how much of a sample remains after three half - lives have occurred?\n1/16 of the original sample\n1/9 of…

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 $n = 3$

When $n = 3$, we have $N=N_0\times\left(\frac{1}{2}\right)^3$.

Step3: Calculate $\left(\frac{1}{2}\right)^3$

$\left(\frac{1}{2}\right)^3=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$. So $N=\frac{1}{8}N_0$.

Answer:

C. 1/8 of the original sample