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Radioactive Decays 1
Radioactive Decaystransmutations 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
What is decay rate? How does decay rate vary with time?
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 .
dNA = – ––––– = N Integration gives
d t
ln N = ln No – t or N = No e – t
Also A = Ao e – t
Radioactive Decays 3
Variation of N as a function of time t
N No
t
N = No e - t
Also A = Ao e - t
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 N = A
No = Ao
Radioactive Decays 4
Decay Constant and Half-lifeVariation of N as a function of time t
N No
t
N = No e - t
Also A = Ao e - t
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
Ln(N or A)
t
ln N1 – ln N2
= ––––––––––– t1 – t2
t½ * = ln 2
Radioactive Decays 5
Apparent Radioactivity of 3 Nuclides
ln Aln Atotal
ln A1
ln A2
ln A3
t
Ln A
t
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.
Analyze and explain
Radioactive Decays 6
Radioactive Consecutive Decay and GrowthRadioactivity of Decay Product
238U 234 Th + 4
Activity due to 238U
Activity due to 234 Th
234Th 234Pa + Ln A
t
Total Activity
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
Nuclide Half life219Th90 1 s26Na11 1s40Cl17 1.4 min32P15 14.3 d14C6 5730 y 235U92 7.04x108 y 238U92 4.46x109 y
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 9
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 DecayAPZ A–4DZ–2
4He2
How do nuclides transform in alpha decay?
Radioactive Decays 10
Heavy Nuclide alpha emitters235U92 231Th90 + 42 (t½, 7.13×108 y)
238U92 234Th90 + 42 (t½, 4.51×109 y)
208Po84 204Pb82 + 42 (t½, 2.9 y)
Nuclide Transmutation of DecayAPZ A – 4DZ – 2 + 4He2
How do nuclides transform in alpha decay? Mass and charge change by what?
Radioactive Decays 11
light nuclides5He 1n0 + 42 (t½, 2×10-21 s), 5Li 1p1 + 42 (t½, ~10-21 s),8Be 2 42 (t½, 2×10-16 s).
Some rare earth (144 Nd, 146Sm, 147Sm, 147Eu, ...174Hf) are emitters:144Nd 140Ce + 42 (t½, 5×1015 y), 174Hf 170Yb + 42 (t½, 2×1015 y).
Nuclide Transmutation of DecayAPZ A – 4DZ – 2 + 4He2
Radioactive Decays 12
Nuclide Transmutation of Decay
Electron emissionAPZ + ADZ + 1 + – (absorbs a neutrino)
or APZ ADZ + 1 + – + (emit antineutrino,
Positron emission
APZ ADZ – 1 + + + or
APZ + ADZ – 1 + +.
Electron captureAPZ + e– ADZ – 1 +
or
APZ + e– + ADZ
– 1
Beta decay consists of three processes: emitting an electron, emitting a positron, or capturing an electron from the atomic orbital.
What is beta decay?
Radioactive Decays 13
Other examples of beta decay
14C6 14N7 + – + (t½, 5720 y)40K19 40Ca20 + – + (1.27e9 y)50V23 50Cr24 + – + (6e15 y)87Rb37 87Sr38 + – + (5.7e10 y)115In49 115Sn50 + – + (5e14 y)
Beta Decay of Neutron
Neutron
Proton
Electron
Nuclide Transmutation of – Decay – examples
1n0 1p1 + – +
What is the relationship between the parent nuclide and the daughter nuclide in – decay?
Radioactive Decays 14
In + decay, the atomic number decreases by 1.21Na11 21Ne10 + + + (t½, 22s)30P15 30Si14 + + + (2.5 m)34Cl17 34S16 + + + (1.6 s)116Sb51 116Sn50 + + + (60 m)
Nuclide Transmutation of Decay – examples
What is the relationship between the parent nuclide and the daughter nuclide in + decay?
Radioactive Decays 15
Electron Capture and X-ray Emission
EC
X-ray
Nuclide Transmutation of EC – examples
48V23 48Ti22 + + + + (50%)48V + e– 48Ti + (+ 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
Internalconversion
EC
Electron capture and internal conversion
Explain electron capture and internal conversion processes.
What are internal conversion electrons?
Radioactive Decays 17
99mTc 99Tc + 60Co 60mNi + + (antineutrino) 60mNi 60Ni +
60Co 60Ni + + + (t½, 5.24 y)24Na 24Mg + + + (2.75 MeV, t½, 15 h).
Transmutation of gamma decay
Gamma decay emits energy from atomic nucleus as photons.
Gamma, , decay follows and decay or from isomers.
What is gamma decay?
Radioactive Decays 18
-decay and Internal Conversion
Internal Conversion Electron and X-ray Emission
Internalconversionelectron
X-ray
Internal conversion electrons show up in spectrum.X-ray energy is slightly different from the photon energy.
What are internal conversion electrons?
Radioactive Decays 19
Transmutation in Other DecaysTransmutation in proton decays 53mCo27 —(1.5 %) 52Fe26 + 1p1
—(98.5 %) 53Fe26 + + + .
Beta-delayed Alpha and Proton Emissions:8B 8mBe + + + (t½, 0.78 s)8Li 8mBe + ‑ + (t½, 0.82 s)
8mBe 2
These are called +, and – decays respectively.Another examples of +and +p+ decay:
20Na 20Ne + + + (t½, 0.39 s) 20Ne 16O +
111Te 111Sb + + + (t½, 19.5 s) 111Sb 110Sn + p+.
Apply conservation of mass, nucleon, and charge to explain transmutation in all radioactive decays.
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 PropertiesBe4
6Be, ?p6.019725
7Be, 53.3 dEC 0.867.01928
8Be, 0.06fs2 0.868.005305
9Be, 100%
9.012182
10Be,1.6x106 y 0.5
Li3
5Li, 0.18 sp or 5.01254
6Li, 7.42%
6.015121
7Li, 92.5%
7.016003
8Li, 0.85 s 168.022485
He2
3He,0.0001%3.01603
4He,100%
4.0026
5He,?n, 5.01222
6He 0.81s 3.516.018886
7He8He, 1sn, 148.03392
H1
1H,99.99%1.007825
2H, 0.015%
2.0142
3H, 12.26y 0.01863.014102
Symbol, abundance or half-life, (fs =10–15s, second, minute, year)
N0
1n0, 12 m 0.781.008665
Decay mode: , , energy MeV,Mass in amu
p # n#
0 1 2 3 4 5 6
Chart of some light nuclides with a key in the large square.
Radioactive Decays 22
Isotopes Isotones, and Isobars
No. of Relationships of Isotopesprotons 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
IsomersRecognize 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.
a Nuclide
Radioactive Decays 23
Families of Radioactive Decay Series
Radioactive Decay Series of 238U238U92 234Th90 + 42 (t1/2 4.5e9 y)
234Th90 234Pa91 + – + (t1/2 24.1 d)
234Pa91 234U92 + – + (t1/2
6.7 h) 234U92 . . . (continue)
. . .
206Pb82Only 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
The Decay Path of 4n + 2 or 238U Family 238U234U234Pa
234Th230Th
226Ra
222Rn 218At
218Po214Po214Bi
214Pb
210Po 210Bi206Pb 210Pb 206Tl 210Tl 206Hg
Minor route
Major route
decay
decay
Radioactivity - 238U radioactive decay series
Radioactive Decays 25
Radioactivity - 239Np radioactive decay series
The Decay Paths of the 4n + 1 or 237Np93 Family Series237Np93
233U92 (2e6 y)(1.6e5 y) 233Pa91
229Th90
225Ac89 (7300 y; minor path)
(10 d) 225Ra88
221Fr87
217At85
213Po84 (1 min) 209Bi83 213Bi83
209Pb82
209Tl81
Radioactive Decays 26
Radioactivity - A Closer Look at Atomic Nuclei
Key terms:
mass, (atomic weight) atomic number Zmass number A or Mproton, neutronnucleon, baryon (free nucleon) Lepton (electron)
Proton
neutron
Considering the atomic nucleus being made up of protons and neutrons
Radioactive Decays 27
Properties of Subatomic Particles
Properties of Baryons and Leptons
Baryons_____ _____Leptons______ Proton Neutron Electron Neutrino Units
Rest 1.00727647 1.0086649 5.485799e-4 <10–10 amuMass 938.2723 939.5653 0.51899 <5x10–7 MeVCharge* 1 0 –1 0 e–
Spin ½ ½ ½ ½ (h/2)Magneticmoment* 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 28
Mass of Protons, Neutrons & Hydrogen Atom
Proton Neutron Electron Neutrino UnitsRest 1.00727647 1.0086649 5.485799e-4 <10–10 amuMass 938.2723 939.5653 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 29
Magnetic Moment of Particles
A close-loop current in a uniform magneticfield experiences a torque if the plane of the
loop is not perpendicular to the magnetic field.
i
Radioactive Decays 30
Nuclear ModelsEach 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
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.
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 33
The shell modelQuantum 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 numbers = 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 + j4 + ...plus parity,
J +
Some Excited States of the 7Li Nuclide
½ + ___________ 6.54 MeV
7/2 + ___________ 4.64
½ – ___________ 0.4783/2 – ___________ Ground State
Energy Level Diagram of Nucleons n l j (2j+1) Shell Notation total 7 6 13/ 2+ 1i 14 ~126 6 0 ½– 3p 2 6 1 3/ 2– 3p 4 6 2 5/ 2– 2f 6 6 3 7/ 2– 2f 8 6 4 9/ 2– 1h 10 6 5 11/ 2– 1h 12 ~82 5 0 ½+ 3s 2 5 2 3/ 2+ 2d 4 5 3 5/ 2+ 2d 6 5 4 7/ 2+ 1g 8 5 4 9/ 2+ 1g 10 ~50 4 0 ½– 2p 2 4 1 3/ 2– 2p 4 4 2 5/ 2– 1f 6 4 3 7/ 2– 1f 8 ~28 3 0 ½+ 2s 2 ~20 3 1 3/ 2+ 1d 4 3 2 5/ 2+ 1d 6 2 0 ½– 1p 2 ~8 1 3/ 2– 1p 4 1 0 ½+ 1s 2 ~2
Radioactive Decays 36
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
Energy in Radioactive Decay
Before decay
Recoiling nucleus
Interesting Items:
Spectrum of particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay
Radioactive Decays 38
Gamma Decay Energy
Gamma, , 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
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
Nature of Gamma Transitions
Radioactive Decays 40
Various Gamma Transitions in 7Li
3/ 2– ground state½ – 0.778 MeV
7/ 2+ 4.64 MeV
½+ 6.54 MeV
M1
E1
E3
M3
M2
Gamma Decay Energy and Spectrum
Gamma transition of 7Li
Radioactive Decays 41
Gamma Ray Spectrum of O18
E
Intensity 2h+
2+0+
3.27 MeV
1.981.98 MeV
3.27 MeV
5.25 MeV
Gamma Decay Energy and Spectrum
Radioactive Decays 42
Beta Decay Spectrum
A Typical Beta Spectrum
Intensityor # of
Energy of
E max
Internal conversion electrons
Radioactive Decays 43
Beta Decay Spectra
A Typical Beta Spectrum
E
Intensity
–
+
64Cu
64Zn64Ni
40%–41%EC
19%+
0.66 MeV
0.58 MeV
2+0+
0+1+
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.
A Typical Beta Spectrum
Intensityor # of
Energy of
E max
A Beta Decay Scheme
PZ DZ+1 + – + v
Correct notes
?
Radioactive Decays 45
Positron Decay Energy
Positron Emission
+
–
Positron emissionP Z D Z–1 + e– + + + +
Edecay. Edecay = MP - MD – 2 me.
Radioactive Decays 46
Beta Decay Energy and Half-life
A Sargent Diagram
Log (s–1)
Log E (eV)
210Pb
212Pb214Pb
208Tl234Pa
214Bi
212Bi
228Ac
210Bi The higher the decay energy, the shorter the half-life, but there are other factors.
Radioactive Decays 47
Alpha Decay Energy & SpectrumAn Ideal Alpha Spectrum
MeV
No.of
8 10
211Po 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%1/2+ –
98.9%
Radioactive Decays 48
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
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