# Carbon dating problem

• Jul 21st 2010, 02:41 AM
zcus05
Carbon dating problem
Charcoal collected from a cave at an archaeological site is characterized by an average of 0.97 disintergrations of radioactive carbon-14 per minute per gram. Living wood is characterized by an average of 6.68 disintergrations of carbon-14 per minute per gram. The half-life of carbon-14 is approximately 5700 years. Estimate the date of occupation of the cave.
• Jul 21st 2010, 08:43 PM
CaptainBlack
Quote:

Originally Posted by zcus05
Charcoal collected from a cave at an archaeological site is characterized by an average of 0.97 disintergrations of radioactive carbon-14 per minute per gram. Living wood is characterized by an average of 6.68 disintergrations of carbon-14 per minute per gram. The half-life of carbon-14 is approximately 5700 years. Estimate the date of occupation of the cave.

The number of disintegrations per min/gm is:

$\displaystyle r=(6.68)\times2^{-t/5700}\ \ \ ... (1)$

Where $\displaystyle $$t is measured in years since the wood lived. So if the rate is now \displaystyle$$ r$ you need to solve $\displaystyle $$(1) for \displaystyle$$ t$

CB
• Jul 24th 2010, 01:34 AM
zcus05
Thanks a bunch, I think I was trying to over-think it