How to find the age of charcoal?

Question

A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.00-kg sample of carbon from the wood has an activity equal to 5.00 x 10² decays per min ute. Find the age of the charcoal. Hint: Living material has an activity equal to 15.0 decays/min per gram of carbon present.

Answer 1

So Lily A.,

First of all, as a paleontologist you will never have the luxury of a 1 kg chuck of charcoal left by an ancient campfire. Fuel is precious!

So -- fresh 15 decays/minute/g --> 15000 decays/minute/1 kg

So you've decayed from 15000 dozen to 500 counts/minute. The half-life of C(14) ~ 5730 years. Set up your exponential decay equation and solve! C(t) =C(0)*e^-(t/5730)

--Cheers, -- Mr. d.