how much of a sample remains after five half - lives have occurred?\n1/5 of the original sample\n1/25 of the…

how much of a sample remains after five half - lives have occurred?\n1/5 of the original sample\n1/25 of the original sample\n1/32 of the original sample\n1/64 of the original sample

how much of a sample remains after five half - lives have occurred?\n1/5 of the original sample\n1/25 of the original sample\n1/32 of the original sample\n1/64 of the original sample

Answer

Explanation:

Step1: Recall half - life formula

The amount of a sample remaining $N$ after $n$ half - lives, given an initial amount $N_0$, is $N = N_0\times\left(\frac{1}{2}\right)^n$.

Step2: Substitute $n = 5$

When $n = 5$, we have $N=N_0\times\left(\frac{1}{2}\right)^5$. Since $\left(\frac{1}{2}\right)^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}$, the fraction of the original sample remaining is $\frac{1}{32}$ of the original sample.

Answer:

C. 1/32 of the original sample