A sample contains 10.5 g of the radioisotope Pb-212 and 157.5 g of its daughter isotope, Bi-212. How many half-lives have passed since the sample originally formed?

Assuming the sample began as Pb-212 and the daughter Bi-212 accumulated as it decayed, the original amount was 10.5 g + 157.5 g = 168 g. The remaining Pb-212 is 10.5/168 = 1/16 of the original amount. Since 1/16 = (1/2)^4, four half-lives have passed, so the answer is 4.

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