Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Question

Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Answer 1

Well A = C (0.5)^t/H

C = mass of carbon-14 when person died

A = mass now

H = half life years

t = age of skull

0.02 C = C (0.5) ^t/5600

0.02 = 0.5^t/5600

ln (0.02) = [t/ 5600] ln (0.5)

t = 5600 ln (0.02) / ln (0.5)