To determine the correct formula for calculating the age of a meteorite using the concept of half-life, let's carefully examine the options given:
1. [tex]\( \text{Age of object} = \frac{t_{\frac{1}{2}}}{n} \)[/tex]
2. [tex]\( \text{Age of object} = \frac{n}{t_{\frac{1}{2}}} \)[/tex]
3. [tex]\( \text{Age of object} = n \times t_{\frac{1}{2}} \)[/tex]
4. [tex]\( \text{Age of object} = n + t_{\frac{1}{2}} \)[/tex]
Here, [tex]\( t_{\frac{1}{2}} \)[/tex] represents the half-life of the substance, and [tex]\( n \)[/tex] represents the number of half-lives that have elapsed.
Let's go through each option to understand if it makes sense:
1. [tex]\( \frac{t_{\frac{1}{2}}}{n} \)[/tex] suggests that the age is the half-life divided by the number of half-lives. This does not align with how age typically increases with each half-life.
2. [tex]\( \frac{n}{t_{\frac{1}{2}}} \)[/tex] implies the age is the number of half-lives divided by the half-life duration, which would result in an incorrect unit (age should typically have the units of time).
3. [tex]\( n \times t_{\frac{1}{2}} \)[/tex] means the age is equal to the number of half-lives multiplied by the duration of one half-life. This is the correct approach because for every half-life that passes, the age of the meteorite increases by that half-life duration.
4. [tex]\( n + t_{\frac{1}{2}} \)[/tex] implies simply adding the number of half-lives to the duration of one half-life, which doesn't make sense logically or dimensionally for calculating age.
Hence, the correct formula is:
[tex]\[ \text{Age of object} = n \times t_{\frac{1}{2}} \][/tex]
So the third option is indeed the correct one.
