Nuclear energy

The atomic nuclei (consisting of protons and neutrons) carry the bulk of the mass of matter on Earth as well as in the known part of the present universe (cf. section 2.A). By a nucleus is usually understood a bound system of Z protons and N neutrons (unbound systems, resonances, may be formed under laboratory conditions and they are observed in cosmic ray showers for short periods of time). Such a nucleus contains an amount of nuclear binding energy, given by

Ezn - (NMn + ZMp) c2 = - B, with the difference between the actual energy EZN of the bound system and the energy corresponding to the sum of the masses of the protons and neu trons if these were separated from each other. It thus costs energy to separate all the nucleons, and this is due to the attractive nature of most nuclear forces.

However, if the binding energy B (i.e. the above energy difference with opposite sign) is evaluated per nucleon, one obtains a maximum around 56Fe (cf. section 2.A), with lower values for both lighter and heavier nuclei. Figure 3.82 shows the trends of —B/A, where A = Z + N is the nucleon number. For each A, only the most tightly bound nucleus (Z, A - Z) has been included, and only doubly even nuclei have been included (if Z or N is odd, the binding energy is about 1 MeV lower).

This implies that nuclear material away from the iron region could gain binding energy (and thereby release nuclear energy) if the protons and neutrons could be re-structured to form 56Fe. The reason why this does not happen spontaneously for all matter on Earth is that potential barriers separate the present states of nuclei from that of the most stable nucleus and that very few nuclei are able to penetrate these barriers at the temperatures prevailing on Earth.

Nuclear Binding Energy Per Nucleon
Figure 3.82. Trends of nuclear binding energy of bound nuclei (taken per nucleon) relative to a hypothetical situation in which all nucleons are separated (see text) (based on Bohr and Mottelson, 1969).

A few nuclei do spontaneously transform to more tightly bound systems (the natural radioactive nuclei mentioned in section 3.5.2), but the rate at which they penetrate the corresponding "barriers" is low, since otherwise they would no longer be present on Earth now, some 5 X 109 years after they were formed. As mentioned in section 3.5.2, these nuclei are responsible for 40% of the average heat flow at the surface of continents and contribute almost nothing to the heat flow at the ocean floors.

As schematically illustrated in Fig. 3.83, the barrier which a nucleus of A ~ 240 must penetrate in order to fission is typically a very small fraction (2-3%) of the energy released by the fission process. This barrier has to be penetrated by quantum tunnelling. The width of the barrier depends on the state of the initial nucleus. It is smaller if the nucleus is in an excited state rather than in its ground state. Some heavy isotopes, such as 235U, easily absorb neutrons, forming a compound system with dramatically reduced fission barrier and hence with dramatically increased fission probability. This process is called "induced fission", and it implies that by adding a very small amount of energy to a "fissile" element such as 235U, by slow-neutron bombardment, a fission energy of some 200 MeV can be released, mostly in the form of kinetic energy of the products, but a few per cent usually occurring as delayed radioac-

Nuclear Power Fission Process

Figure 3.83. Schematic view of a nuclear fission process described by a "one-dimensional" shape parameter (axi-ally symmetric shapes are indicated along the lower boundary of the figure). The zero point of the energy scale on the ordinate corresponds to the energy of a (fractional) number of 56Fe nuclei with mass identical to that of the fissioning nucleus.

tivity of unstable fragments. An example of binary fission, i.e. with two end-nuclei plus a number of excess neutrons (which can induce further fission reactions), is

The probability of finding an asymmetrical mass distribution of the fragments is often larger than the probability of symmetric fission. The reason why further fission processes yielding nuclei in the 5626Fe region do not occur is the high barrier against fission for nuclei with Z^/A * »30 and the low probability of direct fission of, say, uranium into three fragments closer to the iron region (plus a larger number of neutrons).

The amount of recoverable fissile material in the Earth's crust would correspond to a fission energy of about 1022 J (Ion, 1975). However, other heavy elements than those fissioning under slow-neutron bombardment can be made fissile by bombardment with more energetic neutrons or some other suitable nuclear reaction, spending an amount of energy much smaller than that which may later be released by fission. An example is 23892U, which may absorb a neutron and emit two electrons, thus forming 23994Pu, which is a "fissile" element, capable of absorbing neutrons to form 24094Pu, the fission cross section of which is appreciable. Including resources by which fissile material may be "bred" is this way, a higher value may be attributed to the recoverable energy resource associated with nuclear fission. This value depends both on the availability of resource material such as 238U (the isotope ratio 238U to 235U is practically the same for all geological formations of terrestrial origin) and on the possibility of constructing devices with a high "breeding ratio". Some estimates indicate a 60-fold increase over the energy value of the "non-breeder" resource (World Energy Conference, 1974).

As indicated in Fig. 3.82, the energy gain per nucleon which could be released by fusion of light elements is several times larger than that released by fission of heavy elements. A number of possible fusion processes have been mentioned in section 2.A. These reactions take place in stars at high temperature. On Earth, they have been demonstrated in the form of explosive weapons, with the temperature and pressure requirements being provided by explosive fission reactions in a blanket around the elements to undergo fusion. Controlled energy production by fusion reactions such as 2H+3H or 2H+2H is under investigation, but at present the necessary temperatures and confinement requirements have not been met. Theoretically, the fusion processes of elements with mass below the iron region are, of course, highly exenergetic, and energy must be added only to ensure a sufficient collision frequency. In practice, it may take a while to realise devices for energy extraction for which the net energy gain is at all positive.

In theory, the nuclear fusion energy resources are much larger than the fission resources, but in any case only a fraction of the total nuclear energy on

Earth (relative to an all-iron state) could ever become energy resources on a habitable planet. In principle, the nuclear energy resources are clearly non-renewable, and the recoverable amounts of fissionable elements do not appear large compared with the possible requirements of man during the kind of time span for which he may hope to inhabit the planet Earth. However, it cannot be denied that the fusion resources might sustain man's energy expenditure for a long time, if, for example, the reaction chain entirely based on naturally occurring deuterium could be realised [cf. the cosmological reactions occurring some 300 s after the singularity in the Big Bang theory (section 2.A), at temperatures between 109 and 108 K]:

The abundance of 2H in sea water is about 34 X 10-6 (mass fraction). The potential nuclear energy released by one of the deuterium-to-helium fusion chains is thus 1013 J m-3 of sea water, or over 1031 J for all the oceans (an energy storage equivalent to the entire thermal energy stored in the interior of the Earth, cf. section 3.5.2).

The prime environmental concern over utilisation of fission or fusion energy is the inherent change in the radioactive environment. The fragments formed by fission reactions cover a wide range of nuclear isotopes, most of which are unstable and emit nuclear radiation of gamma or particle type (see e.g. Holdren, 1974). Also, the fusion devices are likely to produce large amounts of radioactivity, because the high-energy particles present in the reaction region may escape and experience frequent collisions with the materials forming the "walls", the confinement, and thereby induce nuclear reactions. The range of radioactive elements formed by fusion reactions can be partially optimised from an environmental point of view (minimising the production of the most biologically hazardous isotopes) by choosing appropriate materials for the confinement, but the choice of materials is also limited by the temperature and stability requirements (see e.g. Post and Ribe, 1974).

Large-scale implementation of fission- or fusion-based energy conversion schemes will raise the question of whether it will be possible safely to manage and confine the radioactive "wastes" that, if released to the general environment, could cause acute accidents and long-range alterations in the radiological environment to which man is presently adapted. These dangers exist equally for the use of nuclear reactions in explosive weapons, in addition to the destructive effect of the explosion itself, and in this case no attempt is even made to confine or control the radioactive material.

In addition to possible health hazards, the use of nuclear energy may also have climatic consequences, e.g. associated with the enhanced heat flow (during nuclear war; cf. Feld, 1976) or with the routine emissions of radioactive material (e.g. 85Kr from the uranium fuel cycle; cf. Boeck, 1976).

In summary, nuclear energy production based on the existing once-through reactors constitutes a parenthesis in history, given the very limited amounts of fissile resources available for this mode of operation, comparable at most to those of oil. Nuclear fusion research has been ongoing for more than 50 years, so far with little success. Commercialisation is still predicted to happen some 50 years into the future, just as it was at any earlier stage.

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Responses

  • leah
    Why is the 5626Fe nucleus the most stable nucleus?
    7 years ago

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