# Carbon dating problem

• Jul 21st 2010, 03:41 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, 09:43 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:

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

Where $t$ is measured in years since the wood lived.

So if the rate is now $r$ you need to solve $(1)$ for $t$

CB
• Jul 24th 2010, 02:34 AM
zcus05
Thanks a bunch, I think I was trying to over-think it