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

Explanation:

Step1: Recall half - life formula

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

Step2: Identify values

Here, $A_0=115$ grams and $n = 6$.

Step3: Substitute values into formula

$A=115\times\left(\frac{1}{2}\right)^6$.

Step4: Calculate $\left(\frac{1}{2}\right)^6$

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

Step5: Calculate $A$

$A = 115\times\frac{1}{64}=\frac{115}{64}\approx1.8$ grams.

Answer:

$1.8$ grams