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Chapter 31 | Radioactivity and Nuclear Physics
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is a high-energy photon originating in a nucleus.
31.5 Half-Life and Activity
• Half-life is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei as a function of time is
where is the number present at , and is the decay constant, related to the half-life by
• One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity :
• The SI unit for is the becquerel (Bq), defined by
• is also expressed in terms of curies (Ci), where
• The activity of a source is related to and by
• Since has an exponential behavior as in the equation given by
• The binding energy (BE) of a nucleus is the energy needed to separate it into individual protons and neutrons. In terms of
atomic masses,
where is the mass of a hydrogen atom, is the atomic mass of the nuclide, and is the mass of a
neutron. Patterns in the binding energy per nucleon, , reveal details of the nuclear force. The larger the , the more stable the nucleus.
31.7 Tunneling
where is the activity at . 31.6 Binding Energy
• Tunneling is a quantum mechanical process of potential energy barrier penetration. The concept was first applied to explain
decay, but tunneling is found to occur in other quantum mechanical systems. Conceptual Questions
, the activity also has an exponential behavior,
31.1 Nuclear Radioactivity
1. Suppose the range for ray is known to be 2.0 mm in a certain material. Does this mean that every a ray that strikes this material travels 2.0 mm, or does the range have an average value with some statistical fluctuations in the
distances traveled? Explain.
2. What is the difference between rays and characteristic x rays? Is either necessarily more energetic than the other? Which
can be the most energetic?
3. Ionizing radiation interacts with matter by scattering from electrons and nuclei in the substance. Based on the law of conservation of momentum and energy, explain why electrons tend to absorb more energy than nuclei in these interactions.
4. What characteristics of radioactivity show it to be nuclear in origin and not atomic?
