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### Topic: Carbon 14 Dating Calculations  (Read 7540 times)

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##### Carbon 14 Dating Calculations
« on: December 16, 2006, 09:30:23 PM »
For the life of me I can't figure out how to find the age of a unknown sample with only the half-life, the initial rate of disintigration and the final rate of disintigration.  I've looked on various websites trying to lead me in the right direction but it just isn't healping.

Here's the problem:

Carbon-14 has a half-life of 5730 years.  If you find a sample giving off 0.96 disintigrations/min/g, what is the age of the sample?  (Origionally, the Carbon-14 gave off 15.3 disintigrations/min/g.)

Any help would be greatly appreciated.

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#### enahs

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##### Re: Carbon 14 Dating Calculations
« Reply #1 on: December 16, 2006, 11:21:57 PM »
First look at what you are analyzing, this is a first order reaction.
So you know
t1/2 = ln(2)/k

You are told the half-life, and ln(2) is just a number, so solve for k (rate constant for first order reaction).

I do not know if you have had calculus, or are taking a class that employees calculus.
But after a little math, you can turn your
R=k[A]
into
R=-d[A]/dt (this is in terms of time derivative, which a derivative is a rate of change)
Setting them equal,
d[A]/dt = -k[A]
Integrating both side with proper bounds of integration, and then some algebra you can get to this equation (which you might/should recognize):
ln[A] = ln[A]o-kT

Which with some algebra turns into
ln[A/Ao]=-kt

You know k, so you can easily solve for t.
Because of the derivation of the equation, it matters not if it is the concentration or the activity.

Note, A sub 0 ([A]o) is initial.

And none of these equations hold true for a second order reaction.