Radioactivity
Radioactivity is the spontaneous
disintegration of an unstable nucleus.
All spontaneous nuclear reactions are
exothermic.
Three types of radiation are alpha, beta, and
gamma.
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Alpha Radiation
An alpha particle symbolized by α is the
nucleus of a helium atom.
Another way to symbolize an alpha particle is
4 He .
2
An example of alpha decay is given by the
equation:
238U
92
234Th + 4 He
90
2
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During alpha emission, the atomic number
decreases by 2 and the mass number
decreases by 4.
Also indicated in the nuclear equation shown
below is a conservation of mass-energy and
charge.
Mass number which is the number
of nucleons.
238U
92
234Th + 4 He
90
2
Atomic number which is the
number of protons.
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Beta Particles
A beta particle symbolized by β is a high
speed electron.
Another way to symbolize an beta particle is
0e.
1
An example of beta decay is given by the
equation:
1n
0
1p + 0 e
1
1
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During beta emission, the atomic number
increases by 1 and the mass number remains
the same.
Also indicated in the nuclear equation shown
below is a conservation of mass-energy and
charge.
Mass number which is the number
of nucleons.
1n
0
1p + 0 e
1
1
Atomic number which is the
number of protons.
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Gamma Radiation
A gamma particle symbolized by γ is a high
energy photon.
γ decay results from the redistribution of
charge in the nucleus and accompanies most
nuclear reactions.
Because neither the mass number nor the
atomic number changes during γ decay it is
usually omitted from nuclear equations.
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A particular decay series starts with U-238
followed by 4 emissions. The order of the
emissions are an alpha, two beta, and
another alpha decay. What are you left with
after the 4th decay?
238U
92
234Th + 4 He
90
2
234Th
90
234U + 2 0e
-1
92
234U
92
4 He + 230Th
2
90
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Half-Life a Measure of Nuclear Activity
The half-life of a radioisotope (a radioactive
isotope) is the time necessary for one-half of
the atoms/nuclei to decay.
The rate of decay is independent of
environmental conditions such as pressure
and temperature.
Although the half-life remains the same, the
number of nuclei decreases as a function of
time.
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The rate of decay is given by
Rate = kN
where k is the rate or decay constant in units
of /s, /y, etc. and N is the number of atoms
(nuclei) in the sample.
Rates are measure in unit of becquerel (Bq)
which equals 1 disintegration/s.
A decay series come to an end when the
product is stable (no longer radioactive).
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Because the rate of decay is a first-order
kinetics process, the half-life is given by:
t1/2
0.693
=
k
and the integrated rate law is given by:
N
m
ln
= -kt
= ln
m0
N0
where N and N0 are numbers of atoms or
nuclei and m and m0 are masses in the same
units.
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Graph of Decaying Isotope vs Time
The graph shown on the next slide is Mass of
Decaying Isotope vs Time.
The graph shows two important points:
 Nuclear decay is an example of
first-order kinetics which means the
half-life remains constant which is 60
days.
 As a radioactive substance decays, the
amount of radiation decays as well.
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Mass of Decaying Isotope vs Time
Mass Of Decaying
Isotope (mg)
Mass Of Decaying Isotope vs Time
120.0
100.0
80.0
1 half-life (60 days, 50.0 g)
2 half-lives (120 days, 25 g)
60.0
40.0
20.0
0.0
0
100
200
300
400
500
600
Time (days)
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Bi-210 has a half-life of 5.0 days.
Approximately would it take for 12.5% of a
2.00 mg sample of this radioisotope to decay?
t1/2 = 5.0 d
m0 = 2.00 mg
t1/2
0.693
=
k
0.693
k=
5.0
ln m = -kt
m0
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.
0.693
0.875
×
2.00
mg
ln
t
= 2.00 mg
5.0
t = 0.96 days
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Nuclear Stability
Atomic nuclei consist of positively charged
protons and neutrons that are neutral.
According to the law of electrostatics,
protons should repel each other and all nuclei
should disintegrate.
However, at very short distances of
approximately 10-15 m, a strong nuclear
force (a strong attractive force) exists
between nucleons (protons and neutrons).
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The more protons that are packed in the
small dense nucleus, the more neutrons are
needed to provide the “nuclear glue”.
The graph on the next slide shows that the
lighter elements (up to about 20) have
approximately equal numbers of protons and
neutrons.
However, the number of neutrons needed for
stability increases more rapidly than the
number of protons.
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Neutron Number vs Proton Number
Number Of Neutrons vs Number Of Protons
Number Of Neutrons
(A - Z)
82Pb
160
50Sn
140
(1.52:1)
(1.38:1)
120
Too many neutrons
100
80
1:1
6C (1:1)
60
40
Too many protons
20
0
0
20
40
60
80
100
Number Of Protons (Z)
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The blue graph shows the nuclei that do not
decay.
The stable nuclei are said to reside in the
“belt of stability”.
As the number of protons in the nucleus
increases, the ratio of neutrons to protons
also increases to provide nuclear stability.
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Rules for Nuclear Stability
 The neutron to proton ratio required for
nuclear stability varies with atomic number.
For the lighter elements (up to about 20),
the ratio is close to 1:1 as indicated by both
the red and blue graph segments.
As the atomic number increases beyond
20, the ratio of neutrons to protons
increase as indicated by the blue graph
segment.
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 All elements beyond Bi-83 are radioactive.
 Nuclei with an even number of nucleons
are more stable than those with an odd
number of nucleons.
 The unstable region resulting from the
nucleus having too many neutrons (above
the blue segment) undergoes spontaneous
beta decay to become more stable.
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 The unstable region resulting from a
nucleus with too many protons (below the
red segment) undergoes spontaneous
positron decay or electron capture to
become more stable.
For the lighter nuclei nuclei, positron
emission is favored and for the heavier
nuclei, electron capture is favored.
Electron capture occurs when a nucleus
absorbs an innermost electron (n = 1) to
form a neutron.
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1p + 0 e
1
1
1n
0
 There are certain numbers of protons and
neutrons that produce very stable nuclei.
 These numbers are referred to magic
numbers and are 2, 8, 20, 28, 50, 82, and
126.
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Which pair of nuclei is more stable?
1) 6 Li or 9 Li
3
3
6Li is more stable because as a light element,
3
a 1 proton : 1 neutron is required.
Pb or 209At
2) 204
82
85
204Pb is more stable because all elements
82
with Z > 83 are unstable.
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Nuclear Binding Energy
It is always true that a nucleus has less mass
than the sum of its constituent particles.
This difference in mass is called the mass
defect.
The mass defect can be used to calculate the
nuclear binding energy given by:
ΔE = Δmc2
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where m is the mass in kilograms (kg), c is
the speed of light, 3.0 x 108m/s, and E is the
binding energy in joules (J).
The greater the binding energy/nucleon, the
more stable the nucleus.
The energy equivalent of the mass defect is
transformed into the kinetic energy of the
particles.
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When a lithium nucleus collides with a proton,
two helium nuclei are formed each having a
mass of 4.0015 u. Using the given
information below, determine the amount of
energy released in this transmutation.
mLi = 7.0144 u
mp = 1.0073 u
mHe = 4.0015 u
7Li + 1H
3
1
1 amu = 1u = 931 MeV
4
2 2 He + energy
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Δm = mr – mp
Δm = 7.0144 u + 1.0073 u – 2 × 4.0015 u
Δm = 0.0187 u
931 MeV
E = Δm = 0.0187 u ×
1u
E = 17.4 MeV
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