To answer the question about the correct formula for calculating the age of a meteorite using half-life, let's break it down step by step.
1. Understanding Half-Life:
- Half-life (denoted as [tex]\( t_{1/2} \)[/tex]) is the time required for half of the radioactive atoms in a sample to decay.
2. Calculating the Age:
- The age of the meteorite can be calculated by determining how many half-lives have passed since the meteorite formed.
- If [tex]\( n \)[/tex] is the number of half-lives that have elapsed, the age of the meteorite is:
[tex]\[
\text{Age of object} = \text{number of half-lives elapsed} \times \text{half-life duration}
\][/tex]
This can be expressed mathematically as:
[tex]\[
\text{Age of object} = n \times t_{1/2}
\][/tex]
3. Evaluating the Options:
- [tex]\( \frac{t_{1/2}}{n} \)[/tex]: This would give the inverse of what we need and does not represent the age.
- [tex]\( \frac{n}{t_{1/2}} \)[/tex]: Again, this is incorrect as it suggests the age decreases with increasing half-life duration, which is wrong.
- [tex]\( n \times t_{1/2} \)[/tex]: Correct, this matches our derived formula.
- [tex]\( n + t_{1/2} \)[/tex]: This addition does not make sense in the context of calculating the age correctly.
Based on these explanations, the correct formula for calculating the age of a meteorite using half-life is:
[tex]\[
\text{Age of object} = n \times t_{1/2}
\][/tex]
