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A small dose of nuclear physics

Atoms are the basic building blocks of all matter. They consist of a cloud of negatively charged particles called electrons surrounding a small, dense positively charged nucleus. Typically, a nucleus is 100,000 times smaller in dimension than the whole atom, which is itself measured in units of ångstroms, and there are 10,000,000,000 ångstroms in 1 metre. The nucleus contains both positively charged protons and electrically neutral neutrons (collectively termed 'nucleons'). The nucleons are held together by the 'strong nuclear force'. This force acts only over very short ranges equivalent to the size of the nucleus and is sufficient to overcome the electrostatic repulsion of the positively charged protons.

As we move up the periodic table of the elements, the number of protons increases. Every additional proton means another chemically unique element - though the chemical properties are due to the surrounding electrons that also must increase in step with the protons in order to keep the atom electrically neutral. More protons mean increasing electrostatic repulsion within the nucleus, and to compensate additional neutrons are needed to increase the 'strong nuclear forces'. Initially, there are roughly equal numbers of protons and neutrons, but gradually neutrons outnumber protons as the strong force struggles to keep all the nucleons together. Eventually, as the number of protons increases above about 80, the nucleus becomes unstable. A lighter nucleus may also be unstable if the ratio of neutrons to protons is not correct. Whatever the reason for the instability, it will eventually cause the nucleus to change spontaneously into a more stable configuration. This process is called radioactive, or nuclear, decay and is accompanied by the emission of energy and/or particles. The likelihood of this decay occurring depends on the particular nucleus. In some cases, the likelihood is extremely small - this is why radioactive elements such as uranium, created billions of years ago at the birth of our planet, have not all disappeared through radioactive decay and can still be found in nature today (see half-life).

Nuclear fission is an extreme example of this process of change to a more stable configuration, involving the nucleus splitting into two (or sometimes three) fragments called fission products with the release of large amounts of energy. Sometimes, fission occurs spontaneously, though normally it must be induced through a nuclear interaction, usually the capture by the nucleus of a single free neutron. Nuclei that can be readily induced to fission, such as U-235 (see below), are called 'fissile'. The amount of energy released can be calculated by Einstein's well known equation expressing the equivalence between mass and energy: E=mc2. Here, E is the energy released, m is the difference in total mass of all particles before and after the fission, and c is the speed of light in vacuum. The fact that c2 is such a large number means that large amounts of energy are released (despite the small mass differences), certainly many orders of magnitude greater than in normal everyday reactions involving the making and breaking of chemical bonds (such as combustion). This is why nuclear reactors can be relatively compact and the volume of nuclear fuel required so small.

Where does this mass difference come from?

In the most common type of fission in a nuclear reactor, a nucleus of U-235 (the figures refers to the mass, in atomic mass units - since all uranium isotopes must have 92 protons, this isotope of uranium must have 143 neutrons) captures a neutron and the resulting instability causes the nucleus to fission. This typically produces two fission fragments, or products, and two or three separate neutrons, accompanied by the release of energy mainly in the form of kinetic energy of the fragments and neutrons:

235U92 + 1n0 ? fission products + 2 or 3 1n0 (" 1 MeV) + E (" 200 MeV)

where 1n0 depicts a neutron and E is the energy released. Superscripts are the mass numbers and the subscripts refer to the number of protons. A typical pair of fission products formed could be 92Kr36 (krypton) and 141Ba56 (barium), but there is a whole spectrum of possible outcomes. The neutrons released can go on to induce more fissions, thereby creating a chain reaction. However, these neutrons are travelling much too fast (a neutron with a kinetic energy of about 1 MeV - million electron volts - is travelling at over 100 m per second) to be captured by a U-235 nucleus, and must first be slowed down to energies well below 1 eV, or thermalised, through repeated collisions with a lighter material such as ordinary water, heavy water or graphite (see moderator).

Nucleons bound in a nucleus appear 'lighter' than individual free nucleons because they are in a more stable environment; the closer to the mid-point of the periodic table, the more tightly bound the nucleons are and the lighter they appear. If we add up the masses on the left side of the above equation and compare with the sum of the right side, there will be a difference - the right side will be slightly lighter. This is because the nucleons in the fission products are bound more tightly than those in the uranium nucleus (i.e. the nuclei of the fission products, being closer to the mid-point of the periodic table, are in a more 'stable' configuration than the original uranium nucleus). In order to conserve the total mass + energy of the system, the mass difference (or 'mass defect') must appear as energy. In the case of a typical fission of a uranium nucleus, this 'mass defect' equates to c. 200MeV of energy by Einstein's equation, and is predominantly expressed in the kinetic energy of the fission fragments.

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