An example of the situation discussed in Problem 75 is the radioactive isotope ²²⁹Th, an a emitter with a half-life of 7300 years. Its daughter, ²²⁵Ra, is a β emitter with a half-life of 14.8 d. In this, as in many instances, the half-life of the parent is much longer than that of the daughter. Using the expression given in Problem 75 (b), show that, starting with a sample of pure ²²⁹Th containing N_A0 nuclei, the number, N_B, of ²²⁵Ra nuclei will, after a several years, be a constant, given by

The number of daughter nuclei are said to be in “secular equilibrium.”

Transcribed Image Text:

ANA NB