nuclear

posted by Pete

Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760 a.

1. DrBob222

Solve for k using k = 0.693/t1/2, then substitute k into the following:
ln(No/N) = kt
Use No = 8
N = 1
k from above.
t = unknown.

2. Pete

Is that
0.693/
t 1/2

0.693 over t one half ?

3. DrBob222

yes. k = 0.693/5760 = ? yr^-1

4. Pete

In the start of the equation .. for
In(No/N) I understand the No/N is the percentage that the sample is of carbon 14 compared to a living sample, but how do you get the In ? where does it come from ?

5. DrBob222

This is the integrated equation for a first order rate reaction. All of them are
ln(No/N) = kt
I can probably find a place on the web that derives the equation if you really want it. There isn't much to understand about it at this point except how to use it. The problem tells you that the radioactivity is 1/8 of the original; that's the 8/1. No is what you start with and N is what is there currently.

6. DrBob222

http://en.wikipedia.org/wiki/Rate_equation#First-order_reactions

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