2.5 x 105
quantities; 233U, 239Pu, and 241 Pu must be created by transmutation of "fertile" materials, respectively, 232Th, 238U and 240Pu. The 240Pu element must itself be created artificially from 239Pu.
Uranium isotopes cover the range from 227 to 240 daltons, but natural uranium contains only a small percentage of the fissile material:
It is estimated that the Western world has reserves of uranium oxide (U3O8) amounting to some 6 x 109 kg, but only 34 x 106 kg are fissile, corresponding to an available energy of 2600 EJ. Compare this with the 40,000 EJ of available coal energy.
Nuclear fission reaction (with a corresponding release of energy) occurs when a fissile material interacts with neutrons. Consider 235U:
The resulting 236U decays with the emission of alpha particles (lifetime 7.5 seconds). More importantly, the uranium also suffers spontaneous fission; that is, under the proper circumstances, 235 U absorbs a neutron, and the resulting atom splits into smaller nuclei simultaneously releasing, on average, 2.5 neutrons and about 3 x 1°~n joules of energy:
292U + 0n ^ 2.5 ¿n + fission products + 3 x 10"11 J. (1.11)
Per kilogram of 235U, the energy released is
3 x 1°-11-ti- x 6 x 1°26ai°ms --to- ,-k-0^ = 77 TJ/kg.
However, the situation is somewhat more complicated than suggested by the equation above because more energy and additional neutrons are produced by the radioactive decay of the fission products. These additional neutrons are called delayed neutrons. Compare this with chemical reactions that involve energies of the order of a few tens of MJ/kg.
When Otto Hahn, demonstrated uranium fission in 1939, it became immediately obvious that a sustained "chain" reaction might be achievable—all that was needed was to cause one of the emitted neutrons to split a new uranium atom. Using natural uranium, this proves difficult because of the small percentage of the fissile 235U. The emitted neutrons have a much greater probability of being absorbed by the abundant 238U—the reaction simple dies out. The solution is to "enrich" the uranium by increasing the percentage of 235U. This is a complicated and expensive process because one cannot use chemistry to separate the two isotopes since they are chemically identical. Any separation method must take advantage of the minute mass difference of the two isotopes. If the enrichment is carried out far enough, you can build a nuclear bomb. Reactors in the United States use uranium typically enriched to 3.7%; this is insufficient to sustain a chain reaction. An additional trick must be used.
Neutrons resulting from a 235 U fission are high-energy particles (some 1 MeV), and their absorption cross section is about the same for both uranium isotopes. However, slow thermal neutrons (say at °.°5 eV) happen to be absorbed much more readily by the fissile uranium than by the more stable isotope. Thus, some of the emitted neutrons have to be slowed down by making them move through a low atomic mass substance called a moderator. Graphite or water will do. If water is used as a coolant and heat-extraction medium, then it contributes to the moderation process.^
Fast neutrons may be absorbed by impurities in the fuel or in the moderator. Of course, 238U is a major "impurity" in the fuel; it absorbs
^No enrichment is needed if the moderator is heavy water (D2O) as used in the CANDU reactor. This is the CANadian Deuterium Uranium, pressurized heavy water reactor that uses natural (unenriched) uranium and heavy water as both moderator and coolant.
some of the fast neutrons. To reduce neutron losses, it is necessary to place the fuel into a number of long rods embedded in a mass of moderator. This configuration allows most of the fast neutrons to escape the fuel region and reach the moderator where they are slowed and may eventually reenter one of the fuel rods. They now interact with the 235U perpetuating the reaction.
It is essential that exactly one of the released neutrons is, on average, used to trigger a new fission. If more than one, the reaction will grow exponentially; if less, it will die out. Control systems are used to adjust this number to precisely one.
When all is said and done, the only useful output of a fission reactor is heat, which has to be removed by a coolant and transferred to a turbine. Most American reactors use liquid water for this purpose. This limits the temperature to about 300 C, leading to low thermal efficiency. Even then, pressurization is required to keep the water in the liquid phase (hence the label pressurized water reactor). Remember that the vapor pressure of water at 300 C is 85 atmospheres. Any rupture can cause loss of coolant and can lead to a meltdown. Reactors of the class operating in the United States have a number of disadvantages that may be absent in more modern designs:
1. Scarcity of fuel because only the rare isotope, 23fU, is burned
2. Production of dangerously radioactive "ashes"
3. Safety concerns
4. Production of weaponizable materials such as plutonium
The scarcity of fuel problems can be circumvented by using one of the other fissile materials such as plutonium, 23|Pu, and uranium, 233U. These elements are not found in nature but can be obtained by the transmutation that occurs in any type of reactor.
29328U+ 0n ^ 23|U ^ _1e+ 23lNp ^ _i e+ 29349Pu (1.12)
or take 232Th:
By using plutonium, all uranium can be made to yield energy: 320,000 EJ become available. Even larger amounts of energy could be derived from thorium. One type of reactor that can greatly improve the efficiency of fuel use (by some two orders of magnitude) is the heavy-metal fast breeder reactor. Its initial fuel load must contain enough enriched uranium or plutonium not to need moderators; it must operate with fast neutrons so as to transmute 235U into plutonium (Equation 1.12) at a rate larger than that at which fissile fuel is used—it breeds more fuel than it uses (as long as the abundant supply of fertile uranium lasts). Subsequent fuel loads
(during the 60-year life expectancy of the machine) can contain waste fuel, natural uranium, or even depleted uranium. Because fast neutrons are needed and moderators must actually be avoided the coolant must have a large atomic mass; otherwise, it would itself act as a moderator.^ In addition, the coolant must be liquid (have a low melting point) and must have a high boiling point so that high temperatures can be achieved at low pressures. It is also desirable that it be relatively inert chemically. This is one of the disadvantages of using sodium as a coolant, since it reacts explosively when it comes in contact with water. One material that fulfills these requirements is a lead-bismuth alloy, Pb-Bi that, notwithstanding its elevated boiling point of 1679 C, melts at slightly over 100 C.
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