Mass Defect, Binding Energy, Fission and Fusion

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Mass Defect, Binding Energy, Fission and Fusion

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

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Nuclear Energy

• Mass Defect
• Binding Energy
• Nuclear Fission
• Nuclear Fusion
• Comparisons of various forms of energy

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Mass Defect

• The nucleus
• is composed of protons and neutrons
• the actual mass is less than the mass of the
  separate particles.
• The "missing" mass is in the form of energy
  holding the nucleus together.

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Uranium-238
The nuclear mass of uranium-238 is 238.0003 amu
238U
92
A proton is 1.00728 amu
A neutron is 1.00867 amu
What mass is expected for the nucleus of 238U?
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Uranium-238
(92)(1.00728) 92.6698
92 protons
(146)(1.00867) 147.2658
146 neutrons
predicted mass 239.9356
actual mass 238.0003
mass defect 1.9353 amu
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Masses of Atoms
The nuclear mass of 238U is 238.0003
Why does the Handbook of Chemistry and
Physics list the mass of uranium238 as 238.0508?
(92)(0.0005488) 238.0003 238.0508
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Binding Energy

• The mass defect indicates the total energy
  involved in holding the nucleus together.
• To determine the stability of the nucleus, the
  binding energy per nuclear particle is a better
  measure.

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Binding Energy of 238U
1.9353 amu
DE Dmc2 931.5 MeV/amu
What is the binding energy per nucleon of 238U?
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Binding Energy of 238U
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Binding Energy
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Nuclear Fission

• Fissionable materials
• Daughter products
• Energy release
• Nuclear chain reactions
• Nuclear reactors
• Control rods
• Breeder reactor

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Nuclear Fission

• Nuclear process in which the nucleus of the atom
  breaks into two large fragments.
• Fissionable materials
• undergo spontaneous fission or
• can be converted into a fissionable isotope
• Neutron capture can result in daughter products
  which are more fissionable.

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Fissionable Materials
Fissionable
Non-Fissionable
235U
238U
239Pu
207Pb
12C
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Fissionable Materials
Natural abundance 235U 0.7 238U 99.3
What is the percentage of 235U in a commercial
sample of UO2?
235U _at_ 0.0
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Fission Daughter Products
Spontaneous fission is a statistical
process resulting in several different daughter
isotopes.
235U 1n 236U 140Ba 94Kr 2 1n
energy 141Ba 92Kr 3 1n energy 137Te
97Zr 2 1n energy 144Cs 90Rb 2 1n
energy 146La 87Br 3 1n energy
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Nuclear Chain Reaction

• In the previous disintegration process there are
  an average of 2.3 neutrons generated per
  disintegration.
• If one neutron is captured for each nuclear
  disintegration that occurs, the reaction is
  self-sustaining.

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Nuclear Chain Reaction
fissionable material
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Nuclear Chain Reaction
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Control Rods
Control rods regulate the rate of reaction by
controlling the neutron flux.
What kind of material would be used as a control
rod?
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Thermal Neutron Capture Cross-Section
0.00051 0.00001 b
2H
0.5 0.2 b
10B
0.0034 0.0003 b
12C
20000 300 b
113Cd
680 2 b
235U
2.720 0.025 b
238U
Which of these elements would limit excess
neutrons?
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Nuclear Reactor
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Nuclear Reactor
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Breeder Reactor

• Converts non-fissionable material into
  fissionable material

Non-fissionable
Fissionable
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Nuclear Fusion

• Process by which lighter nuclei combine to form
  heavier nuclei.
• 4 1H 2 e 4He2
• Dm 0.02758 gmol1
• The energy source of stars.

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Nuclear Mechanismsproton-proton mechanism

• ( 1H 1H 2H b ) x2
• ( 2H 1H 3He g ) x2
• 3He 3He 4He 2 1H
• ( b e 2 g ) x2

2 e 6 1H 2 3He 4He 2 3He 6 g 2 1H
Whats the overall net nuclear reaction?
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Nuclear Mechanismscarbon cycle mechanism

• 12C 1H 13N g
• 13N 13C b
• 13C 1H 14N g
• 14N 1H 15O g
• 15O 15N b
• 15N 1H 12C 4He
• ( b e 2 g ) x2

2 e 4 1H 4He 7 g
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Reaction Conditions

• For two nuclei to react, they must be moving at
  high velocities to overcome the coulombic
  repulsion of two positive charges.
• Typical thermal energies of _at_107 K in a star.

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Laboratory Attempts

• Laser Fusion
• 3H 2H 4He 1H
• Frozen sample heated to 106 K by laser

• Cold Fusion
• Room temperature process involving deuterium
  dissolved in a metal matrix
• 2H 2H 4He g

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Energy Comparison
C O


products
2
235
1
10
7
U
n

products
1.7 x 10
7.1 x 10
9
8
1
4
H

products
2.4 x 10
5.9 x 10
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On Line File of Nuclide Data

• http//necs01.dne.bnl.gov/CoN/

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