# Question e7a7d

Sep 15, 2017

Here's what I got.

#### Explanation:

For a given radioactive isotope, the nuclear half-life, ${t}_{\text{1/2}}$, tells you the time needed for half of an initial sample of this isotope to undergo radioactive decay.

This means that with every half-life that passes, the mass of the sample will be halved. In your case, you know that the isotope has a half-life of $\text{120 s}$. If you start with an $\text{80-g}$ sample, you will end up with

• $\frac{\text{80 g" * 1/2 = "80 g}}{2} ^ \textcolor{red}{1} \to$ after $\textcolor{red}{1}$ half-life passes
• $\frac{\text{80 g"/2^color(red)(1) * 1/2 = "80 g}}{2} ^ \textcolor{red}{2} \to$ after $\textcolor{red}{2}$ half-lives pass
• $\frac{\text{80 g"/2^color(red)(2) * 1/2 = "80 g}}{2} ^ \textcolor{red}{3} \to$ after $\textcolor{red}{3}$ half-lives pass
$\vdots$

and so on. You can thus say that your sample will contain

• $\text{After 120 s}$

(120 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(1) implies "80 g"/2^color(red)(1) = "40 g"

• $\text{After 240 s}$

(240 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(2) implies "80 g"/2^color(red)(2) = "20 g"

• $\text{After 480 s}$

 (480 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(3) implies "80 g"/2^color(red)(3) = "10 g"#