Fission Fundamentals
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1 Fission Fundamentals Richard Wolfson Benjamin F. Wissler Professor of Physics Middlebury College The Role of Nuclear Power Washington & Lee University June 21, 2007
2 Atoms & Nuclei: A Brief History Democritus (~400 BCE): Matter consists of atoms Physically indivisible No empty space Dalton (1808): ditto J.J. Thomson (1897): Discovery of the electron Atoms are divisible! Plum-pudding model of the atom: +
3 Atoms & Nuclei: A Brief History Democritus (~400 BCE): Matter consists of atoms Physically indivisible No empty space Dalton (1808): ditto J.J. Thomson (1897): Discovery of the electron Atoms are divisible! Plum-pudding model of the atom: Rutherford & colleagues (1911): Discovery of the nucleus Solar-system model of the atom: +
4 Atoms & Nuclei: A Brief History Democritus (~400 BCE): Matter consists of atoms Physically indivisible No empty space Dalton (1808): ditto J.J. Thomson (1897): Discovery of the electron Atoms are divisible! Plum-pudding model of the atom: Rutherford & colleagues (1911): Discovery of the nucleus Solar-system model of the atom: Chadwick (1932): Discovery of the neutron Nucleus consists of protons (positive) and neutrons (neutral) + Helium nucleus
5 Atoms and Elements A positive nucleus attracts electrons In a neutral atom, the number of electrons equals the number of protons in the nucleus Electrons determine the atom s s chemical properties Therefore the number of protons in the nucleus determines chemical properties The number of protons is called the atomic number So all atoms with the same atomic number belong to the same chemical species They re atoms of the same element Helium atom
6 Isotopes Different isotopes of an element have different numbers of neutrons They have the same atomic number, so they re chemically similar They have different mass numbers Mass number: : The total number of nucleons Nucleon: : a proton or neutron Helium He Helium He Their nuclear behavior may be very different!
7 Isotopes Proton: Neutron: 92 Hydrogen (H-1) 143 Deuterium (H-2) Tritium (H-3) Oxygen-16 Oxygen-18 Uranium Uranium-238
8 U-238 Uranium Isotopes 99.3% of natural uranium today Half-life: 4.5 billion years U % of natural uranium Half-life: 700 million years U-233 Does not occur in nature Half-life: 160,000 years
9 U-238 Uranium Isotopes 99.3% of natural uranium today Half-life: 4.5 billion years U % of natural uranium Half-life: 700 million years U-233 Does not occur in nature Half-life: 160,000 years
10 Building Nuclei: Two Forces The electric force acts repulsively between protons This tends to tear the nucleus apart The electric force is weak, but extends over long distances The nuclear force acts attractively between all nucleons Protons-neutrons, protons-protons, neutrons-neutrons The nuclear force is strong, but has a short range Consequence: Larger nuclei need more neutrons than protons But all nuclei with atomic number >83 are unstable
11 Chart of the Nuclides Number of protons Too many protons: Unstable because of repulsive electric force Too many neutrons: Unstable because neutron decays to proton, electron, neutrino 1 n! 1 1 p + "1 0 e + # 0 Number of neutrons Wolfson & Pasachoff, Physics 3e Fig. 43-4
12 Energy from the Nucleus: The Curve of Binding Energy Energy released in forming nucleus Fission [Binding energy per nucleon] Fusion Hydrogen Iron Uranium Element
13 A Brief History of Fission 1934: Fermi & others: neutron bombardment experiments 1938: Hahn & Strassmann identify barium (Z=56)( among products from neutron bombardment of uranium December 1938: Lise Meitner and Otto Frisch interpret Hahn & Strassmann experiments Describe fission process First use of fission Calculate energy released NY Times 1/31/1939
14 A Brief History of Fission 1934: Fermi & others: neutron bombardment experiments 1938: Hahn & Strassmann identify barium (Z=56)( among products from neutron bombardment of uranium December 1938: Lise Meitner and Otto Frisch interpret Hahn & Strassmann experiments Describe fission process First use of fission Calculate energy released 1939: Szilard, Wigner,, Teller get Einstein to sign letter to President Roosevelt 1942: Fermi achieves first fission chain reaction 1945: Trinity, Hiroshima, Nagasaki 1954: First nuclear power plant (Obninsk( Obninsk,, USSR) UK 1956, US 1957
15 Two modes: Spontaneous fission Neutron-induced fission Fissionable isotopes Focus on Fission Will undergo fission if struck by neutrons of sufficiently high energy Include U-235, U-238, many others Fissile isotopes Will undergo fission if struck by low-energy neutrons U-233, U-235, Pu-239
16 Fission Probabilities Probability of fission Thermal energy Energy (million electron volts) Adapted from Uranium Information Centre, Melbourne, Australia:
17 Fission Probabilities Slow neutrons Fast neutrons (from fission) Faster neutrons U-235 Extremely likely Possible Possible U-238 Nearly impossible Extremely unlikely Possible
18 Neutron-induced Fission Neutron Uranium-235
19 Neutron-induced Fission
20 Neutron-induced Fission
21 Neutron-induced Fission
22 Neutron-induced Fission Neutrons
23 About 200 million electron volts (MeV( MeV) per fission Fission Energy Compares with ~4 electron volts (ev( ev) for C+O 2 CO 2 (i.e., burning coal) The Nuclear Difference: A factor of ~ million between nuclear and chemical reactions
24 The Nuclear Difference Refueling a coal plant: 14 trainloads, 110 cars each, per week Refueling a nuclear plant: A couple of truckloads every 18 months
25 Mining requirements The Nuclear Difference: More Implications 17,000 acres for 1 GW coal plant <<2000 acres for 1 GW nuclear plant Waste production Coal 1,000 tons CO 2 per hour 30 tons solid waste per hour ~1 MBq/minute radiation, mostly U, Th & decay products Nuclear 20 tons HLW per year ~50 MBq/minute radiation, mostly inert gases Grade-crossing accidents (!) Wolfson, Energy, Environment, & Climate (2007), Table 7.2
26 E = mc 2 Fission products and neutrons weigh less than the initial neutron + U-235 Mass difference m = E/c 2 But this is true for all energy-releasing events Burning fossil fuels Releasing a stretched rubber band Dropping a ball It s s just more evident in nuclear reactions Again, the Nuclear Difference Don t t blame Einstein for nuclear weapons! or give him credit for nuclear power!
27 About Those Fission Products The origin of nuclear waste, Part 1 U-235 Fission products
28 Neutrons Galore! The origin of nuclear waste, Part 2 Neutron absorption leads to long-lived Plutonium Other transuranics 1 n U! 239 U U! 239 Np + 0 e + # (24 minutes) "1 239 Np! 239 Pu + 0 e + # (2.4 days) "1
29 Chain Reaction!
30 Chain Reaction!
31 Chain Reaction!
32 Chain Reaction!
33 The Fission Chain Reaction
34 Sustaining the Chain Reaction ~2-3 neutrons liberated in each fission event How many of those cause more fission? Multiplication factor, k k<1 Subcritical: : Reaction fizzles out k>1 Supercritical: : Exponential growth Example: k=1.8 fissions 14 kg of pure U-235 in 1 microsecond Like burning 40,000 tons of coal in 1 microsecond That s s a fission bomb! k=1 Critical: : Steady chain reaction with constant rate of energy release (power output) What we want in a nuclear power reactor
35 Sustaining the Chain Reaction ~2-3 neutrons liberated in each fission event How many of those cause more fission? Multiplication factor, k k<1 Subcritical: : Reaction fizzles out k>1 Supercritical: : Exponential growth Example: k=1.8 fissions 14 kg of pure U-235 in 1 microsecond Like burning 40,000 tons of coal in 1 microsecond That s s a fission bomb! k=1 Critical: Steady chain reaction with constant rate of energy release (power output) What we want in a nuclear power reactor
36 Fates of Neutrons Strike U-235 and cause fission Much more likely for slow neutrons Strike U-235 but don t t cause fission Only 1-in-10 chance compared with fission outcome Escape the uranium fuel Strike something else and get absorbed Proton in H 2 O Deuterium U-238 Pu-239 etc Fission products Intentional neutron absorbers CRITICAL MASS
37 Implications for Nuclear Fuel Difficult to sustain a chain reaction in natural uranium 99.3% U-238, 0.7% U-235 U-238 U-235 Need to enrich percentage of U-235 Typical reactor fuel: 3-4% HEU (weapons grade): ~80% or more Enrichment technology is politically sensitive!
38 Implications for Reactor Design Need to slow the fission neutrons Moderator Water, heavy water, graphite Need to control neutron absorption Keep k=1 for steady power output Avoid runaway growth in chain reaction Movable control rods made of neutron absorber Need to remove fission energy (heat) Keep reactor from overheating Deliver useful energy to steam turbine Coolant water, heavy water, gas
39 Moderator/Coolant Choices Reactor type Moderator Coolant Comments Light water LWR (US & worldwide) Water (H 2 O) Water (H 2 O) Inherent safety: loss of coolant is loss of moderator; reaction stops Requires low-enriched uranium CANDU (Canada) Heavy water (D 2 O) Heavy water (D 2 O) Burns natural uranium Proliferation resistant (?) Continuous refueling RBMK (former USSR; Chernobyl) Graphite Water (H 2 O) Danger due to flammable moderator, instabilities Dual use: power and weapons Pu production Gas cooled (UK, France) Graphite etc CO 2, He Can burn natural uranium Fast Breeder (France, etc) None Liquid metal (sodium) Reaction sustained by fast neutrons; breeds Pu-239 from U-238
40 Delayed neutrons Some Fission Subtleties About 1% of fission neutrons aren t t emitted immediately Delays up to ~1 minute Permits mechanical control of reactor Need k=1 with the help of delayed neutrons Grave danger in criticality with prompt neutrons alone! Role of U-238, Pu-239 Neutron absorption in U-238 breeds Pu-239 At the end of its lifetime, typical nuclear fuel produces energy primarily from fission of Pu-239 But only ~2% of U-238 becomes Pu-239 that fissions
41 C.P. Snow on the Two Cultures A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics.. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare s?
42 The Second Law of Thermodynamics Disorder always increases Why? Because ordered states are rare; there are many more disordered states for a system to get into Implication Can t t convert random thermal energy ( heat( heat ) ) into ordered energy (mechanical energy, electricity) with 100% efficiency Efficiency depends on the highest and lowest available temperature ~35% for light-water reactors MWe vs MWth
43 Putting It All Together Fission here Thermal energy here Nuclear waste Electrical energy here Waste heat Wolfson & Paschoff, Physics for Scientists and Engineers 3e, Fig
44
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