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The half life of a radioactive isotope 'X' is 150 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio of 1:15 in a sample of a given rock. The age of the rock was estimated to be

1. 150 years
2. 200 years
3. 250 years
4. 100 years

Correct answer: 250 years

Solution

The ratio of X:Y is 1:15, meaning 1 part of X remains while 15 parts of Y are formed. This implies 1/16 of the original X remains. Using the formula N/N0 = (1/2)^(t/T), where N/N0 = 1/16 and T = 150 years, we solve for t: (1/16) = (1/2)^(t/150). Taking log base 2, t = 4 × 150 = 600 years.

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