RADIOACTIVITY
Chapter 28
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1
What is the RADIOACTIVE?
Radioactivity is a phenomenon in which
an unstable nuclei undergoes
spontaneous decay as a result of which
a new nucleus is formed and energy in
the form of radiation is released.
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RADIOACTIVITY
Nuclear
Radiation
Radioactive
Decay
ALPHA
( @ He)
Law of Radioactive
Decay
The Use of
Radioisotope
BETA
0
( @-1 e)
GAMMA
()
Decay
Constant ()
EXAMPLES
dN
 - N
dt
QUESTIONS
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Half Time
(T12)
ln 2

T1
Radioisotope as
 Tracers
 Sterilization
 Thickness
Gauge
 Carbon – 14
Dating
2
EXAMPLES
QUESTIONS
3
28.1 RADIOACTIVE DECAY
THE OBJECTIVES:
At the end of this chapter, students should be able to:
Explain α, β+, - and γ decays.
State decay law and use dN   N .
dt
Define and determine activity, A and decay
constant,  .
t
 t
Derive and use N  Noe
or A  Aoe .
Define and use half-life T1  ln 2 .

2
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RADIOACTIVITY
Is a spontaneous disintegration process of
heavy unstable elements accompanied by the
emission of alpha particle (), beta particle
(), or gamma rays ().
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RADIOACTIVE DECAY
Is a spontaneous reaction that is unplanned,
cannot be predicted and independent of physical
conditions (such as pressure, temperature) and
chemical changes.
It is a random reaction because the probability of
a nucleus decaying at a given instant is the same
for all the nuclei in the sample.
Radioactive radiations are emitted when an
unstable nucleus decays. The radiations are
  decay,   decay,   decay
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ALPHA DECAY ()
In  decay, the nucleus of heavy radioactive
element emits an -particle.
4
An -particle is a 2 He nucleus consists of two
protons and two neutrons.
It is positively charged particle and its value is
+2e with mass of 4.001502 u.
It is produced when a heavy nucleus (Z > 82)
decays.
Alpha particles can penetrate a sheet of paper.
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When a nucleus undergoes alpha decay it loses 4
nucleons (2 protons and 2 neutrons).
α particle
parent
daughter
The reaction can be represented by general
equation below :
A 4
4
A
Y
 2 He  Q
Z X  Z 2
(Parent) (Daughter) ( particle)
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general equation for -decay:
A
Z
where
X
X
Y
Q
A-4
Z-2
4
2
Y+ He+Q
= parent nucleus
= daughter nucleus
= energy released or -rays
-decay is followed by the emission of gamma rays
for the daughter to be stable
Eamples; A X  A-4 Y+ 4 He+Q
Z
parent
U 
234
90
Ra 
222
86
238
92
226
88
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Z-2
Daughter
2
 particle
Th + 42 He  Q
Rn+ 42 He+Q
10
The energy released appears in the form of
kinetic energy in the daughter nucleus and
the alpha particle which is given by
Q  mx  mY  m c
2
If Q < 0, decay
could not
occur
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BETA DECAY ()
In  decay, the nucleus emits a -particle (+ and -) that
has high velocity (v ~ c).
It has the same mass as electron or 0.000549 u.
Negatron decay, βNegatron (- or 10 e ) decay will happen when the number
of neutrons are more than the number of protons in a
nucleus.
Also called as negatron or electron.
0
0
Symbol; β or 1β or 1 e
It is produced when one of the neutrons in the parent
nucleus decays into a proton, an electron and an
antineutrino.
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Massless,
neutral
General equation of negatron decay process:
A
Z
X
parent
Y+ β  v
A
Z+1
Daughter
0
1
 particle antineutrino
where v is called ‘antineutrino’ (an elementary particle
that exist to account the missing energy in negatron
decay)
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In beta-minus decay, an electron is emitted, thus the
mass number does not charge but the charge of the
parent nucleus increases by one as shown below :
A
Z

X
A
Z 1
0
1

Y
e  Q
(Daughter) ( particle)
(Parent)
Examples of  minus decay :
A
Z
X
(Parent)

234
91
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
Y
(Daughter)
Th 
234
90
A
Z 1
234
91
Pa 
0
1
e  Q
( particle)
Pa 
U
234
92
0
-1
0
-1
eQ
eQ
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Positron decay, β+
Positron (+ or 10e ) decay will happen when the number
of protons is more than the number of neutrons in a
nucleus.
Also called as positron or antielectron.
Symbol;
β+
or β or e
0
1
0
1
It is produced when one of the protons in the parent
nucleus decays into a neutron, a positron and a
neutrino.
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Massless,
neutral
General equation of negatron decay process:
A
Z
X
parent
Y+ β  v
A
Z+1
Daughter
0
1
 particle neutrino
where v is called ‘neutrino’ (an elementary particle that
exist to account the missing energy in positron decay)
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In beta-plus decay, a positron is emitted, this time the
charge of the parent nucleus decreases by one as shown
below :
A
Z
(Parent)
X

A
0

 1
Z-1
(Daughter)
(Positron)
Y
e
Q
Example of  plus decay :
A
Z
X
(Parent)
12
7

0
A
 1 
Z-1
(Daughter) (Positron)
Y
e
Q
N 126C 10e  v  Q
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GAMMA DECAY ()
In -decay, a photon (-ray) is emitted when the
excited nucleus changes from a higher level energy
state to a lower level. The wavelengths of the
electromagnetic radiation are shorter than 10-10 m.
Gamma rays photon are emitted when an excited
nucleus in an excited state makes a transition to a
ground state. This will happen when the nucleus
decays into alpha or beta particles.
thus gamma-ray emission often associates with
other type of decays.
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General equation for gamma decay:
A
*
A
Z
Z
X  X 
X* = excited nucleus
X = stable nucleus
The asterisk (*) indicates that the nucleus is in an
excited state.
There is no change in the proton number and the mass
number of the nucleus
Examples of -decay;
where
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
Po  Pb He  γ
Pa  U  e  γ
Ti  Ti  γ
218
84
234
91
208
81
214
82
234
92
208
81
4
2
0
1
Gamma ray
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-ray is uncharged (neutral) ray and zero mass.
The differ between gamma-rays and x-rays of the
same wavelength only in the manner in which
they are produced; gamma-rays are a result of
nuclear processes, whereas x-rays originate
outside the nucleus.
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Comparison of the properties of the alpha particle,
beta particle and gamma ray.
Table 28.1 shows the comparison between the radioactive radiations
Alpha
Beta
Gamma
Yes
Yes
No
Ionization power
Strong
Moderate
Weak
Penetration power
Weak
Moderate
Strong
Ability to affect a
photographic plate
Yes
Yes
Yes
Ability to produce
fluorescence
Yes
Yes
Yes
Charge
Deflection by
electric and
magnetic fields
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Comparison of the properties of the alpha particle, beta particle
and gamma ray.
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Comparison of the properties of the alpha particle,
beta particle and gamma ray.
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Example 28.1:
Write equations to represent the following radioactive
decay.
238
a) 92 U decays by emitting an alpha-particle and a gamma
photon.
32
b) 15
c) 64
29
P decays by beta-emission.
Cu decays by positron-emission.
You may use X, Y and Z to represent the daughter nuclides.
Solution 28.1:
a)
b)
c)
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Example 28.2:
238
92
U decays through a series of transformations to a final
stable nuclide. The particles emitted in the first five
successive transformations are alpha-particle, negatronparticle, electron-particle, alpha-particle and alpha-particle.
Write an equation to represent each sequence of the nuclear
transformations. You may use A, B, C, D and E to represent
the ‘daughter’ nuclides for the successive transformations.
Solution 28.2:
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Example 28.3:
211
83
Bi decays to Po according to the equation
211
83
Bi  Po  β  γ
where  is a -particle and  is a -ray photon. What is the
proton number (atomic number) of Po?
A. 82
B. 84
C. 207
D. 212
Example 28.4
Complete the following radioactive decays and identify the
radiations emitted.
a)
b)
c)
Th 
234
90
14
6
C 
Na 
22
11
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
Pa 
e
N

Ne 
e + γ

e
27
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QUESTION 1:
Determine the energy released when a Uranium 238
U decays by
92
emitting an -particle to form a Thorium nucleus = 234
90 Th.
234
(mass of 238
U
=
238.0508
u;
mass
of
Th = 234.0436 u; mass of
92
90
4
He = 4.0026 u; 1 u = 934 MeV). (4.3 MeV)
2
QUESTION 2:
Find the energy released during a -decay in which a Thorium
234
nucleus 234
Th
is
converted
to
a
protactinium
nucleus
Pa.
90
91
234
(mass of 234
Th
=
234.0436
u;
mass
of
91 Pa = 234.04330 u; 1 u =
90
934 MeV). (0.27 MeV)
QUESTION 3
Polonium 216
84 Po undergoes an -decay to produce a daughter
nucleus that itself undergoes of -decay. What is the atomic number
and mass number of the final nuclide?
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dN
  N
dt
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DECAY CONSTANT ()
Decay constant, 
Decay law states that the rate of disintegration of
a given nuclide at any time (rate of decay) is
directly proportional to the number of nuclei N
present at that time.
OR
 dN 


 dt 
For a radioactive source, the decay rate
is
directly proportional to the number of radioactive
nuclei N remaining in the source.
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 dN 

 N
 dt 
dN
 N  At
dt
Decay
rate
known as
Activity,
A
dN
 At
dt
Negative sign means the number
of nuclei present decreases with
time
Unit is the Becquerel, (Bq)
 1 Bq is the rate of decay of
1 nucleus per second
= the activity
= the decays per second
= the disintegrations per second by the radioactive
nucleus
(1 Bq = 1 decay/s)
(1 Ci (curie) =3.7 × 1010 Bq)
N = the number of nuclei remain (present).
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dN
 N  At
dt
λ = decay constant

dN
dt
N
• Hence, the Decay constant of a nuclide is the probability
that a radioactive atom will decay in one second.
• Its unit is s-1.
• It has different values for different nuclides.
• Decay constant is the characteristic of the
radioactive nuclide.
• The larger the decay constant, the greater is the
rate of decay.
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DERIVATION
From the equation dN  N , dN  dt
dt
N
At time t=0, N=N0 (initial number of radioactive nuclei in the
sample) and after a time t, the number of radioactive nuclei
present is N.
By integrating the equation from t = 0 to time t :
t
dN
N0 N   0 dt
N
t
ln N N0  t 0
N
ln
  λt
N0
N
Exponential law of
radioactive decay
N  N 0 e  λt
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
N
No
1
t
dN    0 dt
N
ln
N
N
No
 t
ln N  ln N o   λt
 N 
   λt
ln 
 No 
N
 e  λt
No
N  N o e  λt
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Graph of N (number of remaining nucleus)
versus t (decay time)
N
No
N = Noe-t
No / 2
T½ = Half-life
No / 4
No / 8
0
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T½
2T½
3T½ 4T½
time, t
37
From the law of radioactive decay, dN  N and definition of
Activity,
Thus,
dt
dN
 At
dt
A  N and

A   N 0e t

N  N 0e
  N 0 e t
A  A0 e
Activity at time t
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and
 t
A0  N 0
 λt
Activity at time, t =0
38
T1 
2
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ln 2

39
HALF-LIFE, T 1
2
• time required for the number of radioactive nuclei to
decrease to half of the original number of nuclei
• At t = T 1 and N = N0 / 2
N  N o e  λt
from
2
1
2
N o  N o e  λT1/2
1
2
 e  λT1/2
e λT1/2  2
λT1/2  ln 2
T1 
2
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ln 2

40
• The half-life of any given radioactive nuclide is
constant, it does not depend on the number of nuclei
present.
• The units of the half-life are second (s), minute (min),
hour (hr), day and year (yr).
• Its depend on the unit of the decay constant.
Table 28.2
shows the value
of half-life for
several
isotopes.
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Isotope
Half-life
238
92 U
226
88 Ra
4.5  109 years
210
884 Po
234
90Th
222
86 Rn
138 days
214
83 Bi
20 minutes
1.6  103 years
24 days
3.8 days
41
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Example 28.5
A sample of
32
15
P of mass 4.0 × 10-12 kg emits 4.2 × 107 -particles
per second. What is the decay constant of
32
15
P?
Solution 28.5:
Mass of 1 mol of
× 1023 atoms.
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32
15
P is 0.032 kg. Hence 0.032 kg 32
15 P contains 6.02
43
• Example 28.6:
Initially, a radioactive sample contains
1.0  106 of radioactive nucleus. Half-life of
the sample is T½. Find the number of
nucleus that still remains after 0.5 T½.
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• Solution 28.6:
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•
Example 28.7:
Thorium-234 has T1 = 24 days. Initial
2
activity of this particular isotope source is 10
Ci.
a) How much is the activity of this source after
72 days?
b) How long does it take for the activity to
become 2.5 Ci?
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• Solution 28.7:
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47
• Solution 28.7:
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Example 28.8:
The activity of a sample of Radon-222 contains 3.0 × 107
radon atoms is 120 Bq. The half-life of Radon-222 is 3.8
days.
a) What is the decay constant of Radon-222?
b) Calculate the number of Radon-222 atoms in the
sample.
c) How many atoms of Radon-222 remain in the sample
when the activity is 40 Bq?
d) How many Radon-222 atoms present after 19 days?
e) Find the activity of the Radon after 19 days.
Solution 28.8:
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Solution 28.8:
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Solution 28.8:
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Solution 28.7:
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Quiz!!!!
• One of the usages of radioactive is the radioactive
dating which is a method to determine the age of a
thing base on the rate of decay and the half-life of
the known element. The half-life of C-14 is known
as 5 600 years. If a 10 g of carbon sample from a
living tree gives a rate of decay of 500 per hour
whereas a 10 g carbon sample obtained from an
antique gives a rate of decay of 100 per hour,
determine the age of the antique.
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• Solution
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QUESTION 1:
Find the half-life of radioactive sample if its activity decreased to 1/8
of its initial value in 9 days. (9 days)
QUESTION 2:
The half-life of Radon 219
86 Rn is 4.0 s.
a) What do the numbers 86 and 219 represent in the symbol 219
86 Rn?
b) Calculate the decay constant of 219
86 Rn.
c) Given that 219 g of Radon contains 6.02  1023 atoms, calculate
the rate of disintegration of 1.00 g of 219
86 Rn.
(0.173 s-1, 4.761021 Bq)
QUESTION 3:
87
Kr  has a half-life of 78 minutes. Calculate
An isotope of krypton 36
the activity of 10µg of krypton (in Bq and Ci). (1.02  1013 Bq, 275.7 Ci)
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QUESTION 4:
A sample of radioactive material has an activity of 9.00 x 1012 Bq.
The material has a half-life of 80.0 s. How long will it take for the
activity to fall to 2.00 x 1012 Bq ?
(174 s)
QUESTION 5:
What mass of radium 227 would have an activity of 1.0 x 106
Bq? The half-life of radium 227 is 41 minutes.
(1.34  10-12 g)
QUESTION 6:
a) The half-life of the isotope 45K is 17.3 minutes. How long will it
take for 75% of the nuclei of the isotope to decay? (34.6 min)
b) After 4 hours, 80% of the initial number of nuclei of a radioactive
isotope have undergone decay. Calculate the half-life. (1.72 h)
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28.2 RADIOISOTOPE AS
TRACERS
THE OBJECTIVES:
At the end of this chapter, students should be able to:
Explain the application radioisotope as
tracers.
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58
28.2 The use of Radioisotope
Nuclear techniques are widely used in industry &
environmental management.
Modern industry uses radioisotopes in a variety of
ways to improve productivity and in some case, to
gain information that cannot be obtained in any
other way.
a)
Radioisotope as tracers
Radioisotope (unstable isotope) is an isotope which is
exhibits radioactivity (known as radioactive isotope).
The progress of a small amount of a weak radioisotope
injected into a system can be traced by a detector.
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Examples:
i) To investigate metabolic pathways or blood flow:
A small quantity of iodine-131 is injected into a patient’s
bloodstream and later builds up in the kidneys. The
process of the iodine is measured by a detector outside
the body around the kidney region. If there is a blockage,
the count rate will rise.
It is used to investigate organs in human body such as
kidney, thyroid gland, heart, brain, and etc..
It also used to monitor the blood flow and measure
the blood volume.
The volume of blood in the bloodstream, V2 can be
determined by using dilution method as given below.
 A2 
V2   V1
 A1 
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A1 A2

V1 V2
60
where
A1 A2

V1 V2
A1 = activity of the blood drawn from the patient
A2 = activity of the blood in the bloodstream
V1 = volume of the blood drawn from the patient
V2 = volume of blood in the bloodstream of the patient
A1
 activity per unit volume of the blood draw nfrom the patient
V1
A2
 activity per unit volume of the blood in the blood stream
V2
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Example 28.9
A small volume of a solution which contains a
radioactive isotope of sodium Na-24 has an activity of
1.5 x 104 Bq. The solution is injected into the
bloodstream of a patient. The half-life of the sodium
isotope is 15 hours. After 30 hours, the activity of 1.0
cm3 of blood is measured and found to be 0.50 Bq.
Estimate the volume of blood in the patient.
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Solution 28.9
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63
ii) Detecting leaks in underground pipes.
The exact position of an underground pipe can be
located if a small quantity of radioactive liquid is
added to the liquid being carried by the pipe.
Geiger counter can be used to detect the leaks.
Any leaks would be detected by an increase in
radiation reading .
The soil close to the leak becomes radioactive.
The short-lived radioisotope is used to avoid from
the permanent contamination of the soil.
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iii) Detecting brain tumors.
Technitium-99 is a gamma emitter (half-life 6
hours) and is used as a medical tracer.
When injected into the blood stream, 99 Tc will not
be absorbed by the brain, because of the blood-brain
barrier.
However, tumors do not have this barrier.
Thus, brain tumors readily absorb the 99 Tc.
These tumors then show as gamma-ray emitters on
detectors external to the body.
The short-lived radioisotope is used so that it
can quickly eliminate from the body.
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iv) To detect oil leakage:
A gamma emitter is added to the oil. The detector will
show an unusually high count rate at the crack position.
b)
Radioisotope as Sterilization:
Gamma irradiation is widely used for sterilizing medical
instruments and for food by killing bacteria.
Cobalt-60 is the main isotope used since it is an energetic
gamma emitter.
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66
Good luck
For
LAST Semester Examination
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