Rankers Physics

Uncategorized: Practice Problem & Solution

44. The half life of a radioactive isotope 'X' is 50 years. It decay to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1 : 15 in a sample of a given rock. The age of the rock was estimated to be: (2011 Pre)
150 years
200 years
250 years
100 years

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Ratio $X/Y = 1/15$, so fraction of X remaining is $X/(X+Y) = 1/16 = (1/2)^4$. This means 4 half-lives have elapsed. The age is $4 \times 50 = 200$ years.

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