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 a radioactive substance after $n$ half - lives is given by $A = A_0\times\left(\frac{1}{2}\right)^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives.

Step2: Substitute the given values

Here, $A_0 = 125$ grams and $n = 6$. So, $A=125\times\left(\frac{1}{2}\right)^6$.

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

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

Step4: Calculate the final amount

$A = 125\times\frac{1}{64}=\frac{125}{64}\approx1.953125$. Rounding to the nearest gram, $A\approx2$ grams.

Answer:

2 grams