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 $A = A_0\times\left(\frac{1}{2}\right)^n$, 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

We are given that $A_0=195$ grams and $n = 6$. Substitute these values into the formula: $A=195\times\left(\frac{1}{2}\right)^6$.

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

$A = 195\times\frac{1}{64}=\frac{195}{64}\approx3.046875$.

Step5: Round the answer

Rounding $\frac{195}{64}$ to the nearest gram, we get $3$ grams.

Answer:

$3$ grams