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(B) The Curve of Binding Energy
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The masses of nuclei can be precisely measured by "mass spectrographs". They differ from the sum of masses of their particles by the binding energy E, the energy needed to break them apart. E is found from Einstein's E = mc2 , where m is the mass difference.
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In light nuclei, binding energy per nucleon usually increases with nuclear mass, because the more nuclear mass, the more energy in the nuclear force holding them together. That force however has a short range, and past iron (56 nucleons) the repulsive force of the positive charge of the protons causes the binding energy per nucleon to decrease.
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Most elements with more than 200 nucleons are unstable because of the above disruptive force, and decay by radioactivity. None exist in nature with more than 238 nucleons (uranium 238). Artificially produced nuclei of greater mass decay even faster.
(C) Fission of Very Heavy Nuclei
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Very heavy nuclei may decay by fission into two unequal parts, releasing much more energy (typically 50-100 times) than radioactive decay.
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Uranium with 235 nucleons (U-235) makes up 0.7% of natural uranium. If approached by a neutron (even a slow one) it fissions. Plutonium Pu-239 produced (with an intermediate step) when U-238 captures a neutron behaves similarly, as does U-233. (Pu-240 undergoes spontaneous fission).
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The "fission fragments" are extremely unstable, because their neutron/proton ratio is much larger than that of stable nuclei with the same number of protons. They emit on the average more than 2 neutrons per fission, in 98% of the cases "promptly" What remains is still dangerously radioactive for many years. If at least one of those neutrons is re-absorbed by U-235 or plutonium, another fission may result, leading to a "chain reaction."
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In relatively pure U-235 or Pu-239, a chain reaction can cause a nuclear explosion. In power-generating reactors, the neutrons are slowed down by collisions with atoms of a moderator like pure carbon or water (especially "heavy water"), and the reaction can be controlled by cadmium rods which absorb neutrons. In a controlled nuclear reaction, heat generated by fission is typically removed by pressurized water, which turns to steam, powering turbines which rotate generators of electric power.
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Partially spent fuel must be reprocessed--to remove "unburned" fuel, also to remove plutonium generated when U-238 absorbs neutrons, as well as fission fragments which absorb neutrons and retard the fission process. Those fragments are dangerously radioactive for centuries and need to be stored away from people and ground water
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Reactors function better and can be smaller if the fraction of U-235 in the fuel is first enriched, by cascades of porous partitions or by fast centrifuges, filtering the gas UF6.
(D) Control of Nuclear reactions
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The traditional control of nuclear reactions uses neutron-absorbing control rods, thrust automatically into the core to dampen the reaction or pulled out to speed it up. Only a 2% margin (due to neutrons emitted with a delay of a second or two) is available (for a given reactor core) between a runaway reaction and a fizzle!
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Even if a reactor is shut down, cooling water must continue to circulate, because radioactive energy continues to be released for a while, enough to produce a "meltdown" of the core. That happened in March 1978 at Three Mile Island in Pennsylvania; that reactor was inside a thick concrete "containment building" which prevented any radioactivity from leaking out.
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The Soviet power reactor at Chernobyl near Kiev (now Ukraina) was moderated by a carbon core and had no containment building. A dangerous experiment in 1986 started a runaway reaction, blowing off the roof and starting a fire which spread dangerous radioactive debris across Europe.
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A breeder reactor uses neutrons of each fission very economically--one to continue the chain reaction, and at least one to be captured by uranium 238 (or thorium 232), converting them into usable fuel--plutonium 239 or uranium 233. In principle therefore a breeder reactor can extract energy from all its uranium or thorium.
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The first experimental reactor started up on 2 December 1942 in Chicago. As of 2009 nuclear energy produces most of the electricity in France, about 20% in the USA, and comparable or larger amounts in Spain, Japan, Germany, Britain and Russia.
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