Radioactive decay, constant scheme

For large cross-sections, short half-lives, and long bombardments, second-order capture products may be formed. If the hrst-order product is radioactive, then its concentration at any time is dep dent on (i) the decay constant, (ii) the cross-section for production of the second-order product, as well as (iii) the cross-section for its own production. These possibilities lead to a scheme such as Figure 15.2. For simplicity, we may assume that the induced nuclear transformations only involve single-neutron capture, and that only decay occurs. However, it should be obvious that the scheme in Figure 15.2, with suitable additions, is applicable to all kinds of nuclear formation and decay reactions. 

In the type of process described here, a radioactive nuclide decays to produce a daughter, which is also radioactive. In a general way, this is similar to the reaction scheme in which a transient state (intermediate) is produced as A —> B —> C, but there are also some significant differences depending on the relative half-fives of the parent and daughter. One significant difference between radioactive decay and chemical reactions is that the latter are reversible to some extent, so they tend toward equilibrium. Radioactive decay proceeds to completion. If subscripts 1,2, and 3 are used to represent the parent, daughter, and final product, respectively, the number of nuclei can be expressed as Ni,Nz, and N3. The rate constants... 

Even though some of the daughters in natural radioactive decay schemes have very short half-lives, all are present because they are constantly forming as well as decaying. It is likely that only about one gram of radium-226 was present in several tons of uraniiun ore processed by Marie Curie in her discovery of radium in 1898. Nevertheless, she was successful in isolating it. The ore also contained only a fraction of a milligram of polonium, which she was able to detect but not isolate. 

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