Answer to Question #122849 in Atomic and Nuclear Physics for daniel

Question

The 14 C activity of some ancient Peruvian corn
was found to be 10 disintegrations per minute
per gram of C. If present-day plant life shows 15
dmp /g, how old is the Peruvian corn? The half
life of 14 C is 5730 years.

Answer 1

Initial number of nuclei is $N_0=15 dmp /g$

Final number of nuclei is $N=10 dmp/g$

The number of nuclei present after time t is

$N=N_0e^{-\frac{t ln2}{T_{1/2}}}$

$10=15e^{-\frac{t ln2}{5730}}$

$t=3352 years$

So the age is $t=3352 years$