[starry]

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

[Arkcon]

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.

[azmanam]

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

[starry]

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.

[Arkcon]

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.

[starry]

Okay, well.. got that part. XD

What are the next steps I need to take?

[ARGOS++]

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⁺⁺