Principle Behind Mother-Daughter Relationship

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A radionuclide generator, also popularly called a “cow”, is composed of a mother-daughter radionuclide relationship where the mother has a longer half-life than the daughter. The daughter is continuously produced by decay of the mother in the generator system, and the daughter can be separated (“milked”) from the generator (“cow) by chemical or physical methods. In this Exercise we are going to use one such system defined in more detail below.

From basic lectures on decay we have the following relation between a radioactive nuclide and its radioactive daughter:
Mother-Daughter formula 2-1.jpg
where the index 1 denotes the mother and index 2 the daughter.

If λ1 << λ2, i.e. the half-life of the daughter is much shorter than the half-life of the mother, we have:

Mother-Daughter formula 2-2.jpg