5.3.3 Radioactivity
(a) describe the spontaneous and random
nature of radioactive decay of unstable
nuclei
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Radioactive decay
Stable
Unstable:
Will emit radiation randomly once
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Radioactive decay
Nuclear decay is spontaneous because:
 the decay of a particular nucleus is not affected by the
presence of other nuclei
 the decay of nuclei cannot be affected by chemical
reactions or external factors such as temperature and
pressure
and is random because:
 it is impossible to predict when a particular nucleus in
the sample is going to decay
 each nucleus in a sample has the same chance of
decaying per unit time
(b) describe the nature, penetration and
range of α- particles, β-particles and γ-rays
2 Protons
ALPHA
2 Neutrons
High Energy
Electron
LEAD
GAMMA
ALUMINIUM
BETA
PAPER
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Radiation penetration
High
Frequency
Wave
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Radiation penetration
Type of decay:
Alpha decay
What is emitted?
Alpha particle (helium nuclei)
Description of
decay:
2 neutrons and 2 protons are
emitted from the nucleus.
Example of decay:
238
92
U 
234
4
Th +
90
 + energy
2
A decreases by 4, Z decreases by 2
Effect on A and Z:
(A-4, Z-2)
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Radiation penetration
Type of decay:
Beta decay
What is emitted?
High energy electron
Description of
decay:
A neutron in the nucleus decays into a
proton and a high energy electron which
is emitted with an anti-neutrino.
Example of decay:
14
C 
6
Effect on A and Z:
14
0
N+
7

+ ν
-1
A stays the same, Z increases by 1
(A=, Z+1)
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Radiation penetration
Type of decay:
Gamma decay
What is emitted?
High energy electromagnetic radiation
Description of
decay:
Nucleus loses energy and becomes
more stable. Gamma radiation is the
energy it loses.
A stays the same, Z stays the same
Effect on A and Z:
(A=, Z=)
(c) define and use the quantities activity and
decay constant
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Activity
The activity of a source is defined as follows:
The activity A of a radioactive sample is the rate
at which nuclei decay or disintegrate
Activity is measured in decays per second (or h-1 or day-1,
etc)
An activity of one decay per second is one becquerel (1
Bq)
1 Bq = 1 s-1
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Decay constant
The decay constant of a source is defined as follows:
The decay constant λ is the probability that an
individual nucleus will decay per unit time interval
For example, in a sample of one million nuclei, if 200 000
in one hour, then the decay constant is
Decay constant λ = 0.20 h-1
(d) select and apply the equation for activity
A = λN
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Activity equation
 Activity of a sample depends on the decay constant λ
 The greater the decay constant, the greater the activity
 Activity also depends on the number of undecayed
nuclei in the sample N
A = λN
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Questions
1.
A sample of carbon-15 initially contains 500 000
Aundecayed
= λN nuclei. The decay constant for this isotope
-1 x 500 000
=
0.30
s
of carbon is 0.30 s-1. Determine the initial activity of the
-1 or 150 000 Bq
=
150
000
s
sample
2.
A small sample of radium gives a received count rate
Count
rate per minute
= 20inma-1 detector.
thereforeIt0.33
s-1 that
of 20 counts
is known
Activity
= 3.310%
s-1 of the decays from the
the counter detects only
sample. The sample contains 1.5 x 109 undecayed
9
Decay
= 3.3
s-1 constant
/ 1.5 x 10of
nuclei. Constant
Determine the
decay
this form of
= 2.0 x 10-9 s-1
radium
(e) select and apply the equations A = Aoe-λt and
N = Noe-λt where A is the activity and N is the
number of undecayed nuclei
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Decay equations
100
Undecayed Atoms [N]
or
Activity [A] (s-1)
50
0
0
14
Time [t] (s)
28
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Decay equations
The decay in the graph can be expressed as an
equation
If N0 is the number of undecayed nuclei, then N
that remain undecayed after time t is given by:
N = Noe-λt
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Decay equations
The activity A of a sample is proportional to the
number of undecayed nuclei N. Hence the
activity of the sample decreases exponentially:
A = Aoe-λt
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Questions
 Now attempt SAQ 13, 14 and 15
 Use Worked Example 5 & 6 for help
(e) define and apply the term half-life
Undecayed Atoms
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Half-life
100
50
0
0
14
Time (s)
28
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Half-life
The half-life t½ of a radioisotope is the mean
time taken for half of the active nuclei in a
sample to decay
(g) select and use the equation λt1/2 = 0.693
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Decay constant and half-life
The decay constant and half-life are connected by the
formula:
λt1/2 = 0.693
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Assessment
 Chapter 14 SAQ’s 1 to 21
 End of Chapter 14 questions 1 - 5
 Radioactivity worksheet questions