8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 1/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 2/22
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.
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 3/22
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.
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 4/22
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.
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 5/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 6/22
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.
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 7/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 8/22
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.
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 9/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 10/22
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.
Electron Capture (EC) and (EC,) Decay.
YXA
1Z
ECA
Z −→→
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 11/22
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
Electron Capture (EC) and (EC,) Decay.
EC
(Gamma)
(partial list of emissions)
Mode Yield Energy
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 12/22
+
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 •
≈
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 13/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 14/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 15/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 16/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 17/22
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()(
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 18/22
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 .
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 19/22
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 20/222
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 21/222
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.
Parent-Daughter Decay
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
8/6/2019 Radioactivity and Modes of Radioactive Decay
http://slidepdf.com/reader/full/radioactivity-and-modes-of-radioactive-decay 22/22
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.
Parent-Daughter Decay
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.