The nuclide 22688Ra decays to gaseous 22286Rn with a t1/2 1600 y. The nuclide 22286Rn in
Chapter 12, Problem 65(choose chapter or problem)
The nuclide 22688Ra decays to gaseous 22286Rn with a t1/2 1600 y. The nuclide 22286Rn in turn a decays with ashorter lifetime, t1/2 3.82 days. If radium is originallyplaced in an evacuated closed container, theamount of radon gas builds up and can be measured.It is found that radon gas builds up to a constant valueand that as much 222Rn is being produced as decays.This process is called secular equilibrium, and the activitiesare equal. (a) Show that radon builds up at therate dN2/dt 1N1 2N2 where 1, N1 and 2, N2 arethe decay constants and number of nuclei present forradium and radon, respectively. (b) Because the decayof 226Ra is so slow, assume that N1 is constant andshow thatN2 l1l2N111 el2t2 (c) Show that after a long time, secular equilibrium isreached.
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