A sample contains 16.75 g of the radioisotope U-236 and 50.25 g of its daughter isotope, Th-232. How long did it take for decay to take place if one half-life of U-236 is 23 million years?

The sample has 16.75 g of U-236 remaining and 50.25 g of daughter isotope, so its original U-236 amount was 67.00 g. The fraction remaining is 16.75 ÷ 67.00 = 1/4, meaning two half-lives have passed (100% → 50% → 25%). At 23 million years per half-life, the elapsed time is 2 × 23 = 46 million years, choice A.

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