To determine the age of a meteorite using the concept of half-life, it's crucial to understand what half-life means and how it relates to age.
Half-life (denoted [tex]\( t_{1/2} \)[/tex]) is the time required for half of a radioactive substance to decay. In the context of meteorites, if you know the number of half-lives that have elapsed (denoted [tex]\( n \)[/tex]), you can calculate the age of the meteorite.
Here's a step-by-step explanation of the correct formula to use:
1. Definition of Half-Life: The half-life [tex]\( t_{1/2} \)[/tex] is the time it takes for half of the radioactive atoms in a sample to decay.
2. Number of Half-Lives (n): The number of half-lives elapsed is the total age of the object divided by the duration of one half-life [tex]\( t_{1/2} \)[/tex].
3. Formula Derivation:
- If one half-life passes, 50% of the original amount remains.
- If two half-lives pass, 25% of the original amount remains.
- The general formula for the amount of substance remaining after [tex]\( n \)[/tex] half-lives is [tex]\( \left(\frac{1}{2}\right)^n \)[/tex] times the original amount.
4. Calculating the Age:
- To find the age of the meteorite, you multiply the number of half-lives elapsed [tex]\( n \)[/tex] by the duration of one half-life [tex]\( t_{1/2} \)[/tex].
Therefore, the correct formula for calculating the age of a meteorite is:
[tex]\[ \text{Age of object} = n \times t_{1/2} \][/tex]
So, the correct option is:
[tex]\[ \text{Age of object} = n \times t_{1/2} \][/tex]
