1 Nuclear Fission Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). Thermal neutron...
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Transcript of 1 Nuclear Fission Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). Thermal neutron...
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1
Nuclear Fission
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
• Thermal neutron fission of 235U forms compound nucleus that splits up in more than 40 different ways, yielding over 80 primary fission fragments (products).
23592U + 1
0n ► 9037Rb + 144
55Cs + 210n
23592U + 1
0n ► 8735Br + 146
57La + 310n
23592U + 1
0n ► 7230Zn + 160
62Sm + 410n
• The fission yield is defined as the proportion (percentage) of the total nuclear fissions that form products of a given mass number. Revisit thermal and look for fast.
1Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
2
Nuclear Fission
Asymmetry
Asymmetry
• Remember neutron excess.• (A,Z) (A,Z+1) or (A-1,Z).
Only left side of the
mass parabola.
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3
Nuclear Fission
• 235U + n 93Rb + 141Cs + 2n• Q = ????• What if other fragments?• Different number of neutrons.• Take 200 MeV as a representative value.
66 MeV 98 MeV
miscalibrated
Heavyfragments
Lightfragments
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
165 MeV average kinetic energy carried
by fission fragments per
fission.
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Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
4
Nuclear Fission• neutrons emitted per fission.• depends on fissioning nuclide and on neutron energy inducing fission.
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5
Nuclear Fission• Mean neutron energy 2 MeV.• 2.4 neutrons per fission (average) 5 MeV average kinetic energy carried by prompt neutrons per fission.
• Show that the average momentum carried by a neutron is only 1.5 % that carried by a fragment. • Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses.
1
2
2
1
m
m
E
E
140
95
98
66
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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6
Nuclear Fission
Distribution of fission energy
Krane sums
them up as
decays.Lost … !
Enge
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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7
Segrè
Lost … !
Nuclear Fission
• How much is recoverable?How much is recoverable?• What about capture gammas? What about capture gammas? (produced by (produced by -1 neutrons)-1 neutrons)
• Why c < (a+b) ?Why c < (a+b) ?
Distribution of fission energy
abc
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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8Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
• and emissions from radioactive fission products carry part of the fission energy, even after shut down. • On approaching end of the chain, the decay energy decreases and half-life increases. Long-lived isotopes constitute the main hazard.• Can interfere with fission process in the fuel. Example?Example? (poisoning).(poisoning).• Important for research.• -decay favors high energy ~20 MeV compared to ~6 MeV for .
• Only ~ 8 MeV from -decay appears as heat. Why?Why?
Nuclear Fission
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9
Nuclear Fission
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
A, Zi
A, Z-1k
A-1, Zj
A, Z+1A+1, Z
-
-
(n,)
(n,)
dNi/dt = Formation Rate - Destruction rate - Decay Rate
iiiikkjjffii NNNNN
dt
dN
f
Ni saturates and is higher with higher neutron flux, larger “fission yield” and longer half-live.
9Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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Investigate both and giving full description for the buildup and decay of fission fragment i.
10
Nuclear Fission
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
iikki NN
dt
dN
iikk NN
• Shutdown
iikk NN HW 8HW 8
HW 7HW 7
Investigate the activity, decay and gamma energies of fission products as a function of time. Comment on consequences (e.g. rod cooling).
10Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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11Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
sMeVTttxtP /)(101.4)( 2.02.011 per watt of original operating power.T = time of operation.
Nuclear Fission
Fission product activity after
reactor shutdown?
11Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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Nuclear Fission
• The fission gamma radiation Prompt within 0.1 s and with average energy of 0.9 MeV. delayed gammas.
• Investigate how prompt Investigate how prompt gammas interact with gammas interact with water, uranium and lead.water, uranium and lead.
12Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
HW 9HW 9
12Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
13
Nuclear Fission
EeE E 29.2sinh453.0)( 036.1HW 10HW 10
The experimental spectrum of prompt neutrons is fitted by the above equation. Calculate the mean and the most probable neutron energies.
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14Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
• Recoverable energy release 200 MeV per 235U fission.• Fission rate = 2.7x1021 P fissions per day. P in MW.• 3.12x1016 fissions per second per MW, or 1.2x10-5 gram of 235U per second per MW (thermal).• Burnup rateBurnup rate: 1.05 P g/day. P in MW. • The fissioning of 1.05 g of 235U yields 1 MWd of energy. • Specific Burnup Specific Burnup = 1 MWd / 1.05 g 950000 MWd/t (pure (pure 235235U !!).U !!).• Fractional Burnup Fractional Burnup = ???• Thermal reactor loaded with 98 metric tons of UO2, 3% enriched, operates at 3300 MWt for 750 days.• 86.4 t U. Specific burnup 28650 MWd/t. • Not all fissions from 235U.• Fast fission of 238U.• 238U converted to plutonium more fission.
Nuclear Fission
Work it out, NOW!
Work it out, NOW!
Actually much less.Actually much less.
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Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
15
Nuclear Fission
•Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor.
)(
)()(
E
EE
f
• Capture-to-fission ratio:
• Consumption rateConsumption rate: 1.05(1+) P g/day.
• Read all relevant material in Lamarsh Read all relevant material in Lamarsh Ch. 4. We will come back to this later.Ch. 4. We will come back to this later.
4.8x1012 m-2s-1
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16Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Nuclear Fission
• 3.1x1010 fissions per second per W.• In thermal reactor, majority of fissions occur in thermal energy region, and are maximum.• Total fission rate in a thermal reactor of volume V
• Thermal reactor powerThermal reactor power (quick calculation) (quick calculation)
fV
10101.3 x
VP f
th
16Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
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Nuclear Fission
• It is necessary to evaluate the potential hazards associated with an accidental release of fission products into the environment.
• It is required to determine a proper cooling time of the spent fuel (before it becomes ready for reprocessing) that depends on the decay times of fission products.
• It is necessary to estimate the rate at which the heat is released as a result of radioactive decay of the fission products after the shut down of a reactor.
• The poisoning is needed to be calculated (the parasitic capture of neutrons by fission products that accumulate during the reactor operation).
17Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
17Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).