Question

after an animal dies it 14^C content decrease with a half-life of 5730 years. if archaeologist finds an acient firepit containing partially consumed firewood and the 14^C content of the 31.9% that of an equal carbon sample of a present day tree. what is the age of the acient site

Answer 1

The time required to decay half of the atom is Halfe Life period. In this case we are finding about C¹⁴.

So, as per the given data after 5730 years 50% of it remains. The years passed after that. Consider another 5730 years over, so 50% of that remains which is 25% of the original. After another 5730 years, 50% of it remains, which is now 12.5% of the original amount -- which we presume to be the same as the present-day tree.

By this argument is clear that the archaeologists have found a tree which is 3x5730 = 17190 years old.

So here 31.9% of the original is there. 31.9%=0.319

=>R=R₀e^-t

R/R₀=0.319

t=-ln(R/R₀)

or t=-1/(ln(R/R₀))

t=T_1/2(ln(R/R₀)/ln2)

t=-5730 * ln(0.319) / ln(2)= 9445.16 years

So the age is 9445.16 years