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, $A_0 = 145$ grams and $n = 6$. So, $A=145\times(\frac{1}{2})^6$.

Step3: Calculate $(\frac{1}{2})^6$

$(\frac{1}{2})^6=\frac{1}{2\times2\times2\times2\times2\times2}=\frac{1}{64}$.

Step4: Calculate the final amount

$A = 145\times\frac{1}{64}=\frac{145}{64}\approx2.265625$.

Step5: Round the answer

Rounding $\frac{145}{64}$ to the nearest gram gives $2$ grams.

Answer:

2 grams