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 175 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.

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 175 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: Determine the decay formula

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

Step2: Identify the values of $A_0$ and $n$

Here, $A_0 = 175$ grams and $n = 3$.

Step3: Substitute the values into the formula

$A=175\times\left(\frac{1}{2}\right)^3=175\times\frac{1}{8}=\frac{175}{8}=21.875$.

Step4: Round the result

Rounding $21.875$ to the nearest gram gives $22$ grams.

Answer:

22 grams