Answer to Question #302009 in General Chemistry for watat

Question

A wooden object found in an Indian burial ground and subjected to radiocarbon dating. The decay rate associated with C- 14 is l0 disintegrations per minute per gram carbon. What is the age of the object?

Answer 1

The specific activity of the wood now is 10 dpm /g. Let us say the fresh bone would have 16 dpm/g at the time of cutting the wood.

Activity Final = Activity Initial e^-kt

k = the decay constant, ln2/half life, and t = decay time in the same time base as k.

k = ln2/5730 years, or = 0.000121/year.

Now, what you want is t, so you get to do some algebra.

A_f = A_i e^-kt

A_f/Ai = e^-kt

ln(A_f/A_i) = -kt

ln(A_f/A_i)/-k = t

SO! for the little example here, assuming that the initial activity was expected to be

16 dpm/gm:

ln(10/16) / -0.000121 = 3884 years