Question

which is the correct formula for calculating the age of a meteorite if using half - life?
age of object = n×t_{\frac{1}{2}}
age of object = n + t_{\frac{1}{2}}
age of object = \frac{n}{t_{\frac{1}{2}}}
age of object = \frac{t_{\frac{1}{2}}}{n}

Explanation:

Step1: Recall half - life formula

The formula for calculating the age of an object using half - life is $t = \frac{\ln(\frac{N_0}{N})}{\lambda}$, where $t$ is the age of the object, $N_0$ is the initial amount of the radioactive substance, $N$ is the remaining amount of the radioactive substance, and $\lambda$ is the decay constant. Also, the relationship between the half - life $T_{1/2}$ and the decay constant $\lambda$ is $\lambda=\frac{\ln(2)}{T_{1/2}}$. If we assume the number of half - lives passed is $n$, and the initial amount of the radioactive substance is $N_0$ and the remaining amount is $N$, and we know that $N = N_0\times(\frac{1}{2})^n$, then $\frac{N_0}{N}=2^n$. So $t = n\times T_{1/2}$.

Step2: Analyze options

Let's assume the half - life is $T_{1/2}$ and the number of half - lives is $n$. The age of the object $t=n\times T_{1/2}$.

Answer:

Age of object = $n\times T_{1/2}$ (assuming the second option from the left has $T_{1/2}$ in it which is not clearly visible in the provided image text. But conceptually, the correct formula for age of object in terms of number of half - lives $n$ and half - life $T_{1/2}$ is Age of object = $n\times T_{1/2}$)