Final Exam
• Wed Dec. 9 from11:30am-2:29pm York 2722
• Will cover all the course material including
the last week
• 25 questions –multiple choice.
• You are allowed to bring 1sheet of paper with
equations on both sides, scratch paper for
calculation, calculator
• You must bring a scantron form and a picture id.
10.1 Nuclear energy
Nuclear Fission
Nuclear Fusion
Curve of the Binding Energy/nucleon
Natural radioactivity
fission
Many elements found in nature are unstable and decay
emitting radioactivity.
fusion
These include Uranium, 238U , Radon
and Potassium 40K. Carbon 14C,
224Ra
The half lives of natural radio-isotopes are long.
Not useful as sources for power.
Low Power output.
Energy can be released by nuclear reactions of
Fusion and Fission
Induced Nuclear reactions
Nuclear Power
Can result in short half lives- fast reactions-high energy density
• Nuclear power requires induced nuclear
fission.
• Nuclear fission can be induced by
neutrons in a chain reaction.
• Nuclear fusion can be induced by
collisions at high temperature.
Combining nuclei (Fusion)
D + 21D ⎯⎯
→ 31T + 11H
2
1
+ Energy
Neutron reactions (Fission)
n+
1
0
235
92
U ⎯⎯
→ 141
56 Ba +
92
36
Kr + 3 01n + Energy
1
Fission of Uranium
Fission of Uranium
Strassman and Hahn (1939)
Fermi (1936)
Fast
neutrons
Slow
neutrons
Bombard uranium with
neutrons
Irradiated Uranium with neutrons
Detected Barium
Conclude Uranium nuclei splits into smaller fragments
Found induced radioactivity
Neutron
Source
(radon+Be)
parafilm
uranium “Transuranium elements”
Liquid Drop model-
n+
1
0
235
92
U ⎯⎯
→ 141
56 Ba + other _ products
Nuclear Chain reaction
Explained fission due to the instability
of the higher larger nucleus.
T1/2 ~10-12 s
n+
1
0
235
92
U ⎯⎯
→ 236
→
92 U ⎯⎯
Lise Meitner
Ba + products
∆E (average) =208 MeV
Chain Reaction
binding of 1 neutron releases ~3 neutrons
Each neutron can initiate another reaction
Two major isotopes of Uranium
235U
Critical Condition for Chain reaction
(0.7%) Fissionable upon neutron capture
235U
(Fission)
n
238U
(99.3%) Non-Fissionable upon neutron capture
n
n
235U
n
(Escape)
238U (Capture)
Nuclear reactor
Reproduction constant
K = no. of neutrons that produce a new fission event
K=1 ( self –sustained reaction)
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Enriched 235U
Centrifuge separation of
isotopes
Natural Uranium is a mixture of 235U (0.7%) and 238U(99.3%)
Most Uranium nuclear reactors use uranium enriched in
(2-3%)
235U.
Nuclear weapons used highly enriched 235U. (~90%)
Enrichment done by mass separation.
Gaseous diffusion
Centrifuge process.
Laser separation
centrifugal
separation
gaseous UF6
Nuclear reactor
Nuclear reactor
fast neutrons must
be slowed down to
react efficiently.
Moderator- slows
neutrons to thermal
velocities.
Control rods- neutron
absorbers to control
the level of neutrons
Critical condition. – When each neutron released initiates
a new reaction.
Plutonium
Plutonium is a fissionable material created in
a nuclear reactor.
238
92
−
U + 01n ⎯⎯
→ 239
94 Pu + 2e
Question
How many gallons of gasoline (1.3x108 J of energy/gallon)
would be equivalent to a kg of Uranium? ∆E=208MeV
No. of fissionable nuclei =N
N = ( fraction235U)(
⎡
⎤
1kg
m
22
) = (0.0072)⎢
⎥ = 1.8 x10
− 27
mass / atom
⎣ 238u(1.66 x10 kg / u) ⎦
Energy released = E = N(∆E)
239Pu
can be made into nuclear bombs.
Pu can be chemically separated from U in spent fuel
rods from nuclear reactors.
[
]
E = N( ∆E) = 1.8 x10 22 ( 208 x10 6 eV ) 1.6 x10 −19 J / eV = 6 x1011 J
gallons of gasoline =V=
E
E / gallon
E
6 x1011 J
=
= 4.6x10 3 gallons
E / gallon 1.3 x10 8 J / gallon
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Nuclear Fusion
Fusion of small nuclei releases energy
Nuclear Fusion
High energy required to bring charged nuclei close together
+Z
D + D ⎯⎯
→ He + n
∆E= 3.27 MeV
D + 21D ⎯⎯
→ 31T + 11H
∆E= 4.03 MeV
D + 31T ⎯⎯
→ 42 He + 01n
∆E=17.6 MeV
2
1
2
1
3
2
1
0
2
1
2
1
v
+Z
+Z +Z
~10-15 M
Requirements for fusion
High Temperatures (T~ 108 K)
High density (n) for long time (τ)
Lawson Criterion
nτ > 1014 s/cm3
Plasma Fusion
Magnetic Confinement
Laser fusionInertial Confinement
Plasma is a gas of ionized atoms
Heated to high temperature
Confined by magnetic forces
Deuterium pellet
T~108 K
Princeton Tokomak
long times
low density
Lawrence Livermore Lab
Nova Laser
Short times
High density
Prospects
• Nuclear energy by fission is currently a source of
much of the electrical power (~15% USA).
• The problems with nuclear energy
– Radioactive waste disposal
– Atomic bomb threats
• Nuclear fusion reactions promise an unlimited
source of energy.
– Controlled fusion reactions are not yet possible.
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