Question

the half - life of a radioisotope is 146.5 years. how many years are there in 4.083 half - lives? report only 3 sig - figs.

Explanation:

Step1: Identify the relationship

We know that the total time $T$ is the product of the number of half - lives $n$ and the half - life period $t_{1/2}$. The formula is $T = n\times t_{1/2}$.

Step2: Substitute the given values

Given $n = 4.083$ and $t_{1/2}=146.5$ years. So $T=4.083\times146.5$.
$T = 4.083\times146.5=598.1695$ years.

Step3: Round to 3 significant figures

Rounding $598.1695$ to 3 significant figures gives $598$ years.

Answer:

$598$