A certain radionuclide is being manufactured in a

Chapter , Problem 35

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A certain radionuclide is being manufactured in a cyclotron at a constant rate R. It is also decaying with disintegration constant l. Assume that the production process has been going on for a time that is much longer than the half-life of the radionuclide. (a) Show that the number of radioactive nuclei present after such time remains constant and is given by N ! R/l. (b) Now show that this result holds no matter how many radioactive nuclei were present initially. The nuclide is said to be in secular equilibrium with its source; in this state its decay rate is just equal to its production rate.

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