Question

Characol pieces of tree is found from an archeological site. The carbon-14 content of this characol is only 17.5% that of equivalent sample of carbon from a living tree. What is the age of tree?

Answer 1

activity R = 17.5%

T_1/2 = 5730 yr

The activity of the sample R = R₀ e^-λt

e^-λt = R₀/R

By taking the algorithm on bothsides, we get

t = `1/lambda ln ("R"/"R"_circ)`

`"T"_(1/2) = (ln2)/lambda`

t = `("T"_(1/2)/(ln 2) ln ("R"/"R"_circ)`

t = `5730/(ln2) ln (1/0.175) = 14,400` yr

t = `1.44 xx 10^4` yr