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 190 grams of a radioactive isotope, how much will be left after 4 half - lives? use the calculator provided and round your answer to the nearest gram.
Answer
Answer:
12 grams
Explanation:
Step1: Determine decay formula
The formula for radioactive - decay after $n$ half - lives is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives.
Step2: Identify values
Here, $A_0 = 190$ grams and $n = 4$.
Step3: Calculate final amount
Substitute the values into the formula: $A=190\times(\frac{1}{2})^4=190\times\frac{1}{16}=\frac{190}{16}=11.875$ grams.
Step4: Round the result
Rounding $11.875$ to the nearest gram gives 12 grams.