The Los Angeles County Police want to use neutron activation analysis to look for a tiny residue of barium in gunpowder. The suspected residue is placed in a nuclear reactor, where it is activated by the neutron flux. Natural barium contains 71.7% 138Ba. The β- emitter 139Ba is produced in the 138Ba(n, γ ) 139Ba reaction. The half-life of 139Ba is 83.1 min. 139Ba beta decays to 139La, 72% going to the ground state and 27% going to the first excited state at 0.166 MeV. Scientists think they need a count rate for the 166-keV γ ray (decay to the ground state) of at least 1000 Bq 30 min after the residue is removed from the reactor in order to make a positive identification of barium. (a) How many 139Ba nuclei must be present at the end of the activation? (Remember the decay and fraction going to the first excited state.) (b) How many grams of 139Ba must be produced? If the original amount of barium was 0.01 μg, what fraction of the 138Ba was activated?
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