# Question #7bdb7

##### 1 Answer

#### Answer:

Here's what I got.

#### Explanation:

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

In your case, you know that it takes **minutes** for **half** of any amount of polonium-218 that you have to undergo radioactive decay.

If you take **remains undecayed** after a given period of time

#A_t = A_0 * (1/2)^n#

Here

#n# is thenumber of half-livesthat pass in the given period of time#t#

In your case, you know that it takes **minutes** to transport the sample of polonium-238, which implies that you have

#n = (30 color(red)(cancel(color(black)("minutes"))))/(3color(red)(cancel(color(black)("minutes")))) = 10#

So if **half-lives** pass in **minutes** and you know that you must end up with

#"0.10 g" = A_0 * (1/2)^10#

Rearrange to solve for

#A_0 = "0.10 g" * 2^10 = "102.4 g"#

Now, I'll leave the answer rounded to two **sig figs**, but you could round it to one significant figure based on the value you have for the half-life of the isotope.

#color(darkgreen)(ul(color(black)("amount needed" = 1.0 * 10^2color(white)(.)"g")))#