Stable vs. Unstable Nuclei
Nuclear Chemistry
Chapter 21
1. Most nuclei are stable – do not change
2. Some nuclei are unstable (radioactive)
•
•
•
Change into a different nucleus
Spontaneous process – happens naturally, by
itself
Releases radiation
Only nuclear reactions can change a nucleus.
No chemical process can
Nuclear Radiation
Radium

Radon
+ Radiation
• Is spontaneously emitted from a radioactive
nucleus
• Can not be seen, smelled, heard
• Can be detected using a Geiger counter or
photographic film
1. The radium was unstable (radioactive)
2. Turned into a different element (decayed)
3. The lost mass was turned into radiation
Uses of Radiation
1.
2.
3.
4.
5.
6.
Nuclear fuel (235U and 239Pu)
Nuclear Weapons
Irradiated Food
Smoke Alarms (Amercium-241)
Cancer treatment (Cobalt-60)
Medical Tracers
1
Types of Nuclear Radiation
Alpha particle Helium nucleus
2 p+
(42He)
Beta particle
2n
fast-moving electron.
e-
(0-1e)
Gamma rays
The Electromagnetic Spectrum
Light
high energy form of
electromagnetic radiation
What Stops Radiation
Dangerous (ionizing)
Safe radiation (non-ionizing)
Paper
Radio Radar Micro
Visible
Light
IR
UV
Xrays
Gamma
Al Foil
Lead.
Wood
Iron,
Alpha ( )
Concrete
Beta ( )
Produced
by nuclear
decay
Decay Equations
Alpha Decay
238 U  4 He +
92
2
Beta Decay
234 Th  0 e +
90
-1
234
234
90Th
Gamma ( )
Decay Equations
Gamma Decay
Occurs with alpha and beta decay
No change in atomic mass (gamma radiation
has no mass 00 )
91Pa
2
Decay: Ex 1
Decay: Ex 2
What product is formed when radium-226
undergoes alpha decay?
226
88Ra

4
2He
What element undergoes alpha decay to form
lead-208?

+
4
2He
+
208
82Pb
Decay: Ex 3
What isotope is produced when thorium-231
beta decays?
231
90Th

0
-1e
+
Positron Emission
– Same mass an electron, but opposite charge
– Form of anti-matter
0 e
1
Electron Capture
– Nucleus captures a core electron
– electron is added rather than lost
Common Particles
Particle
Symbol
Alpha
4 He
2
Beta
0 e
-1
Positron
0 e
1
Electron
0 e
-1
Proton
Neutron
1 H
1
Decay: Ex 4
Write the equation that describes oxygen-15
undergoing positron emission.
Write the equation that describes mercury-201
undergoing electron capture
or 11p
1 n
0
3
Which nuclei are radioactive (unstable)
1. All elements have at least one radioactive
isotope
2. All isotopes of elements heavier than Lead
(element 82) are radioactive
3. All elements heavier than 92 (U) are manmade and radioactive
82
Pb
At least one
radioactive isotope
207.2
All isotopes are
radioactive
• Belt of stability – based on neutron:proton
ratio
– Below ~20 = 1:1 ratio stable
– Ratio increases with increasing # protons
– Isotopes outside the belt try to decay and get on
the belt
Decay Modes
• Atomic # >84
– Alpha Decay
• Above belt
– Too many neutrons
– Beta emission
• Below belt
– Too few neutrons
– electron capture or positron emission
• Most heavy isotopes
(above 84) decay by
alpha emission
• Slide down to lead206
4
Decay Modes: Ex 1
Predict the decay mode for carbon-14
Too many n’s, prefers 1:1
8n : 6p
14
6C

Decay Modes: Ex 2
Predict the decay mode for xenon-118
64n : 54p =1.2
118
54Xe
118
54Xe
Too few n’s (check graph)
Or
Decay Modes: Ex 3
Predict the decay mode for plutonium-239
Predict the decay mode for indium-120
Further Observations
• Magic #’s - Nuclei with 2, 8, 20, 28, 50 or 82
protons or 2, 8, 20, 28, 50 or 126 neutrons
are especially stable.
• Nuclei with even #s of both protons and
neutrons are more stable than those with
odds numbers.
Ex: 63Cu and 65Cu are abundant, but 64Cu is
not. Why?
Transmutation
• Rutherford(1919) – First successful
alchemist
14 N + 4 He  17 O + 1 H
7
2
8
1
14 N( p) 17 O
7
8
Transmutation: Ex 1
Write the balanced nuclear equations for the
process : 2713Al(n, ) 2411Na
• Modern methods
– Particle Accelerators (Cyclotrons)
– Use neutrons or other elements (creation of
transuranium elements)
5
Transmutation: Ex 2
Write the shorthand notation for:
16
8O
+ 11H 
13
7N
Transmutation: Neutrons
• Neutrons produced from radioactive decay
• Cobalt-60 is used in radiation therapy
+ 42He


26Fe
59 Co + 1 n 
27
0
58
59
Transmutation: Transuranium
Elements
238
1
92U + 0n
 23992U  23993Np + 0-1e
239
94Pu
+ 42He  24296Cm + 10n
209
83Bi
+ 6428Ni  272111Rg + 10n
Half-Life
26Fe
+ 10n
59
59
26Fe
27Co
60 Co
27
+ 0-1e
Half-Life
• Half-life - The time during which one-half of
a radioactive sample decays
– Ranges from fraction of a second to billions of
years.
– You can’t hurry half-life.
Carbon-14 dating
Isotope
Uranium-238
Half-life
4.51x109 years
Lead-210
20.4 years
Polonium-214
1.6x10-4 seconds
• Upon death, 14C radioactively decays.
(half-life = 5730 y)
• Reasonable to up to 50,000 years.
• 15% margin of error
• Mummies, the Dead Sea Scrolls, Shroud of
Turin
The polonium-214 will decay much sooner than the uranium. The uranium will be
radioactive pretty much until the earth is destroyed when our sun goes out in 10
billion years.
6
Half-life: Example 1
Carbon-14 has a half-life of 5730 years and
is used to date artifacts. How much of a
26 g sample will exist after 3 half-lives?
How long is that?
Half-life: Example 2
Tritium undergoes beta decay and has a half
life of 12.33 years. How much of a 3.0 g
sample of tritium remains after 2 half-lives?
Half-life: Example 4
Cesium-137 has a half-life of 30 years. If you
start with a 200 gram sample, and you now
have 25 grams left, how much time has
passed?
Half-life: Example 3
Radon-226 has a half-life of 1600 years? How
much of a 30 gram sample remains after
6400 years?
Half-life: Example 5
Calcium-45 has a half-life of 160 days. If you
start with a 500 gram sample, and you now
have 31.25 grams left, how much time has
passed?
7
Rate Law
First order rate law
Rate = kN (N is the initial concentration)
Rate =
- N
=
dN = -kN
t
dt
dN = -kN
dt
dN = -kdt
N
∫dN = ∫-kdt
N
∫dN = -k∫dt
N
lnNt = -kt
N0
or
Nt = Noe-kt
N0
Calculating k or the half-life
lnNt = -kt
(Integrate left from N0 to Nt
and time from 0 to t)
Rate Law: Ex 1
Uranium-238 has a half-life of 4.5 X 109 yr. If
1.000 mg of a 1.257 mg sample of uranium238 remains, how old is the sample?
ln1 = -kt½
2
k = 0.693
k = 0.693
k = 0.693
t½
t½
lnNt = -kt
4.5 X
=
109
1.5 x10-10 yr-1
yr
Rate Law: Ex 2
N0
ln 1.000 = -(1.5 x10-10 yr)t
1.257
t = 1.5 X 109yr
A wooden object is found to have a carbon-14
activity of 11.6 disintegrations per second.
Fresh wood has 15.2 disintegrations per
second. If the half-life of 14C is 5730 yr, how
old is the object?
8
Rate Law: Ex 2
Rate Law: Ex 3
A wooden object is found to have a carbon-14
activity of 11.6 disintegrations per second.
Fresh wood has 15.2 disintegrations per
second. If the half-life of 14C is 5730 yr, how
old is the object?
After 2.00 yr, 0.953 g of a 1.000 g sample of
strontium-90 remains. How much remains
after 5.00 years?
ANS: 2230 yr
x =0.887 g
Ex 4
A sample for medical imaging contains 18 F
(1/2 life = 110 minutes). What percentage of
the original sample remains after 300
minutes?
E = mc2
• Energy changes in chemical reactions
– Exothermic – gives off energy, products mass
less than reactants
– Endothermic – absorbs energy, products mass
more than reactants
– THESE MASS CHANGES ARE WAY TOO
SMALL TO MEASURE
ANS: 15.1%
• Energy Changes in nuclear decay
– Mass loss from nuclei
– Energy always released
– This energy is additional kinetic energy given to
the products (products move faster than
reactants)
c = 3.00 X 108 m/s
9
E = mc2: Ex1
238

92U
238.0003 amu
238.0003 amu
234
4 He
+
2
233.9942 amu 4.0015amu
237.9957 amu
90Th
m = -0.0046 g/mol = -4.6 X 10-6 kg/mol
E = mc2
E = (4.6 X 10-6 kg/mol)(3.00X108 m/s)2
E = 4.1 X 1011 J/mol
(can power a 60-W light bulb for 217 years)
E = mc2: Ex 3
The following decay produces 2.87 X 1011
J/mol of 116C. What is the mass change in
this decay?
11
6C

11
5B
+
0
1e
E = mc2: Ex 2
Calculate the energy released from the
following decay.
60 Co
60 Ni
 0-1e +
27
28
60
0
27Co
-1e
60 Ni
28
59.933819 amu
0.00054858 amu
59.930788 amu
ANS: 2.23 X 1011 J/mol
Binding Energy
• The mass of nuclei are ALWAYS less than
the masses of individual protons and
neutrons (nucleons).
• Mass defect
ANS: -3.19 X 10-3 g/mol
• Nuclear Binding Energy – energy needed
to separate nucleus into p & n
– The larger the binding energy, the more stable
the isotope
– Iron-56 has the highest binding energy
– Stars only make up to Iron-56 (unless
supernova)
10
The Four Forces
Force
Range
Description
Strong Nuclear Force
Short
Range
(nucleus)
Strongest, holds nucleus together
(gluons)
Electromagnetic
Infinite
Range
Between positive and negative
charges (virtual photons)
Weak Nuclear Force
Short
Range
(nucleus)
Involved in some nuclear decay
and fusion(quark to quark
transmutations, J particle)
Gravity
Infinite
Range
Weakest, between any object with
mass, even dark matter (gravitons)
Binding Energy: Ex 1
Calculate the binding energy for a helium-4
nucleus given the following information:
4
2He
proton
neutron
4.00150 amu
1.00728 amu
1.00866 amu
Mass defect = 0.03038 g/mol
0.03038 g 1 kg
1 mol
1mol
1000 g 6.022X1023 atoms
Strong Nuclear Force
• Strong Nuclear Force
– Short-range force – operates only within nuclear
distances
– Force between p and n that overcomes protonto-proton repulsion
Mass of individual nucleons
protons 2(1.00728 amu)
neutrons 2(1.00866 amu)
total
2.01456 amu
2.01732 amu
4.03188 amu
Mass defect
4.03188 amu
-4.00150 amu
0.03038 amu
E = 4.534 X10-12 J/atom
or
E = 4.534 X 10-12J/ 4 nucleons
E = 1.13X10-12 J/nucleon
= 5.045 X 10-29 kg/atom
E=mc2
E = (5.045 X 10-29 kg/atom)(3.00 X 108 m/s)2
11
Binding Energy: Ex 2
Calculate the binding energy for an iron-56
nucleus given the following information:
56
26Fe
proton
neutron
55.92068 amu
1.00728 amu
1.00866 amu
ANS: 1.41 X 10-12 J/nucleon
Turbine
Fission: Chain Reaction
• Must absorb some of those neutrons or
fission continues unchecked (explosion?)
Moderator (water)
Steam
Control Rods
Uranium Fuel Rods
Nuclear Fission Power
• Uses 235U
• First commercial nuclear power - 1957 at
Shippingport, PA
• People living near a nuclear power plant =
1/10 radiation of a coast-to-coast jet plane
trip (cosmic radiation).
• Three-Mile Island (1979) - partial
meltdown due. No fatalities, no serious
release of radiation.
• Chernobyl, Ukraine (1986) – full meltdown.
31 deaths, 260,000 exposed to high levels
of radiation.
12
Nuclear Fission: Bombs
• Nuclear bombs (uranium or plutonium)
• Critical Mass – minimum mass required for
a chain reaction
– Subcritical mass
– Critical mass (1 kg)
Fusion
• Fusion: Combining 2 nuclei of lighter element
• Thermonuclear fusion occurs at high
temperatures like in the sun (3 to 40 million
K).
– 657 million tons of hydrogen is fused to 653
million tons of helium each second
– Energy released = sunlight
• Not yet feasible for commercial reactors
13
Sources of Exposure to Radiation
Natural Exposure (~80%)
1. The atmosphere (Radon and carbon-14)
2. Particles that come from outer space
3. Rocks, soil and bricks (Uranium and
Thorium)
4. Foods (carbon-14)
Technological Sources (~20%)
1. Nuclear weapons testing
2. High-altitude plane flights
3. X-rays (even though they are not alpha,
beta or gamma)
4. Fossil fuel and nuclear electrical generation
5. Disturbances in rocks from mining, building
6. Smoking (VERY high levels)
Measuring Exposure to Radiation
1. Units
rad – total exposure
rem – [roentgen equivalent man] – total
damaging exposure
millirem (mrem) – 1/1000th of a rem
2. mrem is the unit used to measure possible
damage to human tissue.
3. U.S. Average = 360 mrem/year
Ionizing Radiation
• UV light and X-rays
and from nuclear
decay
• Produces “free
radicals”
• Affects bone marrow,
blood, lymph nodes
Danger of Radon
1. Radon-222 gas passes in and out of the lungs.
2. Produced by decay of radium-226 from rocks,
soil, and building materials.
3. Radon has a half-life of 3.825 days and decays
into solid polonium-218.
4. Polonium-218 emits alpha particles which can
damage lung tissue.
14
222
86Rn

218
218
84Po

214
84Po
+
4
82Pb
+
4
2He
2He
12.a) 19179Au
b) 20179Au
c) 19879Au
d) 18879Au
+ 0-1e  19178Pt
 20180Hg + 0-1e
 19880Hg + 0-1e
 18878Pt + 01e
14. a) 2411Na  2412Mg + 0-1e
b) 18880Hg  18879Au +01e
c) 12253I  12254Xe + 0-1e
d) 24294Pu  23892U + 42He
18.a) Positron emission, electron capture
b) Beta
c) Beta
d) Positron emission, electron capture
20.a) Even, even – more abundant
b) odd, even – more abundant
c) even, even – more abundant
d) even, even – more abundant
28.a) 3215P
b) 73Li
c) 18775Re
d) 9943Tc
e) 9938Sr
34. 2.6 min
36.85 d
40. 3520 y
46. 1.6143 X 1013 J/mol
48.a) 1.20 X 10-12 J/nucleon
b) 1.40 X 10-12 J/nucleon
c) 1.35 X 10-12 J/nucleon
50.a) -1.697 X 1012 J/mol
b) -3.13 X 1011 J/mol c) -1.773 X 1012 J/mol
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