Question

the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 170 grams of a radioactive isotope, how much will be left after 4 half - lives? use the calculator provided and round your answer to the nearest gram.

Explanation:

Step1: Recall half - life formula

The formula for radioactive decay after $n$ half - lives is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount, $n$ is the number of half - lives, and $N$ is the remaining amount.

Step2: Identify values

Here, $N_0 = 170$ grams and $n = 4$.

Step3: Calculate remaining amount

$N=170\times(\frac{1}{2})^4=170\times\frac{1}{16}=\frac{170}{16}=10.625$ grams.

Step4: Round the answer

Rounding $10.625$ to the nearest gram gives $11$ grams.

Answer:

11 grams