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)

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. $(1/2)^n$