Chapter 24 : Nuclear Reactions
and Their Applications
24.1 Radioactive Decay and Nuclear Stability
24.2 The Kinetics of Radioactive Decay
24.3 Nuclear Transmutation: Induced Changes in Nuclei
24.4 The Effects of Nuclear Radiation on Matter
24.5 Applications of Radioisotopes
24.6 The Interconversion of Mass and Energy
24.7 Applications of Fission and Fusion
Comparison of Chemical and
Nuclear Reactions
Chemical Reactions
Nuclear Reactions
1. One substance is converted to
1. Atoms of one element typically
another, but atoms never change
change into atoms of another.
identity.
2. Orbital electrons are involved as 2. Protons, neutrons, and other
bonds break and form; nuclear
particles are involved; orbital
particles do not take part.
electrons rarely take part.
3. Reactions are accompanied by
3.Reactions are accompanied by
relatively small changes in energy
relatively large changes in energy
and no measurable changes in mass. and measurable changes in mass.
4. Reaction rates are influenced by
4. Reaction rates are affected by
temperature, concentration,
number of nuclei, but not by
catalysts, and the compound in
temperature, catalysts, or the
which an element occurs.
compound in which an element
Table 24.1
occurs.
A X
Z
A - mass number = p+ + n0
Z - number of protons(atomic no.) = p+
Number of neutrons(N) in a nucleus
N=A-Z
238 U
0
N
=
238
92
=
146
of
n
92
238 U has 92e- 92 p+
92
235U - atomic bomb
Subatomic elementary particles
Electron
0
Proton
1
Neutron
1
-1
1
e
p
0n
Nuclide - nuclear species with specific
numbers of two types of nucleons
Nucleons - made up ofprotons and neutrons
Properties of
Fundamental Particles
• Particle Symbol
Charge
Mass
•
(x10-19 Coulombs) (x 10-27 kg)
• Proton
p
+1.60218
1.672623
• Neutron
n
• Electron
e
0
-1.60218
1.674929
0.0005486
NUCLEAR STABILITY
Modes of Radioactive Decay
Alpha decay–heavy isotopes: 42He2+ or
Beta decay–neutron rich isotopes: e- or
Positron emission–proton rich isotopes:
Electron capture–proton rich isotopes: x-rays
Gamma-ray emission( )–Decay of nuclear
excited states
• Spontaneous fission–very heavy isotopes
•
•
•
•
•
Fig. 24.1
(p. 1046)
Alpha Decay–Heavy Elements
•
238U
234Th
+ α +e
t1/2 = 4.48 x 10 9 years
•
210Po
206Pb
+ α +e
t1/2 = 138 days
•
256Rf
252No
+ α+e
t1/2 = 7 ms
•
241Am
237Np
t1/2 = 433 days
+ α +e
Beta Decay–Electron Emission
p+ + β− + Energy
• n
•
•
90Sr
14C
90Y
t1/2= 30 years
14N + β− + Energy
t1/2= 5730 years
• 247Am
•
131I
+ β− + Energy
247Cm
+ β− + Energy
t1/2= 22 min
131Xe + β− + Energy
t1/2 = 8 days
Electron Capture–Positron Emission
p+ + ep+
51Cr
n + Energy = Electron capture
n + e+ + Energy = Positron emission
+ e-
51V
+ Energy
t1/2 = 28 days
7Be
7Li
+ β+ + Energy
t1/2 = 53 days
177Pt
+ e-
177Ir
+ Energy
t1/2 = 11 s
144Gd
144Eu
t1/2 = 4.5 min
+ β+ + Energy
Fig. 24.2
Number of Stable Nuclides for Elements 48 through 54
Element
Atomic
Number (Z)
Number of
Nuclides
Cd
48
8
In
49
2
Sn
50
10
Sb
51
2
Te
52
8
I
53
1
Xe
54
9
Table 24.3 (p. 1049)
Distribution of Stable
Nuclides
• Protons
•
•
•
•
Even
Even
Odd
Odd
Neutrons
Even
Odd
Even
Odd
Stable Nuclides
157
53
50
7
Total = 267
(c.f. Table 24.4, p. 1050)
%
58.8
19.9
18.7
2.6
100.0%
The 238U Decay
Series
Fig. 24.3
CHEM 1332
Exam 1 is Friday Feb. 11 at 5:30 PM
Room 117 SR1
Web site http://www.uh.edu/~chem1p
User ID = chem1332
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Predicting the Mode of Decay
Unstable nuclide generally decays in a mode
that shifts its N/Z ratio toward the band of
stability.
1. Neutron-rich nuclides undergo ß decay, which
converts a neutron into a proton, thus reducing
the value of N/Z.
2. Proton-rich nuclides undergo positron decay
or electron capture, thus increasing the value of
N/Z.
3. Heavy Nuclides Z > 83 undergo alpha decay,
thus reducing the Z and N values by two units
per emission.
24.26
243
95Am
239
93Np
239
235
94Pu
92U
4 He
2
0
4
+
239
-1ß +
239
2He
4
+
2He +
93Np
94Pu
235 U
92
231
90Th
Kinetics of Radioactive Decay
The decay rate or activity(A) = - N/ t
N = Change in number of nuclei
t = change in time
SI unit of radioactivity is the becquerel(Bq), defined
as one disintegration per second(d/s): 1Bq = 1 d/s
1 curie(Ci) equals the number of nuclei
disintegrating each second in a 1g of
radium- 226.
1 Ci = 3.70 X 1010 d/s
For a large collection of radioactive nuclei,the
number decaying per unit time is proportional
to the number present:
Decay rate (A) α N or A = kN
k = decay constant
The larger the value of k, the higher is the
decay rate. A = -∆N/∆t = kN
The activity depends only on N raised to the
first order so radioactivity decay is a firstorder process. We consider the number of
nuclei than their concentration.
Half-life of Radioactive Decay
t1/2
The half-life (t1/2) of a nuclide is the time it
takes for half the nuclei present to decay.
14 C
14 N + 0 ß
6
7
-1
The number of nuclei remaining is halved after
each half-life.
Natural Decay Series of Existing Isotopes
40K
40Ar
t1/2 = 1.29 x 109 years
232 Th
208 Pb
t1/2 = 1.4 x 1010 years
235U
207 Pb
t1/2 = 7 x 108 years
238U
206
t1/2 = 4.5 x 109 years
Pb
Natural Decay Series for Uranium-238
238U
234 Th
234Pa
234U
230 Th
226Ra
222Rn
218Po
218At
214Bi
214Po
= α decay
= β− decay
238U:
8
decays and 6
214Pb
210 Tl
210Pb
210Bi
210
Po
206Pb
decays leaves you with 206Pb
206Hg
206Tl
Natural Decay Series for Uranium-235
235U
231 Th
231Pa
227Ac
227 Th
=
decay
=
decay
223Fr
223Ra
219Ra
219At
215Bi
215Po
215At
211Pb
211Bi
211Po
235U:
8
decays and 4
decays leaves you with 207Pb
207 Tl
207Pb
Natural Decay Series for Thorium-232
232
Th
228Ra
228Ac
228 Th
224Ra
=
decay
=
decay
220Rn
216Po
212Bi
212Po
232 Th:
7
decays and 4
212Pb
208Tl
208Pb
decays leaves you with 208Pb
Fig. 24.A
Decrease in Number of 14C
Nuclei Over Time
Fig. 24.4
ln Nt / No = - kt
ln No / Nt = kt No is the number of nuclei
at t = 0 and Nt is the number of nuclei remaining
at any time t.
To calculate the half-time ; set Nt = 1/2 N0
ln No / (1/2No) = k t 1/2 ;
t 1/2 = ln2 / k
The half-life is not dependent on the number of
nuclei and is inversely related to the decay
constant. Large k short t 1/2.
Decay Constants (k) and Half-lives (t1/2)
of Beryllium Isotopes
Nuclide
k
7 Be
4
1.30 x 10-2/day
8 Be
4
1.0 x 1016/s
9 Be
4
4Be
10
11
4
Be
t1/2
53.3 day
6.7 x 10 -17s
Stable
4.3 x 10 -7/yr
1.6 x 106 yr
5.02 x 10-2/s
13.8 s
Table 24.5 (p. 1054)
Radioisotopic Dating
14
7N
12C
+
1
0n
14
1 p
C
+
6
1
/ 14C ratio is constant in living organisms.
Dead organism 12C / 14C ratio increases.
14C
decays
14
6C
14
7N
+
0
-1ß
Radiocarbon Dating for Determining
the Age of Artifacts
Fig. 24.5
Nuclear Transmutation
14
7N +
4 He
2
1
14N
(α , p)
Notation
27
13Al
+
Notation
1H
4 He
2
27Al(α
, n)
+
17
8O
17O
1 n
0
30P
+
30
15P
Fig. 24.6A
The Cyclotron Accelerator
Fig. 24.7
Formation of Some Transuranium Nuclides
Reaction
Half-life of Product
239 Pu
94
+
4
2He
239 Pu
94
+
4
2He
242 Cm
96
+
1
4 He
2
245 Bk
98
+
1 H
1
6C
+ 4 10n
244 Cm
96
+
240 Am
95
+ 11H + 2 10n
238 U
92
+
12
246 Cf
98
253 Es
99
+
4 He
2
256
101Md
252 Cf
98
+
5B
10
256
103Lr
Table 24.6 (p. 1059)
+
0n
1
50.9 h
163 days
+ 2 10n
0n
+ 6 10n
4.94 days
36 h
76 min
28 s
Fig. 24.8
Units of Radiation Dose
rad = Radiation-absorbed dose
The quantity of energy absorbed per kilogram of
tissue: 1 rad = 1 x 10-2 J/kg
rem = Roentgen equivalent for man
The unit of radiation dose for a human:
1 rem = 1 rad x RBE
RBE = 10 for α
RBE = 1 for x-rays, γ-rays, and β’s
Examples of Typical Radiation Doses from
Natural and Artificial Sources–I
Source of Radiation
Natural
Cosmic radiation
Radiation from the ground
From clay soil and rocks
In wooden houses
In brick houses
In light concrete houses
Radiation from the air (mainly radon)
Outdoors, average value
In wooden houses
In brick houses
In light concrete houses
Internal radiation from minerals in
tap water and daily intake of food
( 40K, 14C, Ra)
Table 24.7 (p. 1062)
Average Adult Exposure
30-50 mrem/yr
~25-170 mrem/yr
10-20 mrem/yr
60-70 mrem/yr
60-160 mrem/yr
20 mrem/yr
70 mrem/yr
130 mrem/yr
260 mrem/yr
~40 mrem/yr
Examples of Typical Radiation Doses from
Natural and Artificial Sources–II
Source of Radiation
Average Adult Exposure
Artificial
Diagnostic x-ray methods
Lung (local)
Kidney (local)
Dental (dose to the skin)
Therapeutic radiation treatment
Other sources
Jet flight (4 hr)
Nuclear tests
Nuclear power industry
Total Average Value
Table 24.7 (p. 1062)
0.04-0.2 rad/film
1.5-3.0 rad/film
≤ 1 rad/film
locally ≤ 10,000 rad
~1 mrem
< 4 mrem/yr
< 1 mrem/yr
100-200 mrem/yr
Acute Effects of a Single Dose of
Whole-Body Irradiation–I
Dose
(rem)
Effect
5-20
Lethal Dose
Population (%) No. of Days
Possible late effect; possible
—
chromosomal aberrations
20-100 Temporary reduction in
—
white blood cells
50+
Temporary sterility in men
—
(100+ rem = 1 yr duration)
100-200 “Mild radiation sickness”:
vomiting, diarrhea, tiredness
in a few hours
Reduction in infection resistance
Possible bone growth retardation
in children
Table 24.8 (p. 1063)
—
—
—
Acute Effects of a Single Dose of
Whole-Body Irradiation–II
Dose
(rem)
Effect
Lethal Dose
Population (%) No. of Days
300+
Permanent sterility in women
—
—
500
“Serious radiation sickness”:
marrow/intestine destruction
50-70
30
60-95
30
100
2
400-1000 Acute illness, early deaths
3000+
Acute illness, death in hours
to days
Table 24.8 (p. 1063)
(p. 1064)
24.6
Inter conversion of Mass and Energy
Nuclear Fission: A heavy nucleus splits into two
lighter nuclei.
Nuclear Fusion: Two lighter nuclei combine to
form a heavier one.
The Mass Defect (∆m) - The mass decrease that
occurs when nucleons combine to form a nucleus
The size of the mass change is nearly 10 million times
that of bond breakage.
NUCLEAR ENERGY
• EINSTEIN’S
EQUATION FOR THE
CONVERSION OF
MASS INTO ENERGY
2
• E = mc
•
m = mass (kg)
•
c = Speed of light
•
c = 2.998 x 10 m/s
8
Nuclear Binding Energy
Energy required to break up 1 mol of
nuclei into their individual nucleons.
Nucleus + nuclear binding energy
nucleons
For 12C ∆E = ∆mc2
= (9.894 x 10-5kg/mol)(2.9979 x108m/s)2
= 8.8921 x 1012 J/mol
Fig. 24.12
Units Used for Nuclear Energy Calculations
Electron volt (ev)
The energy an electron acquires when it moves through
a potential difference of one volt:
1 ev = 1.602 x 10-19J
Binding energies are commonly expressed in units
of megaelectron volts (Mev)
1 Mev = 106 ev = 1.602 x 10 -13J
A particularly useful factor converts a given mass defect
in atomic mass units to its energy equivalent in electron
volts:
1 amu = 931.5 x 10 6 ev = 931.5 Mev
Binding Energy per Nucleon
of Deuterium
Deuterium has a mass of 2.01410178 amu.
Hydrogen atom = 1 x 1.007825 amu = 1.007825 amu
Neutrons = 1 x 1.008665 amu = 1.008665 amu
2.016490 amu
Mass difference = theoretical mass - actual mass
= 2.016490 amu - 2.01410178 amu = 0.002388 amu
Calculating the binding energy per nucleon:
Binding energy
Nucleon
0.002388 amu x 931.5 Mev/amu
=
2 nucleons
= 1.1123 Mev/nucleon
Calculation of the Binding Energy per
Nucleon for Iron-56
The mass of iron-56 is 55.934939 amu; it contains 26 protons and
30 neutrons
N=A-Z
Theoretical mass of Fe-56 :
Hydrogen atom mass = 26 x 1.007825 amu = 26.203450 amu
Neutron mass = 30 x 1.008665 amu = 30.259950 amu
56.463400 amu
Mass defect = theoretical mass - actual mass:
56.463400 amu - 55.934939 amu = 0.528461 amu
Calculating the binding energy per nucleon:
Binding energy
Nucleon
=
0.528461 amu x 931.5 Mev/amu
56 nucleons
= 8.7904 Mev/nucleon
Calculation of the Binding Energy per
Nucleon for Uranium-238
The actual mass of uranium-238 = 238.050785 amu; it has
92 protons and 146 neutrons
N=A-Z
Theoretical mass of uranium-238:
Hydrogen atom mass = 92 x 1.007825 amu = 92.719900 amu
Neutron mass = 146 x 1.008665 amu = 147.265090 amu
239.98499 amu
Mass defect = theoretical mass - actual mass:
239.98499 amu - 238.050785 amu = 1.934205 amu
Calculating the binding energy per nucleon:
Binding energy
1.934205 amu x 931.5 Mev/amu
=
Nucleon
238 nucleons
= 7.5702 Mev/nucleon
Mass and Energy in Nuclear Decay–I
Consider the alpha decay of 212Po
212Po
211.988842 g/mol
208Pb
t1/2 = 0.3 µs
+ α + Energy
207.976627 g/mol + 4.00151 g/mol
Products = 207.976627 + 4.00151 = 211.97814 g/mol
Mass = Po - Pb + α = 211.988842
-211.97814
0.01070 g/mol
E = mc2 = (1.070 x 10-5 kg/mol)(3.00 x 108m/s)2
= 9.63 x 1011 J/mol
9.63 x 1011 J/mol
-12J/atom
=
1.60
x
10
6.022 x 1023 atoms/mol
Mass and Energy in Nuclear Decay–II
The energy for the decay of 212Po is 1.60 x 10-12J/atom
1.60 x 10-12J/atom
1.602 x 10-19 J/ev
= 1.00 x 107 ev/atom
10.0 x 106 ev
1.0 x 10-6 Mev
x
= 10.0 Mev/atom
atom
ev
The decay energy of the alpha particle from 212Po is 8.8 Mev.
Fig. 24.13
Fig. 24.14 Critical Mass: Mass needed to achieve a
chain reaction.
Fig. 24.15B
Neutron Induced Fission–
Bombs and Reactors
There are three isotopes with sufficiently long half-lives and
significant fission cross-sections that are known to undergo
neutron induced fission, and are useful in fission reactors, and
nuclear weapons. Of these, only one exists on earth (235U which
exists at an abundance of 0.72% of natural uranium) and that is the
isotope that we use in nuclear reactors for fuel and some weapons.
The three isotopes are:
233U
t1/2 = 1.59 x 105 years
sigma fission = 531 barns
235U
t1/2 = 7.04 x 108 years
sigma fission = 585 barns
239Pu
t1/2 = 2.44 x 105 years
sigma fission = 750 barns
Breeding Nuclear Fuel
There are two relatively common heavy isotopes that will not undergo
neutron induced fission, that can be used to make other isotopes that
do undergo neutron induced fission, and can be used as nuclear fuel in
a nuclear reactor.
Natural thorium is 232 T which is common in rocks.
232 Th
233 Th
+ 10n
233Pa
233 Th
+ Energy t1/2 = 22.3 min
233Pa + β− + Energy
t1/2 = 27.0 days
233U + β− + Energy
t1/2 = 1.59 x 105 years
Natural uranium is 238U which is common in rocks as well.
238U
239U
239Np
+
1 n
0
239U
+ Energy
239Np + β− + Energy
239Pu + β− + Energy
t1/2 = 23.5 min
t1/2 = 2.36 days
t1/2 = 24400 years
Hydrogen Burning in Stars and
Nuclear Weapons
+ β+ + 1.4 Mev
1H
+ 1H
2H
1H
+ 2H
3He
2H
+ 2H
3He
2H
+ 2H
3H
+ 1H + 4.0 mev
2H
+ 3H
4He
+ 1n + 17.6 Mev
2H
+ 3He
4He
+ 1H + 18.3 Mev
1H
+ 7Li
4He
+ 4He + 17.3 Mev
+ 5.5 Mev
+ 1n + 3.3 Mev
Easiest!
Highest
crosssection!
Helium Burning Reactions in Stars
12C
+ 4He
16O
16O
+ 4He
20Ne
20Ne
+ 4He
24Mg
28Si
32S
36Ar
+ 4He
+ 4He
+ 4He
+ 4He
24Mg
28Si
32S
36Ar
40Ca
Element
Synthesis
in the
Life Cycle
of a Star
Fig. 24.C
(p. 1077)
The Tokamak Design for Magnetic
Containment of a Fusion Plasma
Fig. 24.16
24.42
k = 0.693/t 1/2 = 0.693/1.6 x 103 yr = - 4.331x10 -4 yr-1
ln Nt / No = -kt
t = ln (0.185g/2.50g) / -4.33 x 10-4 yr-1 = 6.01 x105 yr
24.44
k = 0.693/5730yr = 1.21 x 10 -4 yr-1
t = ln (Nt/No)/ -k = ln(0.735/1.000)/ -1.21x10-4 yr-1
t = 2.54 x 10 3 yr