Carbon dating from activity of sample

[div4200]

Homework Statement

A certain artifact is found to have a carbon-14 activity of 0.12 Bq per gram of carbon. What is the age of the object?

Homework Equations

A = A(initial) * (1/2)^(t/h)

where

A = current amount
A(initial) = initial amount
t = time
h = half-life (aka half-time)

The Attempt at a Solution

The problem gives you the activity, 0.12 Bq. I was thinking that if I could look up the activity of a standard sample of carbon then I could compare it to this given value to find the ratio A/(A(initial)) of carbon-14 that had decayed. I could then use the above formula to find the time. However I can't seem to find the standard activity anywhere. Am I looking at this wrong? Thanks in advance!

 

[ideasrule]

You need to know how much C-14 there is in one gram of carbon. Wikipedia suggests 600 atoms per mole, but in reality this quantity changes over time, and scientists have to use calibration tables to determine a sample's actual age.

 

[epenguin]

You need to know how much C-14 there is in one gram of carbon. Wikipedia suggests 600 atoms per mole, but in reality this quantity changes over time, and scientists have to use calibration tables to determine a sample's actual age.

That is true but I presume the OP is only required for the moment to get an reasonably good approximate date.

The point is and the principle is: You can derive the age of a sample in the way indicated by the OP if you know the half-life of ¹⁴C, the ¹⁴C now, which he does, and at the time when it was fixed in the sample.

What was it when fixed? Assume it is what it is now. The ¹⁴C level in the atmosphere is appropriately constant. It is in a steady state between being created by cosmic rays etc. (in upper atmosphere and then mixed with world CO₂ within a year or two) and its radioactive decay.

Then as a refinement this atmospheric level has not been exactly constant. It has varied with varying cosmic ray intensity. But by extensive systematic studies of tree rings and other growth indicators the original levels over the last 20,000 years have been constructed. That is what ideasrule means by calibration. These variations can enable the age of a homogeneous sample to be fixed to within 5 years during periods when it was varying rapidly, 50 years in other periods. However only professional archaeologists are concerned with such refinements.