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 150 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: 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 = 150) grams and (n = 3). So, (A=150\times\left(\frac{1}{2}\right)^3).

Step3: Calculate the result

First, (\left(\frac{1}{2}\right)^3=\frac{1}{8}). Then (A = 150\times\frac{1}{8}=\frac{150}{8}=18.75).

Step4: Round the answer

Rounding (18.75) to the nearest gram gives (19) grams.