Modes of Radioactive DecayGE-PP-22502

Author: Ken Jenkins

Approved: Michael J. KurtzmanDate: 06/14/2003

Revision: 00

GE-PP-22502-00 2

Nuclear StabilityForces Acting Within the

Nucleus

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Nuclear StabilityThe repulsive electrostatic forces between the

protons have an impact on nuclear stabilityThe number of neutrons must increase more

rapidly than the number of protons to provide ‘dilution’ and to add additional nuclear forces

If the nuclear (attractive) and electrostatic (repulsive) forces do not balance, the atom will not be stable

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Nuclear StabilityAn unstable nucleus will eventually achieve

stability by changing its nuclear configuration

This includes changing neutrons to protons, or vice versa, and then ejecting the surplus mass or energy from the nucleus

This emitted mass or energy is called radiation

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Nuclear StabilityWhen an atom transforms to become more

stable it is said to disintegrate or decayThe time required for half of a sample of atoms

to decay is known as the half-lifeThe property of certain nuclides to

spontaneously disintegrate and emit radiation is called radioactivity

The atom before the decay is the parent and the resulting atom is called the daughter

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Neutron / Proton Ratio

0 20 40 60 80 100 120 1400

20

40

60

80

100

NU

MB

ER

OF

PR

OT

ON

S (

Z)

NUMBER OF NEUTRONS (N=A-Z)

LINE OFSTABILITY

Z

N1

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Beta DecayBetas are physically the same as electrons,

but may be positively or negatively chargedNegative beta is a beta minus or negatronPositive beta is a beta plus or positronBetas are ejected from the nucleus, not from

the electron orbitals In all beta decays the atomic number changes

by one while the atomic mass is unchanged

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Beta (β-) Minus DecayOccurs in neutron-rich nuclidesThe nucleus converts a neutron into a proton

and a beta minus (which is ejected from the nucleus with an anti-neutrino)

Mass and charge are conserved

epn 01

11

10

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Beta (β-) Minus DecayFor beta minus decays,

011YX A

ZAZ

01

9039

9038 YSr

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Beta (β-) Minus Decay

ParentK-40

Beta Particle

Anti-neutrino

01

DaughterCa-40

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Beta (β-) Minus DecayDuring radioactive decay energy is released Source of this energy is from the conversion

of massSince energy is conserved, energy equivalent

of the parent must equal energy equivalent of daughter, particles, and any energy released

Energy is released as kinetic energy of beta minus particle and an anti-neutrino

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Beta (β-) Minus DecayFor beta minus, energy of decay reaction (Q) is,

)5.931)((1 amu

MeVMMQ

YX AZ

AZ

Mass of beta minus particle is not included since an additional electron is gained due to increase of Z

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Beta (β-) Minus DecayCalculate Q for β- decay of Co-60.

01

6028

6027 NiCo

Mass of Co-60 is 59.933813 amuMass of Ni-60 is 59.930787 amu

)amu

MeVmu)(931.559.930787a-mu59.933813a(Q

MeVQ 819.2

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Beta (β-) Minus DecayThe Q value for beta minus decay of Co-60,

for example, is always the sameHowever, negatrons rarely are emitted with

the same energiesTheir energies can range from 0 MeV to the

calculated maximum, Emax

The anti-neutrino carries energy difference between actual and calculated values

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Beta (β-) Minus Decay#

of b

etas

wit

h en

ergy

E

EnergyMaxE3

1 MaxE

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Co6027

Ni6028

99+%

0.013%

0.12%

1.17

3

2.15

8

0.83

1.33

2

Co-60 Decay Scheme

Q

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Beta (β+) Plus DecayOccurs in proton-rich nuclidesThe nucleus converts a proton into a neutron

and a beta plus (which is ejected from the nucleus with a neutrino)

As with negatrons, the positron can have a range of energies from 0 to EMax MeV

Positron is the negatron’s anti-particleA positron and a negatron will annihilate one

another and release two 0.511 MeV photons

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01

136

137 CN

Beta (β+) Plus DecayFor beta plus decays,

011YX A

ZAZ

enp 01

10

11

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Beta (β+) Plus Decay

ParentF-18

Beta Particle

Neutrino

01

DaughterO-18

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Beta (β+) Plus DecayFor beta plus, energy of decay reaction (Q) is,

)5.931)](2()[( 011 amu

MeVMMMQ

eYX AZ

AZ

Since the energy equivalent of two electron masses is 1.022 MeV, the equation can be rewritten as,

MeVamu

MeVMMQ

YX AZ

AZ

022.1)]5.931)([(1

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Beta (β+) Plus Decay

C136N13

7

•••

• •••

•

••••••

•+

e-

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Beta (β+) Plus DecayCalculate Q for β+ decay of F-18.

01

188

189 OF

Mass of F-18 is 18.000937 amuMass of O-18 is 17.999160 amu

MeVQ 022.1)]amu

MeVmu)(931.517.999160a-amu000937.18[(

MeVQ 633.0

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Electron CaptureProton-rich nuclides may also decay via orbital

electron capture (EC)Usually an innermost K shell electron is

captured and often referred to as K-captureThe electron and a proton are converted into a

neutron and a neutrino is emitted Electrons from higher orbitals will fill vacancy

and usually emit characteristic x-rays

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CrMn EC 5324

5325

Electron CaptureFor electron capture decays,

YeX AZ

AZ 1

01

nep 10

01

11

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Electron CaptureFor electron capture, energy of decay reaction

(Q) is,

)5.931)((1 amu

MeVMMQ

YX AZ

AZ

Since the electron was absorbed into the nucleus and not removed, there is no need to account for electron mass

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Auger ElectronsWhen electrons change shells, x-rays are

usually emitted In some instances, the excess energy is

transferred to another orbital electron, which is then ejected from the atom

This ejected electron is known as an Auger electron

Another orbital vacancy now exists and x-rays may be emitted if they are filled

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••

Auger Electrons

•• •

•

•

• ••

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Beta InteractionsExcitation

The beta, via coulombic interaction, transfers enough energy to an orbital electron to move it to a higher energy level, but not to remove it from the atom

The atom remains electrically neutralThe excited electron will then return to its ground

state and emit the excess energy as x-rays

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Excitation

•

••

•••

- •

•x-ray

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Beta Interactions Ionization

The beta, via coulombic interaction, transfers enough energy to an orbital electron to overcome its binding energy and remove it from the atom

With the loss of the negative electron, the remaining atom is now a positive ion

If the vacancy is filled, an x-ray will be emittedThe formation of each ion pair in air (gas)

requires about 34 eV of energy from the beta

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Ionization

••

••

- •

• ••

•e-

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Beta InteractionsBremsstrahlung

German for ‘braking radiation’Occurs when beta is deflected by the positively

charged nucleusThe kinetic energy lost by the beta is emitted as a

photon (x-ray)Bremsstrahlung increases with higher Z materialsFor example, a lead blanket may shield betas, but

generate higher levels of Bremsstrahlung (x-rays)

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Bremsstrahlung

••

••• • •

- •

x-ray

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Beta InteractionsBetas travel in zig-zag or tortuous paths

Collisions and deflectionsCoulombic interactionsNot mono-energetic

Because of this, betas have a definite, predictable range (given in mg/cm2)

Basic thumb rule is that a 1.0 MeV beta will travel approximately 12 feet in air

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Beta Interactions

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Beta InteractionsAll betas can be stopped, but Bremsstrahlung

photons can be produced Intensity is proportional to number of betas,

their energy, and Z of the absorberShielding is designed to minimize and/or shield

BremsstrahlungLow Z materials such as plastic (hydrocarbons)

or aluminum are common

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Beta InteractionsThe fraction of beta energy that appears as

photon energy (Bremsstrahlung) can be estimated with the following equation:

f = E x Z x 10-3

E = beta energy in MeV

Z = atomic number of target (shield) material

Average energy of the Bremsstrahlung photons is about 1/4 Emax

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Alpha DecayAlphas are large particles ejected by the heavier

nuclidesAlpha decay is primarily limited to nuclides

with Z > 82Source is mainly from fuel-related materialsAlpha contains two protons and two neutrons

(no electrons) and is, in effect, a helium nucleusThus, the atomic number decreases by two and

the mass number decreases by four

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Alpha DecayFor alpha decays,

242

42

HeYX A

ZAZ

242

20682

21084

HePbPo

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Alpha Decay

ParentU-235

Daughter Th-231

242

He

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Alpha DecaySince nothing else is emitted, all energy of

decay goes to the alpha particle (except for a small amount towards recoil of nucleus)

Alphas, therefore, are mono-energeticFor alpha, energy of decay reaction (Q) is,

)5.931)](([ 42

42 amu

MeVMMMQ

HeYX AZ

AZ

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Alpha DecayCalculate Q for the decay of Rn-222.

242

21884

22286

HePoRnMass of Rn-222 is 222.017610 amuMass of Po-218 is 218.009009 amu

)amu

MeVu)](931.54.002603am9amu(218.00900-amu017610.222[ Q

MeVQ 6.5

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Alpha InteractionsAlphas interact primarily through Coulombic

interactions due to their +2 chargeEnergy transfer occurs through excitation and

ionizationOrbital electrons may receive enough energy

to allow them to cause secondary ionizations of other atoms

Bremsstrahlung does not occur since the large alphas are not easily deflected

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Alpha InteractionsBecause of their mass and charge, alphas

travel in relatively straight paths over short distances (higher Z of absorber, less distance)

A 7 MeV alpha travels only about 0.0002 cm in lead

Alphas are considered internal hazards onlyWhen an alpha slows enough, it captures two

free electrons and converts to a helium atom

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Alpha Interactions

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Nuclear De-excitationDaughter nuclei from radioactive decays are

often ‘born’ with excess energyOccasionally the excited nucleus will emit

additional alphas or betasUsually the excited nucleus reaches ground

state via nuclear de-excitationThe excited nucleus and the final ground state

nucleus have the same Z and A and are called isomers

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Nuclear De-excitation If the excited state has a half-life >1 sec, it is

said to be a metastable stateThe metastable state is denoted by the use of a

lowercase ‘m’, such as Ba-137mThe longest known excited state is Bi-210m

with a half-life of 3.5 x 106 yearsDuring de-excitation no nuclear transformation

occurs, so no ‘new’ element is formed

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Nuclear De-excitation Internal Conversion

The excess nuclear energy is transferred to an inner orbital (usually K or L) electron

This electron is then ejected from the atom with a distinct energy

X-ray emission may follow as electrons shift orbitals to fill vacancies

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Nuclear De-excitationGamma emission

Most frequently the excess energy is relieved via the emission of one or more gamma rays

Gammas have no mass or electric chargeIf gammas are emitted by an isomer in the

metastable state, the emission is known as an isomeric transition (IT)

Photon Energy (E) = hf where h is Planck’s Constant (4.14 x 10-15 eV-sec)f is frequency (sec-1)

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Gamma Ray Radiation

ParentCo-60

Gamma Rays

01

DaughterNi-60

Anti-neutrino

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Co6027

Ni6028

99+%

0.013%

0.12%

1.17

3

2.15

8

0.83

1.33

2

Co-60 Decay Scheme

Q

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Gamma InteractionsAlphas and betas (charged particles) interact

multiple times along their pathsGammas usually have only one or two

interactions and all of their energy is transferred

Gammas interact with matter typically through three processes: photoelectric effect, Compton effect, and pair production

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Photoelectric EffectThe gamma ray photon transfers all of its

energy to an orbital electron (usually K shell)The electron is then ejected from the atom

(photoelectron)Probability of the photoelectric effect increases

with increasing Z of the absorberProbability of the photoelectric effect increases

with decreasing gamma energy (<1 MeV)

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Photoelectric Effect

••

••• •

•

•e-

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Compton Effect (Scattering)The gamma ray photon transfers some of

its energy to an orbital electronThe electron is ejected (recoil electron) and

the photon is scattered with a lower energyProbability of the Compton effect

decreases with increasing gamma energy (200 keV 5 MeV)

Compton effect is more common with absorbers of intermediate Z

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Compton Effect

••

••• •

•

•e-

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Pair ProductionPhoton travels in the vicinity of the nucleusPhoton spontaneously converts into a pair of

particles - an electron and a positronSince the rest mass energy of an electron is

0.511 MeV (from E = mc2), the photon must have an initial energy of at least 1.022 MeV

All photon energy in excess of 1.022 MeV is shared as kinetic energy between the particles

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Pair Production

••

••• ••e-

•e+

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Pair ProductionThe electron and positron will lose energy

through excitation, ionization, and Bremsstrahlung interactions

When the positron slows sufficiently it will be attracted to an electron and the two will annihilate one another (anti-particles) resulting in the formation of two 0.511 MeV photons

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Pair ProductionThough pair production is possible at 1.022

MeV, the process rarely occurs until approximately 5 MeV photon energy

The likelihood of pair production also increases proportionally with increasing Z of the absorber

Few isotopes at Vogtle have sufficient energies for pair production to occur

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Gamma Ray AttenuationGammas interact within an absorber via

photoelectric effect, Compton scattering, and pair production

Compton scattering and pair production events result in the emission of photons

The average probability of an event must be considered for shielding

Theoretically no amount of shielding can reduce the gamma dose rate to zero

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Gamma Ray AttenuationGamma ray intensity is reduced exponentially

with a linear increase in absorber thickness

xeII 0

Where:I = emerging gamma intensityI0 = incident gamma intensityx = thickness of absorber (cm) = linear attenuation coefficient (cm-1)

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Gamma Ray Attenuation

Compton Scatter

Photoelectric Effect

No Interaction

Pair Production (annihilation photons)

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Gamma Ray AttenuationA more simplified shielding calculation uses

the concepts of Half Value Layers (HVL) and Tenth Value Layers (TVL)

HVL is the thickness of an absorber necessary to decrease the gamma radiation to one half of the incident value

TVL is the thickness of an absorber necessary to decrease the gamma radiation to one tenth of the incident value

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Gamma Ray AttenuationTo perform calculations with these concepts

use the following equations:

nII )2

1(0 nII )

10

1(0

Where n = the number of HVLs or TVLs respectively

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Decay SchemesVertical lines represent energyHorizontal lines indicate atomic number (Z)Beta minus points down to the rightAlpha and EC point down to the leftBeta plus points down to the left with a 1.022

MeV offsetParent half-lives are shown

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Decay Schemes

Ground states are bold horizontal linesExcited states are light horizontal lines Isomeric states are medium horizontal linesTotal amount of energy for the reaction is

shown (Q)Abundances (probabilities) of transitions are

shown

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Decay SchemesWhat is the half-life of Ar-41?1.83 hoursWhat percentage of the Zr-95 beta minus

decays result in an isomer of Nb-95?2%Cr-51 decays by what method(s)?Electron capture (EC)

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Decay SchemesFor every 100 decays of Rb-86, about how

many 1.078 MeV gammas will be produced?9 (100 x 8.8%)For every 100 decays of Mn-56, about how

many 1.811 MeV gammas will be produced?29 (100 x 30% x 97.8%)What will be the most abundant gamma

energy produced during the decay of Fe-59?1.095 MeV

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Chart of the Nuclides

I1318.040 d

- 0.606, . . .

364.5, . . .

0.7, 8

E 0.971

Isotope

Half-life (color indicates 1-10 days)

Beta decay with most prominent energy (MeV)

Most prominent gamma energy (keV)

Thermal neutron cross-section (barns)Beta disintegration energy (MeV)

Fission product

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Chart of the NuclidesWhite backgrounds are artificially radioactiveGray backgrounds are stable and include

percent abundancesLower half colors represent neutron absorption

propertiesBlack bar across top of box indicates a

naturally-occurring radioactive isotopeHeavy black outlines indicate ‘magic’ numbers