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Chemistry Forums for Students => High School Chemistry Forum => Topic started by: starry on February 21, 2008, 05:11:40 PM

Title: Half-life/integrated rate law problem?
Post by: starry on February 21, 2008, 05:11:40 PM
Could someone explain to me how to go about this problem? Thanks:

The half-life for radioactive decay (a first-order process) of plutonium-239 is 24,000 years.

How many years would it take for one mole of this radioactive material to decay so that just one atom remains?

t = __?__ yrs
Title: Re: Half-life/integrated rate law problem?
Post by: Arkcon on February 21, 2008, 05:34:19 PM
Humph.  Cute question they've given you.  Ok, for starters, you should ask yourself what the definition of half-life is, that's a pretty easy one.  You're given half-life, in years.  You're told you have a mole of Pu, and the answer is in atoms(well, 1 atom,) so you'll have to convert those to units.
Title: Re: Half-life/integrated rate law problem?
Post by: azmanam on February 21, 2008, 05:40:00 PM
Start here:

http://www.colorado.edu/physics/2000/isotopes/radioactive_decay3.html
http://www.chem.arizona.edu/~salzmanr/480a/480ants/kinintro/kinintro.html
http://www.chm.davidson.edu/ChemistryApplets/kinetics/IntegratedRateLaws.html
http://www.cartage.org.lb/en/themes/sciences/chemistry/NuclearChemistry/NuclChemIndex/Kineticsradioactive/Kineticsradioactive.htm
http://en.wikipedia.org/wiki/Half-life
Title: Re: Half-life/integrated rate law problem?
Post by: starry on February 21, 2008, 05:45:35 PM
Aye, I think I converted the units. since its mass is 239, that's one mole of it. One atom 6.02*10^23?

Not sure where to go from that though.
Title: Re: Half-life/integrated rate law problem?
Post by: Arkcon on February 21, 2008, 06:07:01 PM
Quote from: starry on February 21, 2008, 05:45:35 PM
Aye, I think I converted the units. since its mass is 239, that's one mole of it. One atom 6.02*10^23?

Not sure where to go from that though.

OK, 6.022 x 1023 atoms is one mole.  You won't be needing atomic mass this time, because the problem never mentions mass. ;)  Keep that in mind for the next problem 'tho.
Title: Re: Half-life/integrated rate law problem?
Post by: starry on February 21, 2008, 07:16:18 PM
Okay, well.. got that part. XD

What are the next steps I need to take?
Title: Re: Half-life/integrated rate law problem?
Post by: ARGOS++ on February 21, 2008, 07:51:58 PM
Dear Starry;

If you got that, and also the Definition of the “Half-Lifetime”:
How many Moles of 239Pu will be remaining after the first “Half-Lifetime”?
And how many Moles will be left after the second “Half-Lifetime”?
And after the fourth, - and so on?

Do you realise that it will end in a so called “Geometric Series”?

Will this hint bring you a Step ahead, or do you know how this Kinetic is calculated?

Good Luck!
                    ARGOS++