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Thank you for working the problem.
1 mole of water (18 grams) contains 6.02*10^23 molecules. This amounts to 3.34*10^22 molecules per gram of water. How many atoms of Th is there in 1 gram of water, if its concentration is 0.03 ppb?
N'=(3.34*10^22)*(0.03*10^-9)=0.10*10^13=1.0*10^12 (atoms of thorium per gram of water)
For one liter, N=1000*N'=1.0*10^15 atoms
Thus the decay rate is R=k*N=(1.15*10^-8) * (1.0*10^15) = 1.15*10^7 decays per second.
The activity in Curies is:
A= R/(3.7*10^10) = (1.15*10^7) / (3.7*10^10 ) = 3.11*10^-4 Ci