Calculating Age of Native American Campfire Using Radioactive Decay of CaCO3

[AryaUnderfoot]

Homework Statement

Archeologists removed some charcoal from a Native American
campfire, burned it in O2, and bubbled the CO2 formed into
Ca(OH)2 solution (limewater). The CaCO3 that precipitated was
filtered and dried. If 4.58 g of the CaCO3 had a radioactivity of
3.2 d/min, how long ago was the campfire?

Homework Equations

C + O2 --> CO2
CO2 + Ca(OH)2 --> CaCO3 + H2O

The Attempt at a Solution

Activity = kN
So k = Activity/N = (3.2 atoms/min)/(0.04576 mol * 6.022*10^23 atoms/mol)
= 1.2*10^-22 min^-1
half life = ln2/k
= 5.776*10^21 min

And that's all I know..I don't have the initial and final moles of the CaCO3, so how should I calculate the time that passed?

 

[Borek]

You can easily calculate total amount of carbon, and I bet your textbook (or lecture notes) states what is the typical fraction of C-14 in natural samples. If not, you will need to look for this information.

Note, that in reality this is not a single number, as the fraction of C-14 in the atmosphere is not constant. There are tables that can be used to find more precise data.