a sample of radium - 226 will decay to ¼ of its original amount after 3200 years. what is the half - life of…

Explanation:

Step1: Understand decay concept

The amount of a radioactive - substance reduces by half in one half - life. If the substance decays to $\frac{1}{4}$ of its original amount, it has gone through 2 half - lives. Because $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step2: Calculate half - life

Let $t_{1/2}$ be the half - life. We know that the time passed $t = 3200$ years and the number of half - lives $n = 2$. The relationship between time passed $t$, number of half - lives $n$, and half - life $t_{1/2}$ is $t=nt_{1/2}$. So, $t_{1/2}=\frac{t}{n}$. Substituting $t = 3200$ years and $n = 2$ into the formula, we get $t_{1/2}=\frac{3200}{2}=1600$ years.

Answer:

1600