Question b599d

Oct 12, 2017

Here's what I got.

Explanation:

The idea here is that radioactive nuclide's half-life tells you the time needed for half of an initial sample of this nuclide to undergo radioactive decay.

In your case, the chemical is said to have a half-life of $5$ years, which means that with every $5$ years that pass, i.e. with every passing half-life, the amount of this chemical will be reduced by half.

So if you start with $\text{100 g}$, you can say that you will be left with

• $\frac{\text{100 g" * 1/2 = "100 g}}{2} ^ \textcolor{red}{1} \to$ after $\textcolor{red}{1}$ half-life
• $\frac{\text{100 g"/2 * 1/2 = "100 g}}{2} ^ \textcolor{red}{2} \to$ after $\textcolor{red}{2}$ half-lives
• $\frac{\text{100 g"/4 * 1/2 = "100 g}}{2} ^ \textcolor{red}{3} \to$ after $\textcolor{red}{3}$ half-lives
$\vdots$

and so on. So after

$\text{10 years" = color(red)(2) * "5 years}$

you can say that your sample will be reduced to

"100 g" * 1/2^color(red)(2) = color(darkgreen)(ul(color(black)("25 g")))#

I'll leave the answer rounded to two sig figs, but keep in mind that based on the values given to you, you can only justify one significant figure for the answer.

Oct 12, 2017

Can i just clarify something? Stefan is correct, you'll have 25g of radioactive element, but 75g of stable stuff. It won't weigh (or more technically, have a mass of) 25g in the packet after 5 years.