Question

how much of a sample remains after five half - lives have occurred?
1/5 of the original sample
1/25 of the original sample
1/32 of the original sample
1/64 of the original sample

Explanation:

Step1: Recall half - life formula

The amount of a sample remaining after \(n\) half - lives is given by \(A = A_0\times(\frac{1}{2})^n\), where \(A_0\) is the initial amount and \(n\) is the number of half - lives.

Step2: Substitute \(n = 5\)

When \(n = 5\), we have \(A=A_0\times(\frac{1}{2})^5\).
Since \((\frac{1}{2})^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}\), the fraction of the original sample remaining is \(\frac{1}{32}\) of \(A_0\).

Answer:

C. 1/32 of the original sample