Calculating the Age of a Rock Using Radioactive Isotope Decay

Question:

Based on the given data, how many years old is the rock that originally contained 10 grams of a radioactive isotope but now contains 1.25 grams?

Answer:

The rock is 3.6 billion years old because it has gone through three half-lives (as it now contains 1/8 of the original amount of the isotope), and each half-life is 1.2 billion years long. The correct option is A.

Explanation:

Understanding the Data: The given data states that a rock originally contained 10 grams of a radioactive isotope, which now has decayed to 1.25 grams. The half-life of the isotope is 1.2 billion years.

Calculating the Number of Half-Lives: To determine the age of the rock, we need to calculate the number of half-lives that have passed. Since the remaining amount of the isotope is 1.25 grams from an original 10 grams, which is 1/8 of the original amount, it indicates that three half-lives have occurred (as (1/2)^3 = 1/8).

Determining the Total Age: Multiplying the number of half-lives by the length of each half-life gives us the total age of the rock. Therefore, 3 half-lives * 1.2 billion years/half-life = 3.6 billion years. Thus, the correct answer is A - 3.6 billion years.