radioactivity and modes of radioactive decay

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Radioactivity and Modes of

Radioactive Decay

Stuart Jackson PhD FCCPMUniversity of Alberta

2007

Radiation Dose and RadioactivityRadiation Dose Units

Exposure

Surface Exposures

Absorbed Dose

Kerma Integral Dose

Equivalent Dose

Effective Dose

Relative Biological

Effectiveness Quality Factors

Radioactivity

• Decay Constant

• Half life

• The Decay Equation

• Modes of Decay

• Decay Diagrams

• Parent-Daughter Decay

• Radioactive Equilibra



Radioactivity

Most nuclei are very stable.

Some nuclei are unstable (not in thelowest energy state)

Free neutrons are unstable (half life 636 sec)

Excited atoms will usually move to alower energy state by emitting a photon

to carry away the excess energy.

Excited nuclei will move to a lower

energy states by emitting photonsand/or particles in various combinations(different decay pathways)

Question.

What is the difference betweena gamma ray and an x-ray?

Radioactive Decay Radioactive decay is a process whereby an unstable nucleus

transforms into a more stable one by emitting particles and/or

photons releasing energy in the process.

Energy diagrams are used to describe the various processes.



What this section covers:

1. Beta minus Decay

2. Beta minus, Gamma Decay

3. Isomeric Transition (IT) and InternalConversion (IC)

4. Electron Capture (EC) and EC, GammaDecay

5. Positron and Positron-Gamma Decay

6. Alpha Emission and Nuclear Fission

Line of Stability Most radioactive transitions have

several steps. For most radionuclides,the first step is an isobaric transition usually followed by an isomeric

transition and interactions with orbiting electrons.

The three types of isobaric transitionsof interest to us are (1) beta emission,(2) positron emission, and (3) electron

capture.

In nuclear stability, the neutron-protonratio (N/P) is crucial. If it is too low or

too high, the nucleus will eventuallyrearrange itself into a more stable

configuration.



Line of Stability

Beta radiation, which is the emission

of energetic electrons, results whenan N/P ratio is too high for stability;

Positron emission or electron captureoccurs when it is too low for stability.

These two conditions are representedby specific areas of the nuclide chart

shown. Beta emitters are above thestable nuclides, and positron emitters

and electron capture nuclides are

below.

Beta minus Decay In this process a neutron essentially transforms into a

proton and an electron .

Also a neutrino (anti-neutrino) is involved in theenergetics of the process.

n -----> p+ + e- + + energy

YX1Z

A

Z

A

+

−→ β

At the fundamental level this is due to the conversion of a down quark to anup quark by emission of a W- boson; the W- boson subsequently decays intoan electron and an anti-neutrino.



Beta minus Decay

YX1Z

A

Z

A

+

−

→ β

The parent and daughter represent different chemical elements

since Z changes.

Beta minus decay results in a transmutation.

This is an isobaric decay.(A is constant ).

Kinetic energy is shared between beta particle and neutrino .

EnergyDifference

Increasing Z

max

3

1 β β E E •

≈

Beta minus- Gamma Decay If the nucleus is still “excited” after decay by beta minus

emission, it will typically decay to a more stablearrangement by subsequent gamma emission .

Note that the gamma emission does not result intransmutation.

YYX1Z

A*

1Z

A

Z

A

++

−

→→γ β



Beta minus- Gamma Decay

Internal Conversion (IC)

Internal conversion is another electromagnetic process which can

occur in the nucleus and which competes with gamma emission.

Sometimes the multipole electric fields of the nucleus interact withorbital electrons with enough energy to eject them from the atom.

This process is not the same as emitting a gamma ray which knocks

an electron out of the atom.

It is also not the same as beta decay, since the emitted electron waspreviously one of the orbital electrons, whereas the electron in betadecay is produced by the decay of a neutron.



Isomeric Transition (IT) and

Internal Conversion (IC) Internal conversion is a radioactive decay

process where an excited nucleus interacts with anelectron in one of the lower electron shells,

causing the electron to be emitted from the atom.

Thus, in an internal conversion process, a high-energy electron which appears to be a classical

beta particle is emitted from the radioactive atom,but without beta decay taking place.

The high-speed electrons from internal conversion

are by definition not beta particles, since these aredefined by their method of production, not theircomposition.

K

Internal Conversion (IC)

Since no beta decay takes place in internal

conversion, the element atomic number does

not change (i.e., as in gamma radiation, no

transmutation of one element to anothertakes place in this type of radioactive decay).

The tendency towards internal conversion

can be determined by the internal conversioncoefficient, which is empirically determined

by the ratio of de-excitations that go by theemission of electrons to those that go bygamma emission

K



Internal Conversion (IC) The internal conversion coefficient may be empirically determined

by:

Important points:

- emissions have a spectrum of energies and originate from the

nucleus.

IC electrons have discrete energies + accompanyingcharacteristic x-rays and originate from the atomic electron orbits.

Metastable Radionuclides

Are important for nuclear imaging sincethey have relatively long half lives whichfacilitates chemical separation and theproduction of “pure gamma emitters”.

However, conversion electrons are alsoemitted and only add to patient dose.

The conversion coefficient needs to besmall in order to minimize the dose.

Metastable transitions are isomeric.



PHARMACEUTICAL GIANT DEDICATES BUILDING TOBROOKHAVEN LAB RESEARCHER

Upton, NY - Powell "Jim" Richards, who retired from the U.S.Department of Energy's Brookhaven National Laboratory in 1983,was honored earlier today, when Mallinckrodt Medical dedicated anew building to him at the pharmaceutical firm's Europeanheadquarters in Petten, The Netherlands.

While working in BNL's Medical Department in 1960, Richards wrotethe first scientific publication suggesting the medical use oftechnetium-99m.

These words, which are taken from that 1960 article, are engravedon the bronze plaque set in the Mallinckrodt building:

"Technetium-99m should be a useful research tool; it combines a short half-life and unique radiation characteristics. The absence of beta radiation reduces the amount of damage to biological systems usually associated with radioisotopes."

Technetium-99m is involved in nearly 20 million diagnosticprocedures annually worldwide.

Also, technetium-99m accounts for nearly 85 percent of thediagnostic imaging procedures used in nuclear medicine.

"Nuclear medicine to a large extent owes its emergence andexistence to technetium-99m

(partial list of emissions)

K

Mode Yield Energy



Electron Capture (EC) and (EC,) Decay.

In electron capture, an orbital electron is

captured by the nucleus and combines with a

proton to form a neutron.

The electron is usually in the K or L shell.

A neutrino carries away some of the energy.

The remainder of the energy appears as

characteristic x-rays and Auger electrons.

P+

+ e- n + + energy

-

++ +

+ ++

+ +

+ x-rays and

Auger electrons

Like - decay EC is an isobaric decay

mode, leading to a transmutation ofthe elements.

Often EC results in a metastable or

excited state which then leads to agamma or conversion electron

emission.


YXA

1Z

ECA

Z −→→



Note the direction on the decay

diagram for EC.(atomic number (Z)decreases by one)

Medically important radionuclideswhich decay by EC and (EC, )include:

57Co, 67Ga, 111In, 123I, 125I, 201Tl


EC

(Gamma)

(partial list of emissions)

Mode Yield Energy



+

Positron (+

) and (+

, ) Decay In this mode of decay, a proton in the

nucleus is transformed into a neutron and apositively charged electron (positron).

The positron and a neutrino are ejected fromthe nucleus, sharing the energy.

The positron travels only a few mm before

combining with an electron and producing apair of 511keV annihilation photons, which

are emitted in opposite directions.

P+ n + e+ + v + energy

+n

-

v

511keV

511keV

Since there are 2 x 511keV photons

involved with positron decay, there isa minimum transition energy

requirement of 1.022 MeV.

Positron decay is isobaric and sincethe atomic number decreases by one

a transmutation of the elementsoccurs.

Positron (+) and (+, ) DecayO

15

8

N15

7

MeVmax

7.1E = β

Q=2.722MeV

Y X A

Z

A

Z 1− →

+

β max

3

1 β β E E •

≈



Competitive

+

and EC Decay Positron emission and electron

capture have the same effect on thenucleus. They decrease the atomic

number by one.

Positron decay favours the lighterelements and since the orbital

electrons are closer to the nucleus forheavier element, EC is more frequent.

Some elements will decay by either

mode.

EC - 3%, Positron – 97%

Alpha Emission and Nuclear Fission

Both of these decay modes occur in the very

heavy elements and are of little importance tonuclear medicine.

Decay by alpha emission results in

transmutation, but it is not isobaric since theatomic mass is decreased by four.

The heavy elements decay by many pathways

known as decay series.

Nuclear fission is the source of energy in nuclear

reactors and will be covered at another time.

Y X A

Z

A

Z

4

2

−

− →

α



Radioactive Decay

Stuart Jackson PhDFCCPM

University of Alberta2007

Contents

Activity and the decayconstant

Exponential decay

Half life, Average life

Parent-Daughter Decay

Equilibria and the BatemanEquations



Activity Radioactive decay is a statistical process

and is described in terms of average decayrates.

Activity of a sample is given by the number ofatoms decaying per second.

Activity is proportional to the number ofradioactive atoms present at any particular

time and is expressed as:

N t N λ −=∆

∆Where is the decay constant

The Decay Constant

The decay constant is acharacteristic of each radionuclide.

The activity changes with time butthe decay constant does not.

The decay constant is the fraction ofatoms decaying per unit of time.

Also it represents the probability

that any particular atom will decay inthe unit of time.

Units are 1/time, sec-1

N t

N λ −=

∆

∆

t N

N

∆

∆−=

.λ

If = 0.01 sec-1

On average 1% of atoms will

decay per second



Branching Decay Some radioactive elements undergo decay by more

than one method. In this case, the total decayconstant is given by the sum of the individual

constants.

Example: (18F: 97% by + and 3% by EC)

The fraction decaying by a particular mode is calledthe branching ratio, (B.R.)

..........321 +++= λ λ λ λ total

total

i R B

λ

λ =..

Units of Activity

S.I. units of activity are the

Becquerel (Bq) which correspondsto disintegrations per second.

Conventional units are the Curie

(Ci), where 1 Ci = 3.7x1010 dps.

This is roughly the activity of 1 gram of the

radium isotope 226 Ra

(1mCi = 37 MBq)

In 1896, while investigatingphosphorescence in uranium salts,Becquerel accidentally discoveredradioactivity.

Investigating the work of Wilhelm ConradRöntgen, Becquerel wrapped a fluorescent

mineral, potassium uranyl sulfate, inphotographic plates and black material inpreparation for an experiment requiringbright sunlight.

However, prior to actually performing theexperiment, Becquerel found that thephotographic plates were fully exposed. Thisdiscovery led Becquerel to investigate thespontaneous emission of nuclear radiation.

)107.3(

.)(

10×=

N Ci A

λ



Maria Skłodowska-Curie

The Curie's began a search for the source of the radioactivity anddiscovered two highly radioactive elements, "radium" and "polonium."The Curie's won the 1903 Nobel prize for physics for their discovery.They shared the award with another French physicist, Antoine HenriBecquerel, who had discovered natural radioactivity. In 1906 Pierre,overworked and weakened by his prolonged exposure to radiation,died when he was run over by a horse drawn wagon.

Madame Curie continued her work on radioactive elements and wonthe 1911 Nobel prize for chemistry for isolating radium and studyingits chemical properties. In 1914 she helped found the RadiumInstitute in Paris, and was the Institute's first director. When the firstworld war broke out, Madame Curie thought X-rays would help tolocate bullets and facilitate surgery. It was also important not to movethe wounded, so she invented X-ray vans and trained 150 femaleattendants.

On July 4, 1934, at the age of 67 Madame Curie died of leukemia(aplastic pernicious anemia), thought to have been brought on byexposure to the high levels of radiation involved in her research. Afterher death the Radium Institute was rename the Curie Institute in herhonor.

Exponential Decay

The number of atoms remaining at time (t)in a radioactive sample is given by:

Since activity is related to the number ofatoms:

The exponential curve represent therepeated reduction of the same fraction ofactivity for each period of time.

t t e N N λ −= .)0()(

t t e A A λ −= .)0()(



Exponential DecayThe larger the decay constant, the more rapid the decay

Half -Life

A more intuitive characteristic of exponential

decay for many people is the time required for

the decaying quantity to fall to one half of its

initial value.

This time is called the half-life , and often

denoted by the symbol t 1 / 2

.

The half-life can be written in terms of the

decay constant , or the mean lifetime .



Half -Life

( )

( )

2 / 1

2 / 1

0)0(

:

)0()(

693.0

.693.02ln

2

.2

.

2 / 1

2 / 1

T

T

e

e N N

e N N

T

T

decayed haveatomshalf whentimeaat

t t

=

==

=

=

=

−

−

λ

λ

λ

λ

λ

Half Life - Log and Linear Plots



Average Lifetime The actual lifetimes of

individual atoms varies fromvery short to very long.

The average lifetime ( ) is also

a characteristic of a particularradionuclide and is given by:

τ

2 / 12 / 1

44.1693.0

1T

T ×===

λ τ

τ

t

T1/2

∞

−

∞

−

=

0

0

.

dt e

dt et

t

t

λ

λ

τ

Average Lifetime

Average Lifetime =

Total time/Total # =

100 x 1

+ 80 x 2

+ 60 x 3

= 440/(100+80+60)

=1.83

Decay

0

20

40

60

80

100

120

Time

N

u m b e r R e m a i n i n g

1.83 s



Parent – Daughter Decay

Parent

T1/2 =Tp

Daughter

T1/2 =Td

Grand-daughter

T1/2 =Tg

Td<<Tp Secular Equilibrium Parent half life is very

long compared todaughter. Activity of

daughter builds up tomatch parent and parentand daughter are said to

be in secular equilibrium.


1.00

10.00

100.00

1000.00

0 10 20 30

Daughter Half-Lives

A c t i v i t y

Activity Parent

Activity Daughter

Initial Activity

Parent half Life 100 Hours 500

Daughter half life 1 Hours 1

Time to Max 6.70 Hours 6.70 Daughter Half Lives



Tp> Td, Transient Equilibrium Parent half life greater than

daughter, but not very much.

Daughter activity reaches and

exceeds parent, then followsparent decay pattern with aconstant ratio.

This is transient equilibrium.


0.10

1.00

10.00

100.00

1000.00

0 10 20 30

Daughter Half-Lives

A c t i v i t y

Activity Parent

Activity Daughter

Initial Activity

Parent half Life 30 Hours 500

Daughter half life 10 Hours 1

Time to Max 23.73 Hours 2.37 Daughter Half Lives

Tp<<Td, No Equilibrium

Parent half life much less

than daughter.

Daughter activity reaches

a maximum at some timeas the parent activitydecays and then decays

at its own rate.

radioactivity and modes of radioactive decay

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