy nuclei can undergo: they decay by splitting into two lighter nuclei with the release of several neutrons: • In addition, large amount of energy is released per fission event. Similar process called INDUCED FISSION is used in nuclear reactor.

23. g decay - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay Spontaneous fission - heavy nuclides split into two daughters and neutrons - U most common (fission-track dating) Fission tracks from 238U fission in old zircon

24. Isomeric Transition (IT) • A nuclide formed after a nuclear transformation may be a long-lived metastable or isomeric state. The decay of isomeric state by emission of gamma rays is called isomeric transition (IT). • Mo-99 decay by beta(-) decay into Tc-99m metastable state of Tc-99. It decays by gamma ray emission into Tc-99 ground state with 6 hr half-life.

25. Neutron Emission • There are nuclides which undergo a spontaneous transformation with emission of neutrons: • Br-87 (55.6 s), I-137 (22.0 s), Br-88 (15.5 s)

28. The Radioactive Decay Law • The rate at which a radioactive isotope disintegrates is defines by the following DECAY LAW: • Where • N: Number of atoms of a radioactive isotope at time t • N0: Number of atoms at time zero • λ: Decay constant (each isotope has different ) • tH: Half-life (each isotope has different half-life)

29. The Radioactive Decay Law

30. Radioactive Decay - a radioactive parent nuclide decays to a daughter nuclide - the probability that a decay will occur in a unit time is defined as l (units of y-1) -the decay constant l is time independent; the mean life is defined as =1/l N0 t1/2 = 5730y 5730

31. The Radioactive Decay Law

32. Derivation The solution is easily found using an integrating factor: Where N0 is the number of nuclei at t = 0.

33. Derivation of Decay Law If there is no source (Q = 0), the result is simple exponential decay: Activity is then defined as Probability of decay between t and (t+dt) is

34. The Mean Lifetime The probability density function (pdf) for radioactive decay is defined as: The mean lifetime of radionuclide is defined as

35. The Half-life Units of activity 1 Ci (curie) = 3.7 x 1010 dis/s 1 Bq (becquerel) = 1 dis/s

36. Activity calculations - SA (Specific activity) = disintegrations per sec per g of parent atom) - usually reported in Bq (disintegrations per sec), example (calculate SA of 14C)= ? Bq / gram C - because activity is linearly proportional to number N, then A can be substituted for N in the equation Example calculation: How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD? T=200y t1/2 = 5730y so l = 0.693/5730y = 1.209e-4 y-1 N0=A0/l so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms N(14C)=N(14C)0*e-(1.209e-4/y)*200y = 5.76e10 atoms # decays = N0-N = 2.4e9 decays

37. Serial Radioactive Decay (Chain Decay) • A simple case of chain decay is the decay of a radionuclide (Parent) to a second radionuclide (Daughter), which then decays to a stable element:

38. Serial Radioactive Decay (Chain Decay)

39. General Cases for Chain Decay • There are three general cases for formulating chain decay: • Secular Equilibrium, Tp >> Td • Transient equilibrium, Tp > Td • No equilibrium

40. 234Th 24d Decay chains and secular equilibrium - three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached 238U --> radioactive daughters --> 206Pb Also 235U (t1/2)= 700My And 232Th (t1/2)=10By After ~10 half-lives, all nuclides in a decay chain will be in secular equilibrium, where

41. Secular Equilibrium

42. Decay chains and secular equilibrium (cont) Ex: where l1>>l2 The approach to secular equilibrium is dictated by the intermediary, because the parent is always decaying, and the stable daughter is always accumulating.

43. Transient Equilibrium