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#### starry

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##### Half-life/integrated rate law problem?
« on: February 21, 2008, 11:11:40 AM »

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
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#### Arkcon

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##### Re: Half-life/integrated rate law problem?
« Reply #1 on: February 21, 2008, 11:34:19 AM »

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.
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#### azmanam

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• Mediocrity is a handrail -Charles Louis d'Secondat
##### Re: Half-life/integrated rate law problem?
« Reply #2 on: February 21, 2008, 11:40:00 AM »
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#### starry

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##### Re: Half-life/integrated rate law problem?
« Reply #3 on: February 21, 2008, 11:45:35 AM »

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.
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#### Arkcon

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##### Re: Half-life/integrated rate law problem?
« Reply #4 on: February 21, 2008, 12:07:01 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.
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#### starry

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##### Re: Half-life/integrated rate law problem?
« Reply #5 on: February 21, 2008, 01:16:18 PM »

Okay, well.. got that part. XD

What are the next steps I need to take?
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#### ARGOS++

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##### Re: Half-life/integrated rate law problem?
« Reply #6 on: February 21, 2008, 01:51:58 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++

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