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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.

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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


A Summary of Radioactive Decay Kinetics

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?

Radioactive Decays


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 lN = A

lNo = Ao

Radioactive Decays


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 = Noe– tA = Aoe – t

ln N = ln No – t ln A = ln Ao – t

Determine half life, t½


Radioactive Decays


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


Analyze and explain

Radioactive Decays


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


Radioactive consecutive decay animation

See Simulation in Radioactive Decay in SCI270 website

The simulation will be used to illustrate various conditions.

Radioactive Decays


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.

NuclideHalf life

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.

Radioactive Decays


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


Nuclide Transmutation ofaDecayAPZ®A – 4DZ – 2 + 4He2

Heavy Nuclide alpha emitters

235U92231Th90 + 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


Nuclide Transmutation ofaDecayAPZ ®A – 4DZ – 2 + 4He2

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).

Radioactive Decays


Nuclide Transmutation ofbDecay

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 +b–(absorbs a neutrino) or APZ®ADZ + 1 +b–+ n (emit antineutrino, n)

Positron emission

APZ® ADZ – 1 + b+ + norAPZ+ n® ADZ – 1 + b+.

Electron capture

APZ + e–® ADZ – 1 + norAPZ + e– + n® ADZ – 1

What is beta decay?

Radioactive Decays


Nuclide Transmutation ofb–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


Nuclide Transmutation ofb+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


Nuclide Transmutation ofEC – examples

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?

Radioactive Decays


Electron capture and internal conversion

Explain electron capture and internal conversion processes.

What are internal conversion electrons?

Radioactive Decays


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 + 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?

Radioactive Decays


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


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+.

Radioactive Decays


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.

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.

Radioactive Decays


Isotopes Isotones, and Isobars

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.


a Nuclide

Radioactive Decays


Families of Radioactive Decay Series

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.

Radioactive Decays


Radioactivity - A Closer Look at Atomic Nuclei

Considering the atomic nucleus being made up of protons and neutrons



Key terms:

mass, (atomic weight) atomic number Zmass number A or Mproton, neutronnucleon, baryon (free nucleon) Lepton (electron)

Radioactive Decays


Properties of Subatomic Particles

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.

Radioactive Decays


Mass of Protons, Neutrons & Hydrogen Atom

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)

Radioactive Decays


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


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


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.

Radioactive Decays


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 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.

Radioactive Decays


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


Radioactivity & the shell model

Energy states of nuclei are labelled using J = j1 + j2 + j3 + j4 + parity,

J +

Some Excited States of the 7Li Nuclide

½ + ___________ 6.54 MeV

7/2 + ___________ 4.64

½ – ___________ 0.4783/2 – ___________ Ground State

Radioactive Decays


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


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 particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay

Radioactive Decays


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 = Ei - E f

Radioactive Decays


Nature of Gamma Transitions

Types of Isomeric Transitions and their Ranges of Half-life

Radiation TypeSymbolJPartial 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

Radioactive Decays


Gamma Decay Energy and Spectrum

Gamma transition of 7Li

Radioactive Decays


Beta Decay Spectrum

Internal conversion electrons

Radioactive Decays


Beta Decay Spectra

Decay of 64Cu illustrates several interesting features of beta decay and stability of nuclides.

Radioactive Decays


Beta Decay Spectra and Neutrino


Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.

Radioactive Decays

Correct notes


Positron Decay Energy

Positron emissionP ZD Z–1 + e– + b++ n + Edecay. Edecay = MP - MD – 2 me.

Radioactive Decays


Beta Decay Energy and Half-life

The higher the decay energy, the shorter the half-life, but there are other factors.

Radioactive Decays


Alpha Decay Energy & Spectrum

211Poa 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


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