Radioactive Decay: Calculating Age of Archaeological Sample

[frankR]

Libby's observation that all the carbon in the world's living cycle is kept uniformly radioactive through the production of C-14 by cosmic radiation led to his development of the radioactive carbon dating method. Samples of carbon in the life cycle have been found to have a disintegration rate of 15.0 disintegrations per gram per minute. Upon death of the living organism, the life cycle ceases and the C-14 in the material decays with a half-life of 5730 years. If an archaeological sample was determined to have a disintegration rate of 0.03 disintegrations per gram per minute, how old is the sample?


This problem is killing me.

So far the real thing I've been able to find is how long the sample has been dead:

t = ln(2 &lambda N_o)/lambda

N_o = the initial number of radioactive nuclei

Can I get a hint?

 

[arcnets]

Well, you know that the total C-14 content decreases by a factor 1/2 during one half-life. This is of course also true for the disintegration rate. Now, you know that the disintegration rate has gone down from 15.0 to 0.03. How many half-lifes did that take?

 

[frankR]

Originally posted by arcnets
Well, you know that the total C-14 content decreases by a factor 1/2 during one half-life. This is of course also true for the disintegration rate. Now, you know that the disintegration rate has gone down from 15.0 to 0.03. How many half-lifes did that take?

That's an interesting way to look at the problem.

I'll see what I can do with that.

Thanks

 

[frankR]

I get:

t = 1.62 x 10¹²s

Is this correct?

Thanks

Edit:

Which is 51374 years.

I just looked up how old C-14 dating is good too. It said 50,000 years. So it looks like I'm right.

This problem was easy, I don't know why I struggled with it so much!

 

[arcnets]

Originally posted by frankR
Is this correct?

Yes.