Simulation of Radioactive Decay

[Matthias32]

Okay, I've got this problem in my Chemistry class. It's about half-lifes and all that. If this is the wrong place to post this, then somebody can move it I guess.

I've got a 10.0 g sample of an unknown. They give me the following info, wanting me to plot it on a graph. That's the easy part.

Time(yr)---------------Mass(g)
0----------------------10.0
20---------------------6.50
39---------------------3.80
60---------------------2.20
80---------------------1.20
100--------------------0.500

So I graphed it, but now they want me to locate the time when the mass is 5.00 g. Of course, this is the half-life. But how to find it...?

Then I need to check again at 2.50 g, but I can handle that part if I can just get some help on the 5 grams part. Thanks.

Matthias

 

[mrjeffy321]

You know that after every half life, half of the remaining substance is lost.
So if you have 10 grams, 1 half life later, 5 grams are left, 2 half lifes...2.5 grams.
you could make an equation out of this,
(stuff remaining) = (original amount)*.5^(number of half lives)

so now you sovle it for the number of half lives it has had after a certain amount of time using the data given.
I did this, and my answer isn't quite agreeing with the chart when I check it though.

Just as an example, say you choose to find the number of half lives that have occurred after 100 years.
.5 grams = 10 grams * .5^(100 / x)
where x is the length of a half life. Solve for x by taking the log of both sides and applying some log rules. I found x = 23.17 years.
cheking it,
10*.5^(100/23.17) = .502, close enough.
But say you pick another date to find the length of a half life (20 year), the values for x do not agree.

Maybe they just want you to estimate it from the graph?

 

[Matthias32]

Yeah, later they ask some stuff about "do these two times completely agree?" How convenient. Then they ask how I could use them to approximate the half-life. Maybe the average or something.