1) Radioactivity is the spontaneous disintegration of unstable atomic nuclei through emission of particles like alpha and beta particles or gamma rays. This transforms the parent nucleus into a more stable daughter nucleus. 2) Radioactive decay can produce daughter nuclei in excited states, which then de-excite through gamma or isomeric transitions without changing the nucleus' proton or neutron number. 3) For nuclei with unstable proton-neutron ratios, radioactive decay processes like beta decay can change the nucleus' proton or neutron number to reach a more stable ratio.

1. Radioactivity
Dr. Hiba ZBIB
2015-2016 1

2. Radioactivity
• Is the phenomenon resulting from the spontaneous
disintegration of an unstable atomic nucleus.
• During this phenomenon, in unstable nucleus, called parent
nucleus, is transformed into a more stable daughter nucleus
with the emission of gamma rays and particles alpha , beta,..
• We say that the parent nucleus decays or that there is
transmutation of the parent nucleus into a daughter nucleus.
2

3. Radioactivity
• We distinguish two types of radioactivity:
• Natural: when the parent nucleus is a natural
nucleus .
• Artificial: when the parent nucleus is a
nucleus which is artificially prepared.
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4. The nucleus
• Consists of (nucleons): protons and neutrons.
• The standard form used to denote the
composition of a specific nucleus:
• Z= number of protons
• N= number of neutrons.
• The mass number A = Z + N.
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5. Nuclear Stability
• All nuclei with atomic numbers (proton number)
greater than 82 are unstable.
• Many lighter nuclei (i.e., with Z < 82) are also
unstable.
➢ Energy is released during the decay of radioactive
nuclei.
➢ This energy is termed the transition energy.
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6. Nuclear Stability
• Nuclei tend to be most stable if they contain even numbers of
protons and neutrons, and least stable if they contain an odd
number of both.
• Nuclei are extraordinarily stable if they contain 2, 8, 14, 20,
28, 50, 82, or 126 protons or similar numbers of neutrons.
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7. Nuclear Stability
• Stable nuclei
• The number of neutrons is about equal to the number
of protons in low-Z stable nuclei. As Z increases, the
number of neutrons increases more rapidly than the
number of protons in stable nuclei.
• Nuclei above the line of stability (i.e., the n/p ratio is
too high for stability) tend to emit negatrons by the
process of β− decay.
• Nuclei below the line of stability (i.e., the n/p ratio is
too low for stability) tend to undergo the positron (β+)
decay.
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8. Nuclear stability and decay
• The neutrons and protons reside in specific levels with different binding
energies. (Shell model)
• If a vacancy exists at a lower energy level, a neutron or proton in a higher
level may fall to fill the vacancy.
• This transition releases energy and yields a more stable nucleus. The
amount of energy released is related to the difference in binding energy
between the higher and lower levels.
• The binding energy is much greater for neutrons and protons inside the
nucleus than for electrons outside the nucleus.
• Hence, energy released during nuclear transitions is much greater than
that released during electron transitions.
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9. Nuclear stability and decay
• If a nucleus gains stability by transition of a neutron
between neutron energy levels, or a proton between
proton energy levels, the process is termed an isomeric
transition.
• In an isomeric transition, the nucleus releases energy
without a change in its number of protons (Z ) or neutrons
(N).
• An isomeric transition that competes with gamma decay is
internal conversion, in which an electron from an
extranuclear shell carries the energy out of the atom.
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10. Nuclear stability and decay
• It is also possible for a neutron to fall to a lower energy level reserved for
protons, in which case the neutron becomes a proton. It is also possible
for a proton to fall to a lower energy level reserved for neutrons, in which
case the proton becomes a neutron.
• In these situations, referred to collectively as beta (β) decay, the Z and N
of the nucleus change, and the nucleus transmutes from one element to
• another.
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11. Radioactive decay scheme
1- α decay
2- β+ (positron) decay
3- β−(negatron) decay
4- Isomeric transition
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12. Nuclear Binding Energy
• Nuclear binding energy is the energy required to split the nucleus
of an atom into its component parts. The mass of an atom is less
than the sum of the masses of its neutrons, protons, and electrons.
• The mass difference between the sum of the masses of the atomic
constituents and the mass of the assembled atom is termed the
mass defect .
• When the nucleons are separate, they have their own individual
masses. When they are combined in a nucleus, some of their mass
is converted into energy.
• In Einstein’s equation, an energy E is equivalent to mass m
multiplied by the speed of light in a vacuum, c (2.998 × 108 m/sec)
squared.
12
2
c
m
E 

=
m


13. Laws of conservation
• In any radioactive process :
• the mass number of the decaying (parent)
nucleus equals the sum of the mass numbers of
both the daughter nucleus and the emitted
particle.
• The atomic number Z of the parent nucleus is
equal to the sum of the atomic numbers of both
the daughter nucleus and the emitted particle.
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14. Laws of conservation
• The total energy of a particle is the sum of its kinetic energy and its rest energy .
• The rest energy is determined by the mass-energy equivalence of Einstein: E=m.c2
• The law of conservation of energy can be stated as follows:
• The total energy of the parent nucleus before the nuclear reaction is equal to the sum of the rest
energy and the kinetic energy of the products and the energy of gamma rays (and other rays) after
the reaction.
• (m.c2 + Ek(parent))before = (m’.c2 + Ek(products))after + E of gamma rays and other
particules
• Energy liberated by a radioactive reaction
• El=∆m . c2 =EK (products) + E of gamma rays + E(neutrino and antineutrino) - EK(parent)
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15. Carbon decay
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16. Decay scheme
• The decay scheme of a radioactive substance
is a graphical presentation of all the
transitions occurring in a decay, and of their
relationships.
• Coordinate system:
• the ordinate axis is energy, increasing from
bottom to top,
• the abscissa is the proton number, increasing
from left to right.
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Number of protons
Energy

17. Decay scheme
• The arrows indicate the emitted
particles.
• For the gamma rays (vertical
arrows), the gamma energies
are given;
• For the beta or alpha
decay (oblique arrow), the
maximum beta energy.
• Nickel is to the right of cobalt,
since its proton number (28) is
higher by one than that of
cobalt (27).
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18. Isomeric transitions
• Radioactive decay often forms a daughter nucleus in an energetic
(“excited”) state.
• The nucleus descends from its excited to its most stable (“ground”) energy
state by one or more isomeric transitions.
• Often these transitions occur by emission of electromagnetic radiation
termed γ rays.
• No radioactive nuclide decays solely by an isomeric transition. Isomeric
transitions are always preceded by emission of an α or β(+or−) particle.
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19. Gamma rays
• The nucleus can be in an excited state.
• A gamma is not visible by your eye.
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20. Gamma rays
• Nuclides emit γ rays with characteristic
energies.
– For example, photons of 142 and 140 keV are
emitted by 99mTc,
– photons of 1.17 and 1.33 MeV are released
during negatron decay of 60Co.
• In the latter case, the photons are released
during cascade isomeric transitions of
progeny 60Ni nuclei from excited states to
the ground energy state.
• In an isomeric transition, the nucleus
releases energy without a change in its
number of protons (Z ) or neutrons (N).
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Beta-
excited state
excited state
ground energy state

21. Alpha decay
• Some heavy nuclei A>200 gain stability by : alpha (α) decay.
• The alpha particle poorly penetrating type of radiation that
can be stopped by a sheet of paper.
• Massive particle consisting of an assembly of two protons and
two neutrons. (Helium)
• It is a positively charged particle.
• The nucleus can be in an excited state.
• An example of alpha decay is
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22. Alpha decay
22

23. Negatron Decay
• In nuclei with an n/p ratio too high for
stability, a neutron may be transformed
into a proton :
• where is a negative electron ejected from
the nucleus, and ν˜ is an antineutrino.
n
1
0
p
1
1

0
1
−
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24. Negatron Decay
• A negatron with a maximum
energy (Emax) of 1.17 MeV is
released during 5% of all decays;
• in the remaining 95%, a
negatron with an Emax of 0.51
MeV is accompanied by an
isomeric transition of 0.66 MeV,
where a γ ray is emitted.
• The transition energy is 1.17
MeV for the decay of 137Cs.
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1.176 Mev
0.662 Mev
0 Mev

25. Negatron Decay
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26. Positron Decay
• n/p ratio too low for stability (nb p high , nb
neutron low):
• Positron decay results from the nuclear
transition:
• where represents a positron ejected from the
nucleus during decay, and ν is a neutrino that
accompanies the positron.
• The decay of is representative of positron
decay:

0
1
+
P
30
15
26

27. Orbital Electron Capture
• The n/p ratio of a nuclide may also be
increased by electron capture (ec), in which
one of the extranuclear electrons is captured
by the nucleus and unites with an intranuclear
proton to form a neutron according to the
equation
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28. Decay laws
28

29. Mathematics of radioactive decay
• The rate of decay (number of decays per unit
time) of a radioactive sample depends on the
number N of radioactive atoms in the sample.
• Where is the rate of decay, and the constant
λ is called the decay constant.
• The minus sign indicates that the number of
parent atoms in the sample, and therefore the
number decaying per unit time, is decreasing.
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30. The decay constant
• The decay constant has units of (time)−1, such as
sec−1 or hr−1.
• It has a characteristic value for each nuclide. It
also reflects the nuclide’s degree of instability;
• A larger decay constant connotes a more
unstable nuclide (i.e., one that decays more
rapidly).
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31. Activity
• The rate of decay is a measure of a sample’s
activity, defined as:
• The activity of a sample depends on the number
of radioactive atoms in the sample and the decay
constant of the atoms.
• A sample may have a high activity because it
contains a few highly unstable (large decay
constant) atoms, or because it contains many
atoms that are only moderately unstable (small
decay constant).
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32. Activity
• The SI unit of activity is the becquerel (Bq),
defined as:
• 1 Bq = 1 disintegration per second (dps)
• The curie
32

33. Decay equations
• The number N of parent
atoms present in the
sample at any time t:
• By multiplying both sides
of this equation by λ, the
expression can be
rewritten as:
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11
7
4

34. Decay equations
• The number of atoms N∗ decaying in time t is
N0 – N , or:
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35. HALF-LIFE
• The physical half-life T1/2 of a radioactive
nuclide is the time required for decay of half
of the atoms in a sample of the nuclide.
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36. The atomic mass unit
• Expressing the mass of atomic particles in
kilograms is unwieldy because it would be a very
small number requiring scientific notation.
• The atomic mass unit (amu) is a more convenient
unit for the mass of atomic particles.
• 1 amu : 1/12 the mass of the carbon atom,
• 12C : six protons, six neutrons, and six electrons.
1 amu = 1.6605 × 10−27 kg
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37. Absorbed Dose
• The absorbed dose represents the energy absorbed
by unit of mass .
D= energy (J)/masse(kg)
• SI unit used to measure absorbed dose is the gray
(Gy).
• 1 Gy= 1J/kg
• Gy does not describe the biological effects of the
different radiations.
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38. Equivalent dose
• Equivalent dose is a radiation-weighted dose
quantity which takes into account the type of
radiation producing the dose.
• Equivalent dose HT is calculated using the
absorbed dose deposited in body tissue or organ T,
multiplied by the radiation weighting
factor WR which is dependent on the type and
energy of the radiation R. SI unit is the sievert (Sv).
• The higher the weighting factor numbers for a
type of radiation, the more damaging is the type
of radiation.
• The radiation weighting factor aims to correct the
absorbed dose, for the different biological effect of
different types of radiation.
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Radiation WR
Beta and
gamma
1
Neutron From 5 to 10
Alpha 20
HT : is the equivalent dose
absorbed by tissue T.
DT,R :is the absorbed dose in
tissue T by radiation type R.
WR :is the radiation
weighting factor defined by
regulation

39. Nuclear fission
• Energy is released if a nucleus with a high mass
number separates or fissions into two parts,
each with an average binding energy per
nucleon greater than that of the original
nucleus.
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40. Nuclear fusion
• Certain low-mass nuclei may be combined
to produce a nucleus with an average
binding energy per nucleon greater than
that for either of the original nuclei.
• This process is termed nuclear fusion and is
accompanied by the release of large
amounts of energy.
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41. Diagnostic Radiopharmaceuticals
• Every organ in our bodies acts differently from a chemical
point of view.
• Doctors and chemists have identified a number of chemicals
which are absorbed by specific organs.
– The thyroid takes up iodine.
– the brain consumes quantities of glucose.
• Radiopharmacists are able to attach various radioisotopes to
biologically active substances.
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42. Radioactive tracers
• An atom in a chemical compound is replaced by another
atom (radioactive isotope).
• Is often called radioactive labeling.
• A radioactive compound is introduced into a living organism
and the radio-isotope provides a means to construct an
image showing the way in which that compound and its
reaction products are distributed around the organism.
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radioactive isotope
chemical compound

43. Ioflupane (123I)
• Ioflupane has a high binding affinity for
presynaptic dopamine transporters (DAT)
in the brains.
• In particular the striatal region of the
brain.
• Parkinson's disease: reduction in
dopaminergic neurons in the striatal
region.
• By introducing an agent that binds to the
dopamine transporters a quantitative
measure and spatial distribution of the
transporters can be obtained.
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44. Ioflupane (123I)
• Ioflupane (123I) : radiopharmaceutical drug.
• Used by nuclear medicine physicians for
the diagnosis of Parkinson’s disease.
• I-123 has a half life of approximately 13
hours.
• A gamma photon energy of 159 keV making
it an appropriate radionuclide for medical
imaging.
44
Ioflupane (123I)

45. 45

46. Serial Transformation
• If the decay products of a radioactive material are themselves
radioactive, a decay chain is said to exist.
• The ingrowth of the first decay product is dependent on the
rate of decay of the parent, and so forth through each
daughter-product decay, until a stable isotope finally ends the
chain.
• The decay of krypton-90.
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47. Serial Transformation
• The 90Kr may be assumed to have been completely transformed, in a time period of 10–15 minutes.
• Rubidium-90, the 90Kr daughter, because of its 2.74-minute half-life, will suffer the same fate after
about an hour.
• Essentially, all the 90Kr is, as a result, converted into 90Sr within about an hour after its formation.
The buildup of 90Sr is therefore very rapid.
• The half-life of 90Sr is 28.8 years and its transformation, therefore, is very slow.
• The 90Y daughter of 90Sr, with a half-life of 64.2 hours, transforms rapidly to stable 90Zr.
• Because the 90Y transforms very much faster than 90Sr, a point is soon reached at which the
instantaneous amount of 90Sr that transforms is equal to that of 90Y.
• Under these conditions, the 90Y is said to be in secular equilibrium.
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48. Secular equilibrium
• The quantitative relationship between radionuclides in secular
equilibrium:
• C is stable and is not transformed. Because of the very long
half-life of A relative to B, the rate of formation of B may be
considered to be constant and equal to K.
• Under these conditions, the net rate of change of isotope B
with respect to time, if NB is the number of atoms of B in
existence at any time t after an initial number, is given by:
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TA >>>> TB λA <<<<< λB

49. 49
Secular equilibrium

50. Secular equilibrium
• As time increases, decreases and QB approaches QA.
• Equilibrium may be considered to be established after
about seven half-lives of the daughter. At equilibrium, it
should be noted that:
• Under the conditions of secular equilibrium, the activity
of the parent is equal to that of the daughter and that
the ratio of the decay constants of the parent and
daughter are in the inverse ratio of the equilibrium
concentrations of the parent and daughter.
50

51. Secular equilibrium
• This relationship enables us to
determine the decay rate constant,
and hence the half-life, of a very long
lived radionuclide.
• Secular equilibrium: Buildup of a very
short lived daughter from a very long
lived parent. The activity of the
parent remains constant.
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52. • The parent activity is not relatively constant
• The time rate of change of the number of atoms of species B
is given by the differential equation
• In this equation, is the rate of transformation of species A and is exactly
equal to the rate of formation of species B, the rate of transformation of isotope B
is , and the difference between these two rates at any time is the
instantaneous rate of growth of species B at that time..
Transient Equilibrium
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The half-life of the parent is greater than that of the daughter.
TA > TB λA < λB
rate of formation
rate of transformation
rate of change

53. Transient Equilibrium
• For the case in which the half-life of the parent is very much greater than
that of the daughter:
53
Secular equilibrium
λA <<<<< λB

54. Transient Equilibrium
• Two other general cases should be considered:
• Case 1: the case where the parent half-life is slightly greater
than that of the daughter (λA < λB).
• Case 2: the case in which the parent half-life is less than that
of the daughter (λB < λA).
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55. Transient Equilibrium
• Case 1: (λA < λB), the daughter activity starts from zero, rises to a maximum, and
then seems to decay with the same half-life as that of the parent.
• When this occurs, the daughter is undergoing transformation at the same rate as it
is being produced, and the two radionuclides are said to be in a state of transient
equilibrium.
• The activity of the daughter:
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56. Transient Equilibrium
• Case 1: (λA < λB)
• Since λB is greater than λA, then, after a sufficiently long
period of time, e−λB t will become much smaller than e−λAt :
• This equation may be rewritten as
• In terms of activity units :
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after a sufficiently long period of time

57. Transient Equilibrium
• Radioactive decay of molybdenum-
99 and ingrowth of technetium-99 m
with time (an example of transient
equilibrium). The amount of
radioactivity from each isotope is
plotted as a function of time.
• At transient equilibrium the
daughter activity seems to decrease
at the same rate as the parent
activity.
57

58. Technetium-99m
• The technetium isotope 99mTc is
unusual in that it has a half-life
for gamma emission of 6.03
hours.
• With such a long half-life for the
excited state leading to this
decay, this state is called a
metastable state, and that is the
reason for the designation 99m.
• The dominant decay mode gives
the useful gamma ray at 140.5
keV.
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59. Transient Equilibrium
• The time when the parent and daughter isotopes may be
considered to be equilibrated depends on their
respective half-lives.
• The shorter the half-life of the daughter relative to the
parent, the more rapidly will equilibrium be attained.
• In the case where the half-life of the daughter exceeds
that of the parent, no equilibrium is possible.
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60. No Equilibrium
• Case 2: the case in which the parent half-life is less than
that of the daughter (λB < λA).
• When the daughter half-life is longer than the parent
half-life, there is no equilibrium established between
them.
• As the short-lived parent dies off, the activity of the
daughter starts from zero, grows to a maximum, then
falls slowly at its own decay rate (the parent having since
died off and not able to influence daughter rate any
further).
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61. No equilibrium
61

62. Radioactive decay law
• The number of photons generated (number of
disintegrations) during time T is
62

63. Radioactivity

64. The internal conversion coefficient
• Occurs when nuclear de-excitation causes ejection of an electron from an atomic
shell as an alternative to gamma emission.
• The electron is ejected with kinetic energy Ek equal to the energy Eγ released by
the nucleus, reduced by the binding energy Eb of the electron.
• The internal conversion coefficient for an electron shell is the ratio of the number
of conversion electrons from the shell compared with the number of γ rays
emitted by the nucleus.
• K and L shell electrons are most likely to be involved due to their close proximity to
the nucleus.
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Ek = Eγ − Eb

65. Average Life
• Sum of the lifetimes of the individual atoms divided
by the total number of atoms originally present N0.
• The instantaneous transformation rate of a quantity
of radioisotope containing N atoms is λN.
• During the time interval between t and t + dt, the
total number of transformations is λN dt.
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66. Average Life
• Each of the atoms that decayed during this interval, however, had existed for a total lifetime t
since the beginning of observation on them.
• The sum of the lifetimes, therefore, of all the atoms that were transformed during the time
interval between t and t + dt, after having survived since time t = 0, is tλN dt.
• The average life, τ , of the radioactive species is
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67. Biological half-life
• When radiopharmaceuticals are used in human diagnostic
studies, there are two important characteristic times to
consider.
– The physical half-life of the parent radioisotope,
– The biological half-life: equal to the time for the body to wash out half
of the pharmaceutical.
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