If a parent isotope has a half-life of 1.75 million years, how much of the original sample will remain after 3.5 million years?

• A. 25% of the original sample
• B. 75% of the original sample
• C. 12.5% of the original sample
• D. 50% of the original sample

Answer: (A)

Verified step by step guidance

1. Identify the half-life of the parent isotope, which is given as 1.75 million years. This is the time it takes for half of the original sample to decay.
2. Determine the total time elapsed, which is 3.5 million years in this problem.
3. Calculate the number of half-lives that have passed by dividing the total time elapsed by the half-life: \(\text{number of half-lives} = \frac{3.5}{1.75}\).
4. Use the formula for the remaining fraction of the sample after a certain number of half-lives: \(\text{remaining fraction} = \left( \frac{1}{2} \right)^{\text{number of half-lives}}\).
5. Substitute the number of half-lives into the formula to find the fraction of the original sample remaining after 3.5 million years.