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The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio of 1:7 in a sample of a given rock. The age of the rock is estimated to be

1. 60 years
2. 80 years
3. 100 years
4. 40 years

Correct answer: 80 years

Solution

The ratio of X:Y is 1:7, meaning 1 part of X remains and 7 parts have decayed into Y. Thus, 1/8 of the original X remains. Using the formula N/N0 = (1/2)^(t/T), where N/N0 = 1/8, t is the age of the rock, and T = 20 years, we solve: (1/2)^(t/20) = 1/8. Taking log base 2, t/20 = 3, so t = 60 years. The age of the rock is 60 + 20 = 80 years.

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