Nuclear Transformations
H. FUSION
Nuclear fusion may be considered the reverse of nuclear fission; that is, low-mass nuclei are combined to produce one nucleus. A typical reaction is
1
2H13HS24He01nQ
Because the total mass of the product particles is less than the total mass of the reactants, energy Q is released in the process. In the above example, the loss in mass is about 0.0189 amu, which gives Q = 17.6 MeV.
For the fusion reaction to occur, the nuclei must be brought sufficiently close together so that the repulsive coulomb forces are overcome and the short-range nuclear forces can initiate the fusion reaction. This is accomplished by heating low Z nuclei to very high temperatures (greater than 107 K) which are comparable with the inner core temperature of the sun. In practice, fission reactions have been used as starters for the fusion reactions.
2.9. ACTIVATION OF NuCLIDES
Elements can be made radioactive by various nuclear reactions, some of which have been described in the preceding section. The yield of a nuclear reaction depends on parameters such as the number of bombarding particles, the number of target nuclei, and the probability of the occurrence of the nuclear reaction. This probability is proportional to a quantity called the cross section which is usually given in units of barns, where a barn is 10−24 cm2. The cross
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1
Fission yield, percent
10−1
10−2
10−3
60 80 100 120 140 180
Mass number A
160 Figure 2.10.
plot of nuclear fission yield (%) as a function of mass number of fission nuclei (fragments) produced. (From professor Chung Chieh, with permission:
http://www.science.
uwaterloo.ca/~cchieh/
cact/nuctek/fissionyield .html)
26 part I Basic physics
section of nuclear reaction depends on the nature of the target material as well as the type of the bombarding particles and their energy.
Another important aspect of activation is the growth of activity. It can be shown that in the activation of isotopes the activity of the transformed sample grows exponentially. If both the activation and decay of the material are considered, the actual growth of activity follows a net growth curve that reaches a maximum value, called saturation activity, after several half-lives.
When that happens, the rate of activation equals the rate of decay.
As mentioned earlier, slow (thermal) neutrons are very effective in activating nuclides. High fluxes of slow neutrons (1010 to 1014 neutrons/cm2/s) are available in a nuclear reactor where neutrons are produced by fission reactions.
2.10. NuCLEAR REACTORS
In nuclear reactors, the fission process is made self-sustaining by chain reaction in which some of the fission neutrons are used to induce still more fissions. The nuclear “fuel” is usually 235U, although thorium and plutonium are other possible fuels. The fuel, in the form of cylindrical rods, is arranged in a lattice within the reactor core. Because the neutrons released during fission are fast neutrons, they have to be slowed down to thermal energy (about 0.025 eV) by collisions with nuclei of low Z material. Such materials are called moderators. Typical moderators include graphite, beryllium, water, and heavy water (water with heavy hydrogen 12H as part of the molec- ular structure). The fuel rods are immersed in the moderators. The reaction is “controlled” by inserting rods of material that efficiently absorbs neutrons, such as cadmium or boron. The position of these control rods in the reactor core determines the number of neutrons available to induce fission and thus control the fission rate or power output.
One of the major uses of nuclear reactors is to produce power. In this case, the heat generated by the absorption of g rays and neutrons is used for the generation of electrical power. In addi- tion, because reactors can provide a large and continuous supply of neutrons, they are extremely valuable for producing radioisotopes used in nuclear medicine, industry, and research.
• Radioactivity:
• Emission of radiation from a nucleus in the form of particles, g rays, or both is called radioactivity.
• Activity A of a radioactive element is the rate of disintegration or decay and is given by A = A0 e−lt, where A is activity at time t, A0 is activity at the start of time t, and l is the disintegration constant.
• Half-life T1/2 and l are related by T1/2= 0.693/l.
• Average or mean life Ta = 1/l = 1.44 T1/2.
• The SI unit for activity is Becquerel (Bq). 1 Bq = 1 dps.
• A practical unit of activity is curie (Ci). 1 Ci = 3.7 × 1010 dps.
• Activity of 1 g of radium is 0.975 Ci.
• All of the naturally occurring radioactive elements have been grouped together into three series: uranium, actinium, and thorium. The rest (Z = 93 to 118) are produced artificially.
• Radioactive equilibrium:
• If half-life of the parent nuclide is larger than that of the daughter nuclide, a condi- tion of equilibrium occurs after a certain amount of time. At equilibrium, the ratio of daughter activity to parent activity becomes constant.
• Transient equilibrium occurs when the half-life of the parent (T1) is not much longer than that of the daughter (T2) (e.g., decay of 99Mo to 99mTc). At transient equilibrium, the daughter activity A2 and the parent activity A1 are related by A2= A1× T1 /(T1 – T2).
• Secular equilibrium occurs when the half-life of the parent is much longer than that of the daughter (e.g., decay of 226Ra to 222Rn). At secular equilibrium, A2 ≈ A1.
K e Y p O I N t S
(continued)
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Chapter 2 Nuclear transformations 27
• Modes of decay:
• a particles are helium nuclei and are emitted by high atomic number radionuclides (Z > 82).
• b− particle is a negatively charged electron (negatron) emitted from a nucleus.
• b+ particle is a positively charged electron (positron) emitted from a nucleus.
• b particle does not exist as such in the nucleus but is emitted at the instant of a neu- tron or a proton decay in the nucleus:
n → p++ b−+ antineutrino p+ → n + b++ neutrino
• b particles are emitted with a spectrum of energies, ranging from zero to a maximum.
They share the available kinetic energy with the accompanying neutrino.
• The average energy of b particles is about one-third of the maximum energy.
• Electron capture is a process in which a nucleus captures an orbital electron, thus transforming one of its protons into a neutron:
P++ e− → n + n
• Electron capture creates a vacancy in the electron orbit involved which, when filled by an outer orbit electron, gives rise to characteristic x-rays (fluorescent radiation) and/or Auger electrons. The process is likened to “internal photoelectric effect.”
• Internal conversion is a process in which a nucleus in the excited state transfers its excess energy to one of the orbital electrons, causing it to be ejected from the orbit.
The ejected electron creates a vacancy in the involved shell and, as mentioned in the electron capture process, causes the emission of characteristic x-rays (fluorescent radiation) or Auger electrons.
• Fluorescent yield is Z dependent, increasing from lower Z to higher Z.
• Isomeric transition involves an excited nucleus in the metastable state decaying to the ground state. Example: 99mTc decaying to 99Tc with a half-life of 6 hours.
• Nuclear reactions:
• Nuclear reactions can be produced by bombarding heavier nuclides with lighter nuclides or particles.
• Examples of bombarding particles are a particles, protons, neutrons, deuterons, and g-ray photons.
• The photodisintegration process is responsible for contamination of the high-energy x-ray beams generated by linear accelerators.
• Radioactive sources used in radiation therapy are produced by bombarding nuclides in nuclear reactors or particle accelerators.
• Nuclear fission is a process of splitting high Z nucleus into two lower Z nuclei. The process results in the release of a large amount of energy. Example: fission of 235U nucleus by bombarding it with thermal neutrons (i.e., neutrons of energy < 0.025 eV).
A chain reaction is possible with a critical mass of fissionable material.
• Nuclear fusion is the reverse of nuclear fission—lighter nuclei are fused together into heavier ones. Again, a large amount of energy is released in the process.
• Fusion of hydrogen nuclei into helium nuclei is the source of our sun’s energy.
K e Y p O I N t S
( c o n t i n u e d )R e f e r e n c e
1. U.S. Department of Health, Education, and Welfare. Radiological Health Handbook, rev. ed.
Washington, DC: U.S. Government Printing Office; 1970.
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