Radioactive Decay: Types, Kinetics, and Transmutation
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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 1 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 dt ln N = ln No – t Integration gives Also A = Ao e – t or N = No e – t What is decay rate? Radioactive Decays How does decay rate vary with time? 2 Radioactive Decay Kinetics - plot Variation of N as a function of time t No N N = No e Also A = Ao e - t - t t 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 N =A No = Ao Radioactive Decays 3 Decay Constant and Half-life Variation of N as a function of time t Ln(N or A) No ln N1 – ln N2 = ––––––––––– t1 – t2 N N = No e - t Also A = Ao e - t t 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 t Radioactive Decays Determine half life, t½ 4 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. Apparent Radioactivity of 3 Nuclides ln A ln Atotal ln A1 ln A2 ln A3 Ln A t t Analyze and explain Radioactive Decays 5 Radioactive Consecutive Decay and Growth Radioactivity of Decay Product Ln A 238U 234 Th + 4 234Th 234Pa + Total Activity Activity due to Activity due to 234 Th 238U t 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 Radioactive half life.Decays 6 Radioactive consecutive decay animation See Simulation in Radioactive Decay in SCI270 website The simulation will be used to illustrate various conditions. Radioactive Decays 7 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. Anthropologists, biologists, chemists, diagnosticians, engineers, geologists, physicists, and physicians often use radioactive nuclides in their respective work. Radioactive Decays Nuclide Half life 219Th90 1 s 26Na11 1s 40Cl17 1.4 min 32P15 14.3 d 14C6 5730 y 235U92 7.04x108 y 238U92 4.46x109 y 8 Decay and Transmutation of Nuclides Alpha, , decay emits a helium nucleus from an atomic nucleus. Transmutation of Nuclides in Alpha Decays APZ A – 4DZ – 2 + 4He2 Alpha Decay A Z P A–4 DZ–2 4He2 Radioactive Decays How do nuclides transform in alpha decay? 9 Nuclide Transmutation of Decay APZ A – 4DZ – 2 + 4He2 Heavy Nuclide alpha emitters 235U92 231Th90 + 42 (t , 7.13×108 y) ½ 238U92 208Po84 234Th90 + 42 (t½, 4.51×109 y) 204Pb82 + 42 (t½, 2.9 y) How do nuclides transform in alpha decay? Mass and charge change byRadioactive what? Decays 10 Nuclide Transmutation of Decay APZ A – 4DZ – 2 + 4He2 light nuclides 5He 1n0 + 42 (t , 2×10-21 s), ½ 5Li 1p1 + 42 (t , ~10-21 s), ½ 8Be 2 42 (t , 2×10-16 s). ½ Some rare earth (144 Nd, 146Sm, 147Sm, 147Eu, ...174Hf) are emitters: 144Nd 140Ce + 42 (t , 5×1015 y), ½ 174Hf 170Yb + 42 (t , 2×1015 y). ½ Radioactive Decays 11 Nuclide Transmutation of 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 + 1 + – (absorbs a neutrino) APZ or ADZ + 1 + – + n (emit antineutrino, n) Positron emission Electron capture APZ ADZ – 1 + + + n APZ + n ADZ – 1 + +. or What is beta decay? or Radioactive Decays APZ + e– ADZ – 1 + n APZ + e– + n ADZ – 1 12 Nuclide Transmutation of – Decay – examples 1n 0 1p1 + – +n Beta Decay of Neutron Other examples of beta decay 14N7 + – + n (t½, 5720 y) 40K19 40Ca20 + – + n (1.27e9 y) 50V23 50Cr24 + – + n (6e15 y) 87Rb37 87Sr38 + – + n (5.7e10 y) 115In49 115Sn50 + – + n (5e14 y) 14C6 Proton Neutron Electron What is the relationship between the parent nuclide and the daughter nuclide in – decay? Radioactive Decays 13 Nuclide Transmutation of + Decay – examples In + decay, the atomic number decreases by 1. 21Ne10 + + + n 30P15 30Si14 + + + n 34Cl17 34S16 + + + n 116Sb51 116Sn50 + + + n 21Na11 (t½, 22s) (2.5 m) (1.6 s) (60 m) What is the relationship between the parent nuclide and the daughter nuclide in + decay? Radioactive Decays 14 Nuclide Transmutation of EC – examples 48Ti22 + + + + n (50%) 48V + e– 48Ti + n(+ X-ray) (50%) 48V23 Electron Capture and X-ray Emission X-ray What is the relationship between the parent nuclide and the daughter nuclide in electron capture (EC)? What can be detected in EC? EC Radioactive Decays 15 Electron capture and internal conversion Electron Capture and Internal Conversion EC Internal conversion Explain electron capture and internal conversion processes. What are internal conversion electrons? Radioactive Decays 16 Transmutation of gamma decay Gamma decay emits energy from atomic nucleus as photons. Gamma, , decay follows and decay or from isomers. 99Tc + 60Co 60mNi + + n (antineutrino) 60mNi 60Ni + 99mTc 24Na 60Co ++ + 24Mg + + + 60Ni What is gamma decay? Radioactive Decays (t½, 5.24 y) (2.75 MeV, t½, 15 h). 17 -decay and Internal Conversion Internal Conversion Electron and X-ray Emission X-ray Internal conversion electron Internal conversion electrons show up in spectrum. X-ray energy is slightly different from the photon energy. Radioactive Decays What are internal conversion electrons? 18 Transmutation in Other Decays Transmutation in proton decays 53mCo27 —(1.5 %) 52Fe26 + 1p1 —(98.5 %) 53Fe26 + + + n. Beta-delayed Alpha and Proton Emissions: 8B 8mBe + + + n (t , 0.78 s) ½ 8Li 8mBe + - + n (t , 0.82 s) ½ 8mBe 2 Apply conservation of mass, nucleon, and charge to explain transmutation in all radioactive decays. These are called +, and – decays respectively. Another examples of +and +p+ decay: 20Na 20Ne + + + n (t , 0.39 s) ½ 20Ne 16O + 111Te + + + n (t½, 19.5 s) 111Sb 110Sn + p+. 111Sb Radioactive Decays 19 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 20 Nuclide Chart for Nuclear Properties 6 Be 4 Be, ? p 6.019725 Be, 53.3 d EC 0.86 7.01928 5 Li 3 3 He,0.0001 % 3.01603 He 2 H 1 7 1 H,99.99 % 1.007825 N 0 p# 0 n # 2 H, 0.015% 2.0142 1 0, n 12 m 0.78 1.008665 1 Li, 0.18 s 6Li, 7.42% p or 6.015121 5.01254 4 He,100% 5He,? n, 4.0026 5.01222 3 H, 12.26y 0.0186 3.014102 8 10 Be, 0.06 9Be, 100% Be, fs 1.6x106 y 9.012182 2 0.86 0.5 8.005305 7 Li, 92.5% 8Li, 0.85 s 16 7.016003 8.022485 6 8 He 0.81s 7He He, 1s 3.51 n, 14 6.018886 8.03392 Symbol, abundance or half-life, (fs =10–15s, second, minute, year) Decay mode: , , energy MeV, Mass in amu 2 3 4 5 Radioactive Decays Chart of some light nuclides with a key in the large square. 6 21 Isotopes Isotones, and Isobars No. of protons Relationships of Isotopes Isobars, and Isotones on Chart of Nuclides Isomers I S O T O P E S S S O O a Nuclide T B O A N R E S S 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. No. of neutrons Radioactive Decays 22 Families of Radioactive Decay Series Radioactive Decay Series of 238U 238U92 234Th90 + 42 234Th90 (t1/2 4.5e9 y) 234Pa91 234Pa91 + – + n (t1/2 24.1 d) 234U92 + – + n 234U92 (t1/2 6.7 h) . . . (continue) . . . Only alpha decay changes the mass number by 4. 206Pb82 There are 4 families of decay series. 4n, 4n+1, 4n+2, 4n+3, n being an integer. Radioactive Decays 23 Radioactivity - 238U radioactive decay series The Decay Path of 4n + 2 or 238U Family 234 230 226 222 218 210 Po 210 206 Pb 206 Tl 206 214 Bi 210 Hg Po 214 Pb Bi 214 210 Tl At 218 Rn Po Pb U 238 234 Pa 234 Th Th Ra decay Major route Minor route decay Radioactive Decays 24 U Radioactivity - 239Np radioactive decay series The Decay Paths of the 4n + 1 or 237Np93 Family Series 233 (1.6e5 y) 229 221 213 209 Bi83 209 Po84 Pb82 209 Fr87 217 At85 (1 min) 213 83 Bi Np93 (2e6 y) 233 Pa91 Th90 (7300 y; minor path) 225 (10 d) Ac89 U92 237 225 Ra88 81 Tl Radioactive Decays 25 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 26 Properties of Subatomic Particles Properties of Baryons and Leptons Baryons_____ Proton Neutron Rest 1.00727647 1.0086649 Mass 938.2723 939.5653 Charge* 1 0 Spin ½ ½ _____Leptons______ Electron Neutrino Units 5.485799e-4 <10–10 amu 0.51899 <5x10–7 MeV –1 0 e– ½ ½ (h/2p) Magnetic moment* 2.7928474 N -1.9130428 N 1.00115965B 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 27 Mass of Protons, Neutrons & Hydrogen Atom Rest Mass Proton Neutron 1.00727647 1.0086649 938.2723 939.5653 Electron Neutrino Units 5.485799e-4 <10–10 amu 0.51899 <5x10–7 MeV Mass of protons, neutrons and the H atom mn - mp = 1.0086649 - 1.00727647 = 0.0013884 amu (or 1.2927 MeV) = 2.491 me mH = (1.00727647 + 0.00054856) amu = 1.007825 amu Decay energy of neutrons 1.0086649 –1.007825 amu = 0.000840 amu (= 0.783 MeV) Radioactive Decays 28 Magnetic Moment of Particles A close-loop current in a uniform magnetic field experiences a torque if the plane of the loop is not perpendicular to the magnetic field. i Radioactive Decays 29 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 30 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 31 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. Radioactive Decays Maria Goeppert-Mayer (1906-1972), 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. 32 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 33 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 34 Radioactivity & the shell model Energy Level Diagram of Nucleons n l j 7 6 6 6 6 6 6 0 1 2 3 4 13 6 5 5 5 5 5 0 2 3 4 11 5 4 4 4 (2j+1) Notation /2 + ½– 3 /2 – 5 /2 – 7 /2 – 9 /2 – Shell total 1i 3p 3p 2f 2f 1h 14 2 4 6 8 10 ~126 /2– ½+ 3 /2 + 5 /2 + 7 /2 + 1h 3s 2d 2d 1g 12 2 4 6 8 ~82 4 0 1 2 9 /2 + ½– 3 /2 – 5 /2 – 1g 2p 2p 1f 10 2 4 6 ~50 4 3 7 /2 – 1f 8 ~28 ½ + ___________ 6.54 MeV 3 3 3 0 1 2 ½+ /2 + 5 /2 + 2s 1d 1d 2 4 6 ~20 7/ 2 0 1 3 ½– /2 – 1p 1p 2 4 ~8 1 0 ½+ 1s 2 ~2 3 Energy states of nuclei are labelled using J = j1 + j2 + j3 + j4 + ... plus parity, J+ Some Excited States of the 7Li Nuclide 2 + ___________ 4.64 ½ – ___________ 0.478 3/ – ___________ Ground State 2 Radioactive Decays 35 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 36 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 Energy in Radioactive Decay Before decay Interesting Items: Spectrum of particles Energy in gamma decay Energy in beta decay Energy in alpha decay Recoiling nucleus Radioactive Decays 37 Gamma Decay Energy Gamma, , rays are electromagnetic radiation emitted from atomic nuclei. The bundles of energy emitted are called photons. Excited nuclei are called isomers, and de-excitation is called isomeric transition (IT). Energy for photons Ei ____________ hv=Ei-Ef Ef ____________ hv Eothers _________ Radioactive Decays 38 Nature of Gamma Transitions Types of Isomeric Transitions and their Ranges of Half-life Radiation Type Symbol J p Partial half life t (s) Electric dipole Magnetic dipole Electric quadrupole Magnetic quadrupole Electric octupole Magnetic octupole Electric 24-pole Magnetic 24-pole 1 1 2 2 3 3 4 4 Yes No No Yes Yes No No Yes 5.7e-15 E–3 A–2/3 2.2e-14 E–3 6.7e-9 E–5 A–4/3 2.6e-8 E–5 A–2/3 1.2e-2 E–7 A–2 4.9e-2 E–7 A–4/3 3.4e4 E–9 A–8/3 1.3e5 E–9 A–2 E1 M1 E2 M2 E3 M3 E4 M4 Radioactive Decays 39 Gamma Decay Energy and Spectrum Gamma transition of 7Li Various Gamma Transitions in 7Li ½+ 6.54 MeV M3 E3 M1 E1 M2 7/2+ 4.64 MeV ½ – 0.778 MeV 3/2– ground state Radioactive Decays 40 Gamma Decay Energy and Spectrum Gamma Ray Spectrum of O18 h Intensity 2+ 3.27 MeV 1.98 MeV 1.98 2+ 0+ 3.27 MeV 5.25 MeV E Radioactive Decays 41 Beta Decay Spectrum A Typical Beta Spectrum Intensity or # of Internal conversion electrons E max Energy of Radioactive Decays 42 Beta Decay Spectra A Typical Beta Spectrum 64 Cu 41%EC 1+ 2+ 0+ 40%– 64 64 Ni 0+ Zn 19%+ Intensity – Decay of 64Cu illustrates several interesting features of beta decay and stability of nuclides. + 0.58 MeV 0.66 MeV Radioactive Decays E 43 Beta Decay Spectra and Neutrino A Beta Decay Scheme P D Z Z+1 A Typical Beta Spectrum + +v – Intensity or # of ? E max Energy of Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy. Correct notes Radioactive Decays 44 Positron Decay Energy Positron Emission – + n Positron emission P Z D Z–1 + e– + + + n + Edecay. Edecay = MP - MD – 2 me. Radioactive Decays 45 Beta Decay Energy and Half-life A Sargent Diagram Log (s–1) 210 Pb 212 The higher the decay energy, the shorter the half-life, but there are other factors. 210Bi 228Ac Pb 214 Pb 208 Tl 234 Pa 212Bi 214Bi Log E (eV) Radioactive Decays 46 Alpha Decay Energy & Spectrum An Ideal Alpha Spectrum No. of particle energy: | 98.9% 10.02 MeV | 0.5% 9.45 | 0.5% 8.55 | | 207Pb | 7/ + 2 0.90 MeV – 0.5% 5/ + 2 0.57 MeV – 0.5% 1/ + – 98.9% 2 211Po Radioactive Decays MeV 8 10 47 Radioactive Decays Main Topics (Summary) Radioactive decay, decay kinetics, applications Transmutation in , and decays The atomic nuclei, properties of baryons, models for the nuclei Radioactive decay energy Radioactive Decays 48
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