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

the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 145 grams of a radioactive isotope, how much will be left after 3 half - lives? use the calculator provided and round your answer to the nearest gram.

Answer

Explanation:

Step1: Understand half - life concept

After 1 half - life, the amount of isotope is $\frac{1}{2}$ of the initial amount. After $n$ half - lives, the amount $A$ of the isotope is given by the formula $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives.

Step2: Identify values

Here, $A_0=145$ grams and $n = 3$.

Step3: Calculate the remaining amount

Substitute the values into the formula: $A=145\times(\frac{1}{2})^3=145\times\frac{1}{8}=\frac{145}{8}=18.125$ grams.

Step4: Round the answer

Rounding $18.125$ to the nearest gram gives 18 grams.