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Multiple Choice
A radioactive isotope has a half-life of 1.2 billion years. As measured by the presence of the isotope and its stable decay product, a rock originally contained 10 grams of the radioactive isotope and now contains 1.25 grams. Approximately how many years old is the rock?
A
10,000 years
B
12 billion years
C
0.3 billion years
D
1,000 years
E
3.6 billion years
Verified step by step guidance
1
Understand the concept of half-life: The half-life of a radioactive isotope is the time it takes for half of the isotope to decay into its stable decay product.
Identify the initial and remaining amounts of the isotope: Initially, the rock contained 10 grams of the radioactive isotope, and now it contains 1.25 grams.
Calculate the number of half-lives that have passed: Use the formula \( n = \frac{\log(\text{final amount} / \text{initial amount})}{\log(0.5)} \) to find the number of half-lives.
Determine the age of the rock: Multiply the number of half-lives by the half-life duration (1.2 billion years) to find the age of the rock.
Verify the result: Ensure the calculated age matches one of the provided options, which is approximately 3.6 billion years.