Rankers Physics

Nucleus: Practice Problem & Solution

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 1 : 7 in a sample of a given rock. The age of the rock is estimated to be: (2013)
100 years
40 years
60 years
80 years

Solution Explained:

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

The fraction of remaining radioactive isotope is $X/(X+Y) = 1/(1+7) = 1/8 = (1/2)^3$. Three half-lives have passed, so age $t = 3 \times 20 = 60$ years.

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