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Chemical Engineering 412
Introductory Nuclear Engineering
Lecture 10Nuclear Fission
Spiritual Thought
D&C 121:41-43
No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned;By kindness, and pure knowledge, which shall greatly enlarge the soul without hypocrisy, and without guileβReproving betimes with sharpness, when moved upon by the Holy Ghost; and then showing forth afterwards an increase of love toward him whom thou hast reproved, lest he esteem thee to be his enemy;
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The BIG Picture3
Neutron Interactions
β’ Elastic scattering (n,n) β collision with no reaction and no change in total kinetic energies. Energy neutral.
β’ Inelastic scattering (n,nβ) β collisions with energy absorption by nucleus. endoergic
β’ Radiative capture (n,Ξ³) β Capture of neutron by nucleus followed by Ξ³-ray emission. exoergic.
β’ Charged particle reactions (n,Ξ±) β Neutron reaction to form Ξ± particles or protons. endoergic and exoergic.
β’ Neutron producing reactions (n,xn) β Reactions with a net increase in neutrons. endoergic. (n,2n) important for 2H and 9Be.
β’ Fission (n, ) forms multiple products β Nucleus forms daughters. Generally exoergic.
Capture and Absorption
β’ Decelerating Neutrons from fission energies (2-5 MeV) to thermal energies (0.025 eV)β’ Requires many collisionsβ’ Smaller Nuclidesβ’ Risk of βcaptureβ
β’ Capture occurs in βresonance energy regionsβ (fuel)β’ Also could be absorbed by the βmoderatorβ (water)β’ Can calculate probability of capture or absorption
β’ Resonance integral β’ Absorption cross-sections
How to Decelerate a Neutron
βπΈπΈπΈπΈ
=1 β πΌπΌ
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π’π’ = lnπΈπΈπππΈπΈ
ππ = βπ’π’ = 1 βπ΄π΄ β 1 2
2π΄π΄lnπ΄π΄ + 1π΄π΄ β 1
= 1 +πΌπΌ
1 β πΌπΌlnπΌπΌ β
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π΄π΄ + 23
πΌπΌ =π΄π΄ β 1π΄π΄ + 1
2collision parameter
Lethargy; πΈπΈππ is an arbitrary πΈπΈ, usually the highest neutron energy in the system. As neutrons decelerate, π’π’increases.
limπ΄π΄β1
ππ = 1
Neutron Energies
β’ Fission neutronsβ’ Distribution of speedsβ’ 2 MeV typicalβ’ Interested βslowingβ neutronsβ’ Collisions required to slow from energy πΈπΈ1 to πΈπΈ2 is given
by:
β’ Thermal neutrons:β’ equilibrated with the vibrating atomic nuclei at room
temperature (293 K)β’ Average energy of 0.025 eV (2200 m/s)β’ Maxwellian distribution of speedsβ’ likely to lose OR GAIN energy from medium nucleiβ’ Readily produce fissions in U235, U233, Pu239
ππ =1ππ
lnπΈπΈ1πΈπΈ2
Collision parameters
Atom π¨π¨ πΆπΆ ππ ππH 1 0.000 1.000 18.2H2O 1, 16 0.920 19.8D 2 0.111 0.725 25.1D2O 2, 16 0.509 35.8He 4 0.360 0.425 42.8Be 9 0.640 0.207 88.1B 11 0.694 0.171 106.3C 12 0.716 0.158 115.3O 16 0.779 0.120 151.7Na 23 0.840 0.084 215.4Fe 56 0.931 0.035 515.6238U 238 0.983 0.008 2171.6ππ values here assume a neutron slowing from 2 MeV to 0.025 eV
Neutrons Eventually Are Captured
ππ + πππ΄π΄ππ β ππ
π΄π΄+1ππ β β πππ΄π΄+1ππ + πΎπΎ
ππ + 90232πππ β 90
233πππ β β 90233πππ + πΎπΎ
π½π½ββ
22 ππ91233ππππ
π½π½ββ
27 ππ92233ππ
ππ + 510π΅π΅ β 5
11π΅π΅ β β 37πΏπΏπΏπΏ + πΎπΎ + πΌπΌ
ππ + 92238ππ β 92
239ππ β β 92239ππ + πΎπΎ
π½π½ββ
24 ππ93239ππππ
π½π½ββ
56 π94239πππ’π’
Control rods
βFertileβ isotopes form βfissileβ isotopes through neutron absorption
Fission Reactions
92235ππ is fissile (undergoes fission)
92238ππ is fertile (converts to a fissionable isotope)
ππ + 92235ππ β
92235ππ + ππ πππππππππππΏπΏππ πππππππππππππ π
92235ππ + ππ + πΎπΎ πΏπΏπππππππππππππΏπΏππ πππππππππππππ π
92236ππ + πΎπΎ π π πππππΏπΏπππππΏπΏππππ πππππππππ’π’π π πππππ»π» + πππΏπΏ + π¦π¦1 + π¦π¦2 + β― πππΏπΏπππππΏπΏππππ
Possible outcomes of 92235ππ reaction with neutron
Fission (logarithmic) Timeline
Scission (10-20 s)
Prompt Neutrons (10-17 s)
Gamma emission (10-14 s)
Return to background energy (10-12 s)
Absorption
Delayed Neutrons (1-100 s)
Emitted/Recoverable Energy
Fission Product Distribution
Product Distribution at High Energy
Delayed Neutrons
β’ A small fraction (<1%) of total neutron production occur seconds or minutes after scission, represented by π·π· below. These delayed neutrons are essential to reactor control.
β’ Fast neutron emission alone is far too rapid to allow control.
Delayed Neutron Data
Neutron Energy Spectrum
Decay Heat