Question

you start with 200 g of thallium 207. after 20 minutes, there is only 12.5 g of thallium left. what is the half - life of the decay process?
25
50
12.5
200
100
4
81
20
82
5
207
this is a required question

Explanation:

Step1: Determine the number of half - lives

We know the radioactive decay formula $N = N_0(\frac{1}{2})^n$, where $N$ is the final amount, $N_0$ is the initial amount, and $n$ is the number of half - lives. Given $N_0=200$ g and $N = 12.5$ g. So, $12.5=200\times(\frac{1}{2})^n$. Then $(\frac{1}{2})^n=\frac{12.5}{200}=\frac{1}{16}$. Since $\frac{1}{16}=(\frac{1}{2})^4$, $n = 4$.

Step2: Calculate the half - life

We know that the time elapsed $t = 20$ minutes and the number of half - lives $n = 4$. Using the formula $t=n\times t_{1/2}$, where $t_{1/2}$ is the half - life. Rearranging for $t_{1/2}$, we get $t_{1/2}=\frac{t}{n}$. Substituting $t = 20$ minutes and $n = 4$, we have $t_{1/2}=\frac{20}{4}=5$ minutes.

Answer:

5