Which of the following is the correct formula for calculating the age of a meteorite using half-life?

• A. t = ext{half-life} imes rac{ext{ln}(rac{N_0}{N})}{ext{ln} 2}
• B. t = rac{ext{half-life}}{ext{number of half-lives}}
• C. t = rac{N_0 - N}{ext{half-life}}
• D. t = ext{half-life} imes rac{N}{N_0}

Answer: (A)

Verified step by step guidance

1. Understand that the age of a meteorite can be calculated by relating the number of radioactive atoms remaining (N) to the original number (N_0) using the concept of half-life.
2. Recall the decay formula that relates the number of atoms remaining after time t: \(N = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{\text{half-life}}}\).
3. Take the natural logarithm of both sides to linearize the equation: \(\ln(N) = \ln(N_0) + \frac{t}{\text{half-life}} \times \ln\left(\frac{1}{2}\right)\).
4. Rearrange the equation to solve for time t: \(t = \text{half-life} \times \frac{\ln\left(\frac{N_0}{N}\right)}{\ln(2)}\).
5. Recognize that this formula expresses the age of the meteorite in terms of the half-life and the ratio of original to remaining atoms, which matches the correct formula given.