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.
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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.
Radioactivity or decay rateA 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
What is decay rate? How does decay rate vary with time?
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 lN = A
lNo = Ao
Ln(N or A)
ln N1 – ln N2 = –––––––––––t1 – t2
t½* = ln 2
Be able to apply these equations!
N = Noe– tA = Aoe – t
ln N = ln No – t ln A = ln Ao – t
Determine half life, t½
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
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.
See Simulation in Radioactive Decay in SCI270 website
The simulation will be used to illustrate various conditions.
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.
219Th90 1 s26Na11 1s40Cl17 1.4 min32P15 14.3 d14C6 5730 y 235U92 7.04x108 y 238U92 4.46x109 y
Anthropologists, biologists, chemists, diagnosticians, engineers, geologists, physicists, and physicians often use radioactive nuclides in their respective work.
Alpha, a, decay emits a helium nucleus from an atomic nucleus.
Transmutation of Nuclides in Alpha Decays
APZA – 4DZ – 2 + 4He2
How do nuclides transform in alpha decay?
Heavy Nuclide alpha emitters
235U92231Th90 + 4a2 (t½, 7.13×108 y)
238U92 234Th90 + 4a2 (t½, 4.51×109 y)
208Po84204Pb82 + 4a2 (t½, 2.9 y)
How do nuclides transform in alpha decay? Mass and charge change by what?
light nuclides5He 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, ...174Hf) areaemitters:144Nd 140Ce + 4a2 (t½, 5×1015 y),174Hf 170Yb + 4a2 (t½, 2×1015 y).
Beta decay consists of three processes: emitting an electron, emitting a positron, or capturing an electron from the atomic orbital.
APZ + n®ADZ + 1 +b–(absorbs a neutrino) or APZ®ADZ + 1 +b–+ n (emit antineutrino, n)
APZ® ADZ – 1 + b+ + norAPZ+ n® ADZ – 1 + b+.
APZ + e–® ADZ – 1 + norAPZ + e– + n® ADZ – 1
What is beta decay?
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?
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?
48V23®48Ti22 + + 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?
Explain electron capture and internal conversion processes.
What are internal conversion electrons?
Gamma decay emits energy from atomic nucleus as photons.Gamma, g, decay follows a and b decay or from isomers.
99mTc ®99Tc + g60Co ® 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?
Internal conversion electrons show up in b spectrum.X-ray energy is slightly different from the photon energy.
What are internal conversion electrons?
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 %)®52Fe26 + 1p1 —(98.5 %)®53Fe26 + b + + n.
Beta-delayed Alpha and Proton Emissions: 8B ® 8mBe + b+ + n (t½, 0.78 s) 8Li ® 8mBe + b‑ + (t½, 0.82 s) 8mBe ® 2 a
These are called b+a, and b–adecays respectively.Another examples of b+a and b+p+decay: 20Na ®20Ne + b + + n (t½, 0.39 s)20Ne ®16O + a
111Te ®111Sb + b + + n (t½, 19.5 s) 111Sb ®110Sn + p+.
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.
Periodictable 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.
No. of Relationships of Isotopesprotons Isobars, and Isotones on
Chart of NuclidesI S O T O P E SS SO OT BO AN RE SSNo. 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 decaysand nuclear reactions.
Radioactive Decay Series of 238U
238U92®234Th90 + 4a2 (t1/2 4.5e9 y)
234Th90®234Pa91 + b– + n (t1/2 24.1 d)
234Pa91®234U92 + b– + n (t1/2 6.7 h)
234U92® . . . (continue)
. . .
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.
Considering the atomic nucleus being made up of protons and neutrons
mass, (atomic weight) atomic number Zmass number A or Mproton, neutronnucleon, baryon (free nucleon) Lepton (electron)
Properties of Baryons and Leptons
Baryons_____ _____Leptons______ProtonNeutronElectronNeutrinoUnitsRest 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/2p)
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.
Proton NeutronElectronNeutrinoUnitsRest 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 amuDecay energy of neutrons
1.0086649 –1.007825 amu = 0.000840 amu (= 0.783 MeV)
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.
The concept of quantum theory will be elaborated during the lecture.
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 (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.
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 numbers = 1/2 or -1/2 the spin q.n.J = vector sum of l and s
The wavefunction n,lis even or odd parity.
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.
Energy states of nuclei are labelled using J = j1 + j2 + j3 + j4 + ...plus parity,
Some Excited States of the 7Li Nuclide
½ + ___________ 6.54 MeV
7/2 + ___________ 4.64
½ – ___________ 0.4783/2 – ___________ Ground State
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.
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
Spectrum of particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay
Gamma, g, 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
h v = Ei - E f
Types of Isomeric Transitions and their Ranges of Half-life
Radiation TypeSymbolJPartial half life t (s)
Electric dipole E1 1 Yes 5.7e-15 E–3A–2/3Magnetic dipole M1 1 No 2.2e-14E–3
Electric quadrupole E2 2 No 6.7e-9E–5A–4/3Magnetic quadrupole M2 2 Yes 2.6e-8E–5A–2/3
Electric octupole E3 3 Yes 1.2e-2 E–7A–2Magnetic octupole M3 3 No 4.9e-2E–7A–4/3
Electric 24-pole E4 4 No 3.4e4 E–9A–8/3Magnetic 24-pole M4 4 Yes 1.3e5E–9A–2
Gamma transition of 7Li
Internal conversion electrons
Decay of 64Cu illustrates several interesting features of beta decay and stability of nuclides.
Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.
Positron emissionP ZD Z–1 + e– + b++ n + Edecay. Edecay = MP - MD – 2 me.
The higher the decay energy, the shorter the half-life, but there are other factors.
211Poa 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%
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