Archaeologists can determine the age of artifacts made of wood or bone by measuring the amount of the radioactive isotope 14C present in the object. The amount of isotope decreases in a first-order process. Of 25.3% of the original amount of 14C is present in a wooden tool at the time of analysis, what is the age of the tool?

The answer is t = 11361 years

Explanation:

The amount left has the relationship with the original amount (nuclear reaction)

N = N0 e^-t/τ (τ is the time constant for the e^-1 life.

half-life = 5730 years for 14C

0.5 N = N0 e^-t/τ - --> τ = t1/2 / ln2 = 8266.64 years

Thus, for 25.3% of original amount of 14C, the time needed is:

t = τ ln (N0/N)

t = 8266.64 * ln (N0/0.253N0)

t = 11361 years