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

A. Age of object [tex]$=\frac{t_{\frac{1}{2}}}{n}$[/tex]

B. Age of object [tex]$=\frac{n}{t_{\frac{1}{2}}}$[/tex]

C. Age of object [tex]$=n \times t_{\frac{1}{2}}$[/tex]

D. Age of object [tex]$=n+t_{\frac{1}{2}}$[/tex]



Answer :

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]