Q1. after three half-lives of an isotope, 1 billion of the original isotope's atoms still remain in a certain amount of this element. how many atoms of the daughter product would you expect to be present?

q2. by measuring the amounts of parent isotope and daughter product in the minerals contained in a rock, and by knowing the half-life of the parent isotope, a geologist can calculate the absolute age of the rock. a rock contains 125 g of a radioisotope with a half-life of 150 000 years and 875 g of its daughter product. how old is the rock according to the radiometric dating method?

 If 1 eighth equals 1 billion 7 eighth equals 7 billion. 

The asker of the second question needs a tutorial in radiometric dating. There is little likelihood that the daughter isotope has the same atomic weight as the parent isotope. To measure the mass isotopes doesn't tell us how many atoms of each exist. To get around that let's pretend — which will likely serve the purpose ineptly intended — that the values give an the particle ratio, 125:875. 

The original parent isotope count was 125 + 875 = 1000. The remaining parent isotope is 125/1000 or 1/8. 1/8 = (1/2)^h, where h is the number of half-lives. 

h = log (1/8) ÷ log(1/2) = 3 

And 3 half-lives • 150,000 years/half-life = 450,000 years.

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