radioactive decays1 radioactive decays transmutations of nuclides radioactivity means the emission...

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.


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


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


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


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 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 consecutive decay animation

See Simulation in Radioactive Decay in SCI270 website

The simulation will be used to illustrate various conditions.


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.


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?


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?


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


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?


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?


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?


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?


Electron Capture and Internal Conversion

Internalconversion

EC

Electron capture and internal conversion

Explain electron capture and internal conversion processes.

What are internal conversion electrons?


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?


-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?


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.


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.


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.


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


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.


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


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


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


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.


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)


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


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.


The potential well of nucleons in a nucleus for the shell model

The concept of quantum theory will be elaborated during the lecture.


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.


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.


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.


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


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 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


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


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


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


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


Beta Decay Spectrum

A Typical Beta Spectrum

Intensityor # of

Energy of

E max

Internal conversion electrons


Beta Decay Spectra


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.


Beta Decay Spectra and Neutrino

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


Intensityor # of

Energy of

E max

A Beta Decay Scheme

PZ DZ+1 + – + v

Correct notes

?


Positron Decay Energy

Positron Emission

+

–

Positron emissionP Z D Z–1 + e– + + + +

Edecay. Edecay = MP - MD – 2 me.


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.


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

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 decays1 radioactive decays transmutations of nuclides radioactivity means the emission...

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