the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to…

Explanation:

Step1: Identify the decay formula

The formula for radioactive decay is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount, $n$ is the number of half - lives, and $A$ is the final amount.

Step2: Substitute the given values

Here, $A_0 = 205$ grams and $n = 5$. So, $A=205\times(\frac{1}{2})^5$.

Step3: Calculate the value of $(\frac{1}{2})^5$

$(\frac{1}{2})^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}$.

Step4: Calculate the final amount

$A = 205\times\frac{1}{32}=\frac{205}{32}=6.40625$ grams.

Step5: Round to the nearest gram

Rounding $6.40625$ to the nearest gram gives $6$ grams.

Answer:

$6$ grams