Radioactive Decays
transmutations 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.
Radioactive Decays
1
A Summary of Radioactive Decay Kinetics
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 .
dN
A = – ––––– =  N
dt
ln N = ln No –  t
Integration gives
Also A = Ao e –  t
or
N = No e –  t
What is decay rate?
Radioactive
Decays
How does decay rate vary with
time?
2
Radioactive Decay Kinetics - plot
Variation of N as a function of time t
No
N
N = No e
Also A = Ao e
- t
- t
t
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
Radioactive Decays
3
Decay Constant and Half-life
Variation of N as a function of time t
Ln(N or A)
No
ln N1 – ln N2
 = –––––––––––
t1 – t2
N
N = No e - t
Also A = Ao e - t
t
t½ *  = ln 2
Be able to apply these
equations!
N = No e– t
A = Ao e – t
ln N = ln No –  t
ln A = ln Ao –  t
t
Radioactive Decays
Determine half life, t½
4
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.
Apparent Radioactivity of 3 Nuclides
ln A
ln Atotal
ln A1
ln A2
ln A3
Ln A
t
t
Analyze and explain
Radioactive Decays
5
Radioactive Consecutive Decay and Growth
Radioactivity of Decay Product
Ln A
238U

234
Th + 4
234Th 234Pa
+
Total Activity
Activity due to
Activity due to
234
Th
238U
t
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 Radioactive
half life.Decays
6
Radioactive consecutive decay animation
See Simulation in Radioactive Decay in
SCI270 website
The simulation will be used to illustrate
various conditions.
Radioactive Decays
7
Applications of Radioactive Decay Kinetic
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.
Radioactive Decays
Nuclide Half life
219Th90 1 s
26Na11 1s
40Cl17
1.4 min
32P15
14.3 d
14C6
5730 y
235U92
7.04x108 y
238U92
4.46x109 y
8
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 Decay
A Z
P
A–4
DZ–2
4He2
Radioactive Decays
How do nuclides transform in alpha
decay?
9
Nuclide Transmutation of  Decay
APZ

A – 4DZ – 2
+ 4He2
Heavy Nuclide alpha emitters
235U92  231Th90 + 42 (t , 7.13×108 y)
½
238U92

208Po84

234Th90
+ 42 (t½, 4.51×109 y)
204Pb82
+ 42 (t½, 2.9 y)
How do nuclides transform in alpha decay?
Mass and charge change byRadioactive
what? Decays
10
Nuclide Transmutation of  Decay
APZ  A – 4DZ – 2 + 4He2
light nuclides
5He  1n0 + 42 (t , 2×10-21 s),
½
5Li  1p1 + 42 (t , ~10-21 s),
½
8Be  2 42 (t , 2×10-16 s).
½
Some rare earth (144 Nd, 146Sm, 147Sm, 147Eu,
...174Hf) are  emitters:
144Nd  140Ce + 42 (t , 5×1015 y),
½
174Hf  170Yb + 42 (t , 2×1015 y).
½
Radioactive Decays
11
Nuclide Transmutation of  Decay
Beta decay consists of three processes: emitting an electron, emitting a
positron, or capturing an electron from the atomic orbital.
Electron emission
APZ
+ n  ADZ + 1 + – (absorbs a neutrino)
APZ

or
ADZ + 1
+ – + n (emit antineutrino, n)
Positron emission
Electron capture
APZ
ADZ – 1 + + + n
APZ
+ n ADZ – 1 + +.
or
What is beta decay?
or
Radioactive Decays
APZ
+ e– ADZ – 1 + n
APZ
+ e– + n ADZ – 1
12
Nuclide Transmutation of – Decay – examples
1n 0

1p1
+
–
+n
Beta Decay of Neutron
Other examples of beta decay
 14N7 + – + n (t½, 5720 y)
40K19  40Ca20 + – + n (1.27e9 y)
50V23  50Cr24 + – + n (6e15 y)
87Rb37  87Sr38 + – + n (5.7e10 y)
115In49  115Sn50 + – + n (5e14 y)
14C6
Proton
Neutron
Electron
What is the relationship between the
parent nuclide and the daughter
nuclide in – decay?
Radioactive Decays
13
Nuclide Transmutation of + Decay – examples
In + decay, the atomic number decreases by 1.
 21Ne10 + + + n
30P15
 30Si14 + + + n
34Cl17  34S16 + + + n
116Sb51  116Sn50 + + + n
21Na11
(t½, 22s)
(2.5 m)
(1.6 s)
(60 m)
What is the relationship between the
parent nuclide and the daughter
nuclide in + decay?
Radioactive Decays
14
Nuclide Transmutation of EC – examples
 48Ti22 + + + + n
(50%)
48V + e–  48Ti + n(+ X-ray) (50%)
48V23
Electron Capture and X-ray Emission
X-ray
What is the relationship
between the parent nuclide
and the daughter nuclide in
electron capture (EC)?
What can be detected in EC?
EC
Radioactive Decays
15
Electron capture and internal conversion
Electron Capture and Internal Conversion
EC
Internal
conversion
Explain electron capture and
internal conversion processes.
What are internal conversion
electrons?
Radioactive Decays
16
Transmutation of gamma decay
Gamma decay emits energy from atomic nucleus as photons.
Gamma, , decay follows  and  decay or from isomers.
 99Tc + 
60Co  60mNi +  + n (antineutrino)
60mNi 60Ni + 
99mTc

24Na 
60Co
++ +
24Mg +  + + 
60Ni
What is gamma decay?
Radioactive Decays
(t½, 5.24 y)
(2.75 MeV, t½, 15 h).
17
-decay and Internal Conversion
Internal Conversion Electron and X-ray Emission
X-ray
Internal
conversion
electron
Internal conversion electrons show up in  spectrum.
X-ray energy is slightly different from the photon energy.
Radioactive Decays
What are internal conversion electrons?
18
Transmutation in Other Decays
Transmutation in proton decays
53mCo27 —(1.5 %) 52Fe26 + 1p1
—(98.5 %) 53Fe26 +  + + n.
Beta-delayed Alpha and Proton Emissions:
8B 8mBe + + + n (t , 0.78 s)
½
8Li 8mBe + - + n (t , 0.82 s)
½
8mBe  2 
Apply
conservation of
mass, nucleon,
and charge to
explain
transmutation in
all radioactive
decays.
These are called +, and – decays respectively.
Another examples of +and +p+ decay:
20Na  20Ne +  + + n (t , 0.39 s)
½
20Ne  16O + 
111Te

+  + + n (t½, 19.5 s)
111Sb  110Sn + p+.
111Sb
Radioactive Decays
19
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.
Radioactive Decays
20
Nuclide Chart for Nuclear Properties
6
Be
4
Be, ?
p
6.019725
Be, 53.3 d
EC 0.86
7.01928
5
Li
3
3
He,0.0001
%
3.01603
He
2
H
1
7
1
H,99.99
%
1.007825
N
0
p# 0
 n
#
2
H, 0.015%
2.0142
1 0,
n 12 m
 0.78
1.008665
1
Li, 0.18 s 6Li, 7.42%
p or 
6.015121
5.01254
4
He,100% 5He,?
n, 
4.0026
5.01222
3
H, 12.26y
 0.0186
3.014102
8
10
Be, 0.06 9Be, 100%
Be,
fs
1.6x106 y
9.012182
2  0.86
 0.5
8.005305
7
Li, 92.5% 8Li, 0.85 s
 16
7.016003 8.022485
6
8
He 0.81s 7He
He, 1s
 3.51
n, 14
6.018886
8.03392
Symbol, abundance or half-life,
(fs =10–15s, second, minute, year)
Decay mode: , ,  energy MeV,
Mass in amu
2
3
4
5
Radioactive
Decays
Chart of some light
nuclides
with a key in the large square.
6
21
Isotopes Isotones, and Isobars
No. of
protons
Relationships of Isotopes
Isobars, and Isotones on
Chart of Nuclides
Isomers
I S O T O P E S
S S
O
O
a Nuclide
T
B
O
A
N
R
E
S
S
Recognize 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.
No. of neutrons
Radioactive Decays
22
Families of Radioactive Decay Series
Radioactive Decay Series of 238U
238U92

234Th90
+ 42
234Th90

(t1/2 4.5e9 y)
234Pa91
234Pa91
+ – + n (t1/2 24.1 d)
 234U92 + – + n
234U92
(t1/2 6.7 h)
. . . (continue)
. . .
Only alpha decay changes the mass number by 4.
206Pb82
There are 4 families of decay series.
4n, 4n+1, 4n+2, 4n+3,
n being an integer.
Radioactive Decays
23
Radioactivity - 238U radioactive decay series
The Decay Path of 4n + 2 or 238U Family
234
230
226
222
218
210
Po
210
206
Pb
206
Tl
206
214
Bi
210
Hg
Po
214
Pb
Bi
214
210
Tl
At
218
Rn
Po
Pb
U
238
234
Pa
234
Th
Th
Ra
 decay
Major route
Minor route
 decay
Radioactive Decays
24
U
Radioactivity - 239Np radioactive decay series
The Decay Paths of the 4n + 1 or 237Np93 Family Series
233
(1.6e5 y)
229
221
213
209
Bi83
209
Po84

Pb82
209

Fr87

217
At85
 (1 min)
213 83
Bi
Np93
 (2e6 y)
233
Pa91
Th90
(7300 y; minor path)
225
(10 d)
Ac89
U92

237
225
Ra88

81
Tl
Radioactive Decays
25
Radioactivity - A Closer Look at Atomic Nuclei
Considering the atomic
nucleus being made up of
protons and neutrons
Proton
neutron
Key terms:
mass, (atomic weight)
atomic number Z
mass number A or M
proton, neutron
nucleon, baryon
(free nucleon)
Lepton (electron)
Radioactive Decays
26
Properties of Subatomic Particles
Properties of Baryons and Leptons
Baryons_____
Proton
Neutron
Rest
1.00727647 1.0086649
Mass
938.2723
939.5653
Charge* 1
0
Spin
½
½
_____Leptons______
Electron
Neutrino Units
5.485799e-4 <10–10 amu
0.51899
<5x10–7 MeV
–1
0
e–
½
½
(h/2p)
Magnetic
moment* 2.7928474 N -1.9130428 N 1.00115965B
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.
Radioactive Decays
27
Mass of Protons, Neutrons & Hydrogen Atom
Rest
Mass
Proton
Neutron
1.00727647 1.0086649
938.2723 939.5653
Electron
Neutrino Units
5.485799e-4 <10–10 amu
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)
Radioactive Decays
28
Magnetic Moment of Particles
A close-loop current in a uniform magnetic
field experiences a torque if the plane of the
loop is not perpendicular to the magnetic field.
i
Radioactive Decays
29
Nuclear Models
Each 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.
Radioactive Decays
30
The potential well of nucleons in a nucleus for the shell model
The concept of quantum theory will be elaborated during the lecture.
Radioactive Decays
31
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.
Radioactive Decays
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.
32
The shell model
Quantum 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 number
s = 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.
Radioactive Decays
33
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.
Radioactive Decays
34
Radioactivity &
the shell model
Energy Level Diagram of Nucleons
n
l
j
7
6
6
6
6
6
6
0
1
2
3
4
13
6
5
5
5
5
5
0
2
3
4
11
5
4
4
4

(2j+1)
Notation
/2 +
½–
3
/2 –
5
/2 –
7
/2 –
9
/2 –
Shell
total
1i
3p
3p
2f
2f
1h
14
2
4
6
8
10
~126
/2–
½+
3
/2 +
5
/2 +
7
/2 +
1h
3s
2d
2d
1g
12
2
4
6
8
~82
4
0
1
2
9
/2 +
½–
3
/2 –
5
/2 –
1g
2p
2p
1f
10
2
4
6
~50
4
3
7
/2 –
1f
8
~28
½ + ___________ 6.54 MeV
3
3
3
0
1
2
½+
/2 +
5
/2 +
2s
1d
1d
2
4
6
~20
7/
2
0
1
3
½–
/2 –
1p
1p
2
4
~8
1
0
½+
1s
2
~2
3
Energy states of nuclei are
labelled using
J = j1 + j2 + j3 + j4 + ...
plus parity,
J+
Some Excited States of the 7Li
Nuclide
2
+ ___________ 4.64
½ – ___________ 0.478
3/ – ___________ Ground State
2
Radioactive Decays
35
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 Decays
36
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
Interesting Items:
Spectrum of particles
Energy in gamma decay
Energy in beta decay
Energy in alpha decay


Recoiling nucleus
Radioactive Decays
37
Gamma Decay Energy
Gamma, , rays are electromagnetic radiation emitted from atomic nuclei.
The bundles of energy emitted are called photons.
Excited nuclei are called
isomers, and de-excitation is
called isomeric transition (IT).
Energy for photons
Ei ____________
hv=Ei-Ef
Ef ____________
hv
Eothers _________
Radioactive Decays
38
Nature of Gamma Transitions
Types of Isomeric Transitions and their Ranges of Half-life
Radiation Type Symbol
J
p
Partial half life t (s)
Electric dipole
Magnetic dipole
Electric quadrupole
Magnetic quadrupole
Electric octupole
Magnetic octupole
Electric 24-pole
Magnetic 24-pole
1
1
2
2
3
3
4
4
Yes
No
No
Yes
Yes
No
No
Yes
5.7e-15 E–3 A–2/3
2.2e-14 E–3
6.7e-9 E–5 A–4/3
2.6e-8 E–5 A–2/3
1.2e-2 E–7 A–2
4.9e-2 E–7 A–4/3
3.4e4 E–9 A–8/3
1.3e5 E–9 A–2
E1
M1
E2
M2
E3
M3
E4
M4
Radioactive Decays
39
Gamma Decay Energy and Spectrum
Gamma transition of 7Li
Various Gamma Transitions in 7Li
½+ 6.54 MeV
M3
E3
M1
E1
M2
7/2+
4.64 MeV
½ – 0.778 MeV
3/2– ground state
Radioactive Decays
40
Gamma Decay Energy and Spectrum
Gamma Ray Spectrum of O18
h
Intensity
2+
3.27 MeV
1.98 MeV
1.98
2+
0+
3.27 MeV
5.25 MeV
E
Radioactive Decays
41
Beta Decay Spectrum
A Typical Beta Spectrum
Intensity
or # of 
Internal conversion electrons
E max
Energy of 
Radioactive Decays
42
Beta Decay
Spectra
A Typical Beta Spectrum
64
Cu
41%EC 1+
2+
0+
40%–
64
64
Ni
0+
Zn
19%+
Intensity
–
Decay of 64Cu
illustrates several
interesting features
of beta decay and
stability of nuclides.
+
0.58 MeV
0.66 MeV
Radioactive Decays
E
43
Beta Decay Spectra and Neutrino
A Beta Decay Scheme
P D
Z
Z+1
A Typical Beta Spectrum
+  +v
–
Intensity
or # of 
?
E max
Energy of 
Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta,
carrying the missing energy.
Correct notes
Radioactive Decays
44
Positron Decay Energy
Positron Emission
–
+
n
Positron emission
P Z  D Z–1 + e– + + + n + Edecay.
Edecay = MP - MD – 2 me.
Radioactive Decays
45
Beta Decay Energy and Half-life
A Sargent Diagram
Log  (s–1)
210
Pb
212
The higher the decay
energy, the shorter
the half-life, but
there are other
factors.
 210Bi
 228Ac
Pb
214
Pb
208
Tl
234
Pa
 212Bi
 214Bi
Log E (eV)
Radioactive Decays
46
Alpha Decay Energy & Spectrum
An Ideal Alpha Spectrum
No.
of


 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/ + 
 – 98.9%
2
211Po
Radioactive Decays
 MeV
8
10
47
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 Decays
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