Unformatted text preview: UCSD Physics 10 Nuclear Energy
Fission, Fusion, the Sun's Energy UCSD Physics 10 What's in a Nucleus The nucleus of an atom is made up of protons and neutrons each is about 2000 times the mass of the electron, and thus constitutes the vast majority of the mass of a neutral atom (equal number of protons and electrons) proton has positive charge; mass = 1.007276 a.m.u. neutron has no charge; mass = 1.008665 a.m.u. proton by itself (hydrogen nucleus) will last forever neutron by itself will "decay" with a half-life of 10.4 min size of nucleus is about 0.00001 times size of atom atom is then mostly empty space UCSD Physics 10 What holds it together? If like charges repel, and the nucleus is full of protons (positive charges), why doesn't it fly apart? repulsion is from electromagnetic force at close scales, another force takes over: the strong nuclear force The strong force operates between quarks: the building blocks of both protons and neutrons it's a short-range force only: confined to nuclear sizes this binding overpowers the charge repulsion UCSD Physics 10 What's the deal with neutrons decaying?! A neutron, which is heavier than a proton, can (and will!) decide to switch to the lower-energy state of the proton Charge is conserved, so produces an electron too and an anti-neutrino, a chargeless, nearly massless cousin to the electron proton Poof! neutron neutrino electron UCSD Physics 10 Insight from the decaying neutron Another force, called the weak nuclear force, mediates these "flavor" changes referred to as beta decay Does this mean the neutron is made from an electron and proton? No. But it will do you little harm to think of it this way Mass-energy conservation: Mass of neutron is 1.008665 a.m.u. Mass of proton plus electron is 1.007276 + 0.000548 = 1.007824 difference is 0.000841 a.m.u. in kg: 1.4 10-30 kg = 1.26 10-13 J = 0.783 MeV via E = mc2 1 a.m.u. = 1.6605 10-27 kg 1 eV = 1.602 10-19 J excess energy goes into kinetic energy of particles UCSD Physics 10 Counting particles A nucleus has a definite number of protons (Z), a definite number of neutrons (N), and a definite total number of nucleons: A = Z + N example, the most common isotope of carbon has 6 protons and 6 neutrons (denoted 12C; 98.9% abundance) Z = 6; N = 6; A = 12 another stable isotope of carbon has 6 protons and 7 neutrons (denoted 13C; 1.1% abundance) Z = 6; N = 7; A = 13 an unstable isotope of carbon has 6 protons and 8 neutrons (denoted 14C; half-life is 5730 years) decays via beta decay to 14N Isotopes of an element have same Z, differing N
Q UCSD Physics 10 Fission of Uranium Barium and Krypton represent just one of many potential outcomes Resulting mass products add up to 99.9% of the mass that went in UCSD Physics 10 Fission There are only three known nuclides (arrangements of protons and neutrons) that undergo fission when introduced to a slow (thermal) neutron: U: 235 U: 239 Pu:
233 hardly used (hard to get/make) primary fuel for reactors popular in bombs Others may split if smacked hard enough by a neutron (or other energetic particle) UCSD Physics 10 How much more fissile is 235U than 238U? Bottom line: at thermal energies (arrow), 235U is 1000 times more likely to undergo fission than 238U even when smacked hard UCSD Physics 10 Uranium isotopes and others of interest
233 234 235 236 237 238 239 232 Abundance (%) 0 0.0055 0.720 0 0 99.2745 no natural Pu 100 half-life 159 kyr 246 kyr 704 Myr 23 Myr 6.8 days 4.47 Gyr 24 kyr 14 Gyr decays by: U U U U U U Pu Th UCSD Physics 10 The Uranium Story No isotope of uranium is perfectly stable: U has a half-life of 704 million years 238 U has a half-life of 4.5 billion years (age of earth)
235 No heavy elements were made in the Big Bang (just H, He, Li, and a tiny bit of Be) Stars only make elements as heavy as iron (Fe) through natural thermonuclear fusion Heavier elements made in catastrophic supernovae massive stars that explode after they're spent on fusion 235 U and 238U initially had similar abundance UCSD Physics 10 Uranium decay The natural abundance of uranium today suggests that it was created about 6 billion years ago assumes 235U and 238U originally equally abundant Now have 39.8% of original 238U and 0.29% of original 235 U works out to 0.72% 235U abundance today Plutonium-239 half-life is too short (24,000 yr) to have any naturally available Thorium-232 is very long-lived, and holds primary responsibility for geothermal heat UCSD Physics 10 Why uranium? Why mess with "rare-earth" materials? Why not force lighter, more abundant nuclei to split? though only three "slow-neutron" fissile nuclei are known, what about this "smacking" business? Turns out, you would actually loose energy in splitting lighter nuclei Iron is about the most tightly bound of the nuclides and it's the release of binding energy that we harvest so we want to drive toward iron to get the most out 2 Q UCSD Physics 10 Binding energy per nucleon Iron (Fe) is at the peak On the heavy side of iron, fission delivers energy On the lighter side of iron, fusion delivers energy This is why normal stars stop fusion after iron Huge energy step to be gained in going from hydrogen (H) to helium-4 via fusion UCSD Physics 10 Fusion: The big nuclear hope Rather than rip nuclei apart, how about putting them together?
alpha (4He) tritium Iron is most tightly bound nucleus Can take loosely bound light nuclei and build them into more tightly bound nuclei, releasing energy Huge gain in energy going from protons (1H) to helium (4He). It's how our sun gets its energy Much higher energy content than fission dueterium proton UCSD Physics 10 Thermonuclear fusion in the sun Sun is 16 million degrees Celsius in center Enough energy to ram protons together (despite mutual repulsion) and make deuterium, then helium Reaction per mole ~20 million times more energetic than chemical reactions, in general
4 protons: mass = 4.029 He nucleus: mass = 4.0015
4 2 neutrinos, photons (light) UCSD Physics 10 E=mc2 balance sheets Helium nucleus is lighter than the four protons! Mass difference is 4.029 4.0015 = 0.0276 a.m.u. 0.7% of mass disappears, transforming to energy 1 a.m.u. (atomic mass unit) is 1.6605 10-27 kg difference of 4.58 10-29 kg multiply by c2 to get 4.12 10-12 J 1 mole (6.022 1023 particles) of protons 2.5 1012 J typical chemical reactions are 100200 kJ/mole nuclear fusion is ~20 million times more potent stuff! works out to 150 million Calories per gram compare to 16 million Cal/g uranium, 10 Cal/g gasoline UCSD Physics 10 Artificial fusion 16 million degrees in sun's center is just enough to keep the process going but sun is huge, so it seems prodigious In laboratory, need higher temperatures still to get worthwhile rate of fusion events like 100 million degrees Bottleneck in process is the reaction:
1 H + 1H 2H + e+ + (or proton-proton deuteron) Better off starting with deuterium plus tritium 2H and 3H, sometimes called 2D and 3T Then:
2 H + 3H 4He + n + 17.6 MeV (leads to 81 MCal/g) UCSD Physics 10 Deuterium everywhere Natural hydrogen is 0.0115% deuterium Lots of hydrogen in sea water (H2O) Total U.S. energy budget (100 QBtu = 1020 J per year) covered by sea water contained in cubic volume 170 meters on a side corresponds to 0.15 cubic meters per second about 1,000 showers at two gallons per minute each about one-millionth of rainfall amount on U.S. 4 gallons per person per year!!! UCSD Physics 10 Tritium nowhere Tritium is unstable, with half-life of 12.32 years thus none naturally available Can make it by bombarding 6Li with neutrons extra n in D-T reaction can be used for this, if reaction core is surrounded by "lithium blanket" Lithium on land in U.S. would limit D-T to a hundred years or so maybe a few thousand if we get lithium from ocean D-D reaction requires higher temperature, but could be sustained for many millennia UCSD Physics 10 Nasty by-products? Practically none: not like radioactive fission products Building stable nuclei (like 4He) maybe our voices would be higher... Tritium is the only radioactive substance energy is low, half-life short: not much worry here Extra neutrons can tag onto local metal nuclei (in surrounding structure) and become radioactive but this is a small effect, especially compared to fission UCSD Physics 10 Why don't we embrace fusion, then? Believe me, we would if we could It's a huge technological challenge, always 50 years from fruition must confine plasma at 50 million degrees!!! all the while providing fuel flow, heat extraction, tritium supply, etc. hurdles in plasma dynamics: turbulence, etc. Still pursued, but with decreased enthusiasm, increased skepticism but man, the payoff is huge: clean, unlimited energy UCSD Physics 10 Fusion Successes? Fusion has been accomplished in labs, in big plasma machines called Tokamaks got ~6 MW out of Princeton Tokamak in 1993 but put ~12 MW in to sustain reaction Hydrogen bomb also employs fusion fission bomb (e.g., 239Pu) used to generate extreme temperatures and pressures necessary for fusion LiD (lithium-deuteride) placed in bomb fission neutrons convert lithium to tritium tritium fuses with deuterium
Q UCSD Physics 10 References and Assignments References: Physics 12, offered spring quarter Energy: A Guidebook, by Janet Ramage Final Exam Review Sessions Wed 6/11 810 PM Solis 104 (Murphy-led) Thu 6/12 810 PM Solis 104 (Wilson-led) Assignments: Read Chap. 34 pp. 671674; skim rest as needed/interested HW8, due 6/06: 30.E.42, 27.E.10, 27.E.11, 27.E.15, 27.E.20, 27.E.29, 28.E.31, 28.E.33, plus four more required problems posted on website Last Q/O due Friday 6/06 by midnight ...
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