the original amount of a radioactive sample should be multiplied by which expression to calculate the amount…

the original amount of a radioactive sample should be multiplied by which expression to calculate the amount of the sample that remains after n half - lives have passed?\n(1/2)×n\n(1/n)^2\n(1/2)^n\n1/(2n)
Answer
Explanation:
Step1: Understand half - life concept
The amount of a radioactive substance reduces by half in each half - life.
Step2: Analyze the formula
If the initial amount is $A_0$, after the first half - life, the amount is $A_0\times\frac{1}{2}$. After the second half - life, it is $A_0\times\frac{1}{2}\times\frac{1}{2}=A_0\times(\frac{1}{2})^2$. In general, after $n$ half - lives, the remaining amount $A = A_0\times(\frac{1}{2})^n$. So the original amount should be multiplied by $(\frac{1}{2})^n$.
Answer:
C. $(1/2)^n$