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 amount of substance $A$ after $n$ half - lives, given an initial amount $A_0$ is $A = A_0\times\left(\frac{1}{2}\right)^n$.

Step2: Substitute the values

Here, $A_0 = 185$ grams and $n = 4$. So $A=185\times\left(\frac{1}{2}\right)^4$.

Step3: Calculate $\left(\frac{1}{2}\right)^4$

$\left(\frac{1}{2}\right)^4=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$.

Step4: Calculate the final amount

$A = 185\times\frac{1}{16}=\frac{185}{16}=11.5625$.

Step5: Round the answer

Rounding $11.5625$ to the nearest gram gives $12$ grams.

Answer:

12 grams