# 15. Assume that a hypothetical radioactive isotope has a half-life of 10,000 years. If the ratio of radioactive parent to stable daughter product is 1:3, how old is the rock containing the radioactive material? What if the ratio were 1:15?

### Question: 15. Assume that a hypothetical radioactive isotope has a half-life of 10,000 years. If the ratio of radioactive parent to stable daughter product is 1:3, how old is the rock containing the radioactive material? What if the ratio were 1:15?

Answer: The Correct Answer is A ratio of 1:1 would be produced in 10,000 years (one half-life). After two half-lives, 25 percent of the original parent would be left, and 75 percent of the daughter would have formed. The ratio (25: 75) is 1: 3, so the sample is 20,000 years old (2 half-lives Ã— 10,000 years per half-life = 20,000 years).

### Reason Explained

The correct is A ratio of 1:1 would be produced in 10,000 years (one half-life). After two half-lives, 25 percent of the original parent would be left, and 75 percent of the daughter would have formed. The ratio (25: 75) is 1: 3, so the sample is 20,000 years old (2 half-lives Ã— 10,000 years per half-life = 20,000 years).

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