1. Radioactive Decays transmutations of nuclides
Radioactivity means the emission of alpha () particles, beta () particles, or gamma photons () from atomic nuclei.
Radioactive decay is a process by which the nuclei of a nuclide emit ,  or  rays.
In the radioactive process, the nuclide undergoes a transmutation, converting to another nuclide.
Radioactive Decays

2. A Summary of Radioactive Decay Kinetics
Radioactivity or decay rate A is the rate of disintegration of nuclei. Initially (at t = 0), we have No nuclei, and at time t, we have N nuclei. This rate is proportional to N, and the proportional constant is called decay constant .
dN A = – ––––– =  N Integration gives d t
ln N = ln No –  t or N = No e –  t
Also A = Ao e –  t
What is decay rate? How does decay rate vary with time?
Radioactive Decays

3. Radioactive Decay Kinetics - plot
Number of radioactive nuclei decrease exponentially with time as indicated by the graph here.
As a result, the radioactivity vary in the same manner.
Note l N = A
l No = Ao
Radioactive Decays

4. Decay Constant and Half-life
Ln(N or A)
ln N1 – ln N2  = ––––––––––– t1 – t2
t½ *  = ln 2
Be able to apply these equations!
N = No e– t A = Ao e – t
ln N = ln No –  t ln A = ln Ao –  t
Determine half life, t½ t
Radioactive Decays

5. Radioactive Decay of Mixtures
The graph shows radioactivity of a sample containing 3 nuclides with rather different half life. Explain why, and how to resolve the mixture.
Ln A t
Analyze and explain
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6. Radioactive Consecutive Decay and Growth
Explain the variation of total radioactivity versus time in a sample containing one pure radioactive nuclide, but its daughter is also radioactive with a much shorter half life.
Radioactive Decays

7. Radioactive consecutive decay animation
See Simulation in Radioactive Decay in SCI270 website
The simulation will be used to illustrate various conditions.
Radioactive Decays

8. Applications of Radioactive Decay Kinetic
Half life is not affected by chemical and physical state of matter.
Dating is an application of radioactive decay kinetics. Describe the principle for this method.
Nuclide Half life
219Th90 1 s 26Na11 1s 40Cl min 32P d 14C y 235U x108 y 238U x109 y
Anthropologists, biologists, chemists, diagnosticians, engineers, geologists, physicists, and physicians often use radioactive nuclides in their respective work.
Radioactive Decays

9. Decay and Transmutation of Nuclides
Alpha, a, decay emits a helium nucleus from an atomic nucleus.
Transmutation of Nuclides in Alpha Decays
APZ  A – 4DZ – 2 + 4He2
How do nuclides transform in alpha decay?
Radioactive Decays

10. Nuclide Transmutation of a Decay APZ ® A – 4DZ – 2 + 4He2
Heavy Nuclide alpha emitters
235U92  Th90 + 4a2 (t½, 7.13×108 y)
238U92  234Th90 + 4a2 (t½, 4.51×109 y)
208Po84  204Pb82 + 4a2 (t½, 2.9 y)
How do nuclides transform in alpha decay? Mass and charge change by what?
Radioactive Decays

11. Nuclide Transmutation of a Decay APZ ® A – 4DZ – 2 + 4He2
light nuclides 5He  1n0 + 4a2 (t½, 2×10-21 s), 5Li  1p1 + 4a2 (t½, ~10-21 s), 8Be  2 4a2 (t½, 2×10-16 s).
Some rare earth (144 Nd, 146Sm, 147Sm, 147Eu, Hf) are a emitters: 144Nd  140Ce + 4a2 (t½, 5×1015 y), 174Hf  170Yb + 4a2 (t½, 2×1015 y).
Radioactive Decays

12. Nuclide Transmutation of b Decay
Beta decay consists of three processes: emitting an electron, emitting a positron, or capturing an electron from the atomic orbital.
Electron emission
APZ + n ® ADZ b– (absorbs a neutrino) or APZ ® ADZ b– + n (emit antineutrino, n)
Positron emission
APZ ® ADZ – 1 + b+ + n or APZ + n ® ADZ – 1 + b+.
Electron capture
APZ + e– ® ADZ – 1 + n or APZ + e– + n ® ADZ – 1
What is beta decay?
Radioactive Decays

13. Nuclide Transmutation of b– Decay – examples
Other examples of beta decay
14C6 ® 14N7 + b– + n (t½, 5720 y) 40K19 ® 40Ca20 + b– + n (1.27e9 y) 50V23 ® 50Cr24 + b– + n (6e15 y) 87Rb37 ® 87Sr38 + b– + n (5.7e10 y) 115In49 ® 115Sn50 + b– + n (5e14 y)
1n0 ® 1p1 + b– + n
What is the relationship between the parent nuclide and the daughter nuclide in b– decay?
Radioactive Decays

14. Nuclide Transmutation of b+ Decay – examples
In b+ decay, the atomic number decreases by 1.
21Na11 ® 21Ne10 + b+ + n (t½, 22s) 30P15 ® 30Si14 + b+ + n (2.5 m) 34Cl17 ® 34S16 + b+ + n (1.6 s) 116Sb51 ® 116Sn50 + b+ + n (60 m)
What is the relationship between the parent nuclide and the daughter nuclide in b+ decay?
Radioactive Decays

15. Nuclide Transmutation of EC – examples
48V23 ® 48Ti b+ + n (50%) 48V + e– ® 48Ti + n (+ X-ray) (50%)
What is the relationship between the parent nuclide and the daughter nuclide in electron capture (EC)?
What can be detected in EC?
Radioactive Decays

16. Electron capture and internal conversion
Explain electron capture and internal conversion processes.
What are internal conversion electrons?
Radioactive Decays

17. Transmutation of gamma decay
Gamma decay emits energy from atomic nucleus as photons. Gamma, g, decay follows a and b decay or from isomers.
99mTc ® 99Tc + g 60Co ® 60mNi + b + n (antineutrino) 60mNi ® 60Ni + g
60Co ® 60Ni + b g (t½, 5.24 y) 24Na ® 24Mg + b + + g (2.75 MeV, t½, 15 h).
What is gamma decay?
Radioactive Decays

18. g-decay and Internal Conversion
Internal conversion electrons show up in b spectrum. X-ray energy is slightly different from the photon energy.
What are internal conversion electrons?
Radioactive Decays

19. Transmutation in Other Decays
Apply conservation of mass, nucleon, and charge to explain transmutation in all radioactive decays.
Transmutation in Other Decays
Transmutation in proton decays
53mCo27 —(1.5 %)® 52Fe p —(98.5 %)® 53Fe26 + b n.
Beta-delayed Alpha and Proton Emissions: 8B ® 8mBe + b+ + n (t½, 0.78 s) 8Li ® 8mBe + b‑ +  (t½, s) 8mBe ® 2 a
These are called b+a, and b–a decays respectively. Another examples of b+a and b+p+ decay: 20Na ® 20Ne + b + + n (t½, 0.39 s) Ne ® 16O + a
111Te ® 111Sb + b + + n (t½, 19.5 s) Sb ® 110Sn + p+.
Radioactive Decays

20. Radioactivity - Nuclide Chart for Nuclear Properties
Nuclide: a type of atoms with a certain number of protons, say Z, and mass number M, usually represented by MEZ, E be the symbol of element Z.
Periodic table of elements organizes chemical properties of elements.
Nuclide chart organizes unique nuclear properties of nuclides (isotopes).
Nuclear properties: mass, binding energy, mass excess, abundance radioactive decay mode, decay energy, half-life, decay constant, neutron capture cross section, cross section for nuclear reactions, energy levels of nucleons, nuclear spin, nuclear magnetic properties etc.
Radioactive Decays

21. Nuclide Chart for Nuclear Properties
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22. Isotopes Isotones, and Isobars
No. of Relationships of Isotopes protons Isobars, and Isotones on
Chart of Nuclides I S O T O P E S S S O O T B O A N R E S S No. of neutrons
Recognize the locations of isobars isotones isomers Isotopes on the chart of nuclides helps you remember meaning of these terms, and interpret the transformation of nuclides in nuclear decays and nuclear reactions.
Isomers
a Nuclide
Radioactive Decays

23. Families of Radioactive Decay Series
Radioactive Decay Series of 238U
238U92 ® 234Th a (t1/2 4.5e9 y)
234Th90 ® 234Pa b– + n (t1/ d)
234Pa91 ® 234U92 + b– + n (t1/2 6.7 h)
234U92 ® (continue)
206Pb82
Only alpha decay changes the mass number by 4.
There are 4 families of decay series. 4n, 4n+1, 4n+2, 4n+3, n being an integer.
Radioactive Decays

24. Radioactivity - 238U radioactive decay series

25. Radioactivity - 239Np radioactive decay series

26. Radioactivity - A Closer Look at Atomic Nuclei
Considering the atomic nucleus being made up of protons and neutrons
Proton
neutron
Key terms:
mass, (atomic weight) atomic number Z mass number A or M proton, neutron nucleon, baryon (free nucleon) Lepton (electron)
Radioactive Decays

27. Properties of Baryons and Leptons
Properties of Subatomic Particles
Properties of Baryons and Leptons
Baryons_____ _____Leptons______ Proton Neutron Electron Neutrino Units Rest e-4 <10– amu Mass <5x10–7 MeV Charge* –1 0 e– Spin ½ ½ ½ ½ (h/2p)
Magnetic moment* mN mN mB
It’s a good idea to know the properties of these subatomic particles. You need not memorize the exact value for rest mass and magnetic moment, but compare them to get their relationship.
Radioactive Decays

28. Mass of Protons, Neutrons & Hydrogen Atom
Proton Neutron Electron Neutrino Units Rest e <10– amu Mass <5x10–7 MeV
Mass of protons, neutrons and the H atom
mn - mp = = amu (or MeV) = me
mH = ( ) amu = amu Decay energy of neutrons
 –  amu =   amu (= MeV)
Radioactive Decays

29. Magnetic Moment of Particles
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30. Nuclear Models
Each model has its own merit. Realize the concept of these models and apply them to explain nuclear phenomena such as nuclear decay and nuclear reactions.
Liquid drop model: strong force hold nucleons together as liquid drop of nucleons (Bohr). Rnucleus = 1.2 A1/3.
Gas model: nucleons move about as gas molecules but strong mutual attractions holds them together (Fermi).
Shell model: nucleons behave as waves occupying certain energy states worked out by quantum mechanical methods. Each shell holds some magic number of nucleons. Magic numbers: 2, 8, 20, 28, 50, 82, 126. Nuclei with magic number of protons or neutrons are very stable.
Radioactive Decays

31. The potential well of nucleons in a nucleus for the shell model
The concept of quantum theory will be elaborated during the lecture.
Radioactive Decays

32. Her former student (at Johns Hopkins), Robert Sachs, brought her to Argonne at "a nice consulting salary". (Sachs later became Argonne's director.) While there, she learned recognized the "magic numbers“. While collecting data to support nuclear shells, she was at first unable to marshal a theoretical explanation. During a discussion of the problem with Enrico Fermi, he casually asked: "Incidentally, is there any evidence of spin-orbit coupling?" Goeppert Mayer was stunned. She recalled: "When he said it, it all fell into place. In 10 minutes I knew... I finished my computations that night. Fermi taught it to his class the next week". Goeppert Mayer's 1948 (volunteer professor at Chicago at the time) theory explained why some nuclei were more stable than others and why some elements were rich in isotopes.
Maria Goeppert-Mayer ( ), received the 1963 Nobel Prize in Physics for her discovery of the magic numbers and their explanation in terms of a nuclear shell model with strong spin-orbit coupling.
Radioactive Decays

33. The shell model
Quantum mechanics treats nucleons in a nucleus as waves.
Each particle is represented by a wavefunction.
The wavefunctions are obtained by solving a differential equation.
Each wavefunction has a unique set of quantum numbers.
The energy of the state (function) depends on the quantum numbers.
Quantum numbers are: n = any integer, the principle q.n. l = 0, 1, 2, ..., n-1, the orbital quantum number s = 1/2 or -1/2 the spin q.n. J = vector sum of l and s
The wavefunction n,l is even or odd parity.
Radioactive Decays

34. The Shell Model
Mayer in 1948 marked the beginning of a new era in the appreciation of the shell model.
For the first time, Mayer convinced us the existence of the higher magic numbers with spin-orbit couplings.
Radioactive Decays

35. Radioactivity & the shell model
Energy states of nuclei are labelled using J = j1 + j2 + j3 + j plus parity,
J +
Some Excited States of the 7Li Nuclide
½ + ___________ MeV
7/2 + ___________ 4.64
½ – ___________ /2 – ___________ Ground State
Radioactive Decays

36. Presentation Speech by Professor I
Presentation Speech by Professor I. Waller, member of the Nobel Committee for Physics (1963)
The discoveries by Eugene Wigner, Maria Goeppert Mayer and Hans Jensen for which this year's Nobel Prize in physics has been awarded, concern the theory of the atomic nuclei and the elementary particles. They are based on the highly successful atomic research of the first three decades of this century which showed that an atom consists of a small nucleus and a surrounding cloud of electrons which revolve around the nucleus and thereby follow laws which had been formulated in the so-called quantum mechanics. To the exploration of the atomic nuclei was given a firm foundation in the early 1930's when it was found that the nuclei are built up by protons and neutrons and that the motion of these so-called nucleons is governed by the laws of quantum mechanics.
Radioactive Decays

37. Radioactive Decay Energy
The law of conservation of mass and energy covers all reactions.
Sum of mass before reaction = Sum of mass after reaction + Q
Q = Sum of mass before reaction - Sum of mass after reaction
Interesting Items:
Spectrum of particles Energy in gamma decay Energy in beta decay Energy in alpha decay
Radioactive Decays

38. Gamma Decay Energy
Gamma, g, rays are electromagnetic radiation emitted from atomic nuclei. The bundles of energy emitted are called photons.
Ei ____________
h v
Ef ____________
Eothers _________
Excited nuclei are called isomers, and de-excitation is called isomeric transition (IT). Energy for photons
h v = E i - E f
Radioactive Decays

39. Types of Isomeric Transitions and their Ranges of Half-life
Nature of Gamma Transitions
Types of Isomeric Transitions and their Ranges of Half-life
Radiation Type Symbol J  Partial half life t (s)
Electric dipole E1 1 Yes 5.7e-15 E–3 A–2/3 Magnetic dipole M1 1 No 2.2e-14 E–3
Electric quadrupole E2 2 No 6.7e-9 E–5 A–4/3 Magnetic quadrupole M2 2 Yes 2.6e-8 E–5 A–2/3
Electric octupole E3 3 Yes 1.2e-2 E–7 A–2 Magnetic octupole M3 3 No 4.9e-2 E–7 A–4/3
Electric 24-pole E4 4 No 3.4e4 E–9 A–8/3 Magnetic 24-pole M4 4 Yes 1.3e5 E–9 A–2
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40. Gamma Decay Energy and Spectrum
Gamma transition of 7Li
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41. Gamma Decay Energy and Spectrum
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42. Beta Decay Spectrum
Internal conversion electrons
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43. Beta Decay Spectra
Decay of 64Cu illustrates several interesting features of beta decay and stability of nuclides.
Radioactive Decays

44. Beta Decay Spectra and Neutrino?
Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.
Radioactive Decays
Correct notes

45. Positron Decay Energy
Positron emission P Z  D Z–1 + e– + b+ + n + Edecay. Edecay = MP - MD – 2 me.
Radioactive Decays

46. Beta Decay Energy and Half-life
The higher the decay energy, the shorter the half-life, but there are other factors.
Radioactive Decays

47. Alpha Decay Energy & Spectrum
211Po  a particle energy: | 98.9% MeV | % | % | | Pb | 7/2+  MeV  – 0.5% 5/2+  MeV  – 0.5% 1/2+   – 98.9%
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48. Radioactive Decays Main Topics (Summary)
Radioactive decay, decay kinetics, applications
Transmutation in a, b, and g decays
The atomic nuclei, properties of baryons, models for the nuclei
Radioactive decay energy
Radioactive Decays