A piece of wood from the ruins of an ancient building was found to have a C14 activity of 12 disintegrations per minute per gram of its carbon content. The 14C activity of the living wood is 16 disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given the half-life of C14 is 5760 years.
Rate of disintegration in old wood sample of C-14 radioactive atms is 12 atoms per min gm. Initially rate of distintegration of C−14 when the tree was live =16 atoms per min per gm. T1/2 of C-14 nuclei =5760 years According to radioactive decay law =N0e−λtorR=R0e−λt 12=16e−λt⇒eλt=1216 logeeλt=loge34 λt=loge34 t=λ2.303×log1034(∵λ=T1/20.6931) =0.69312.303×(log4−log3)×5760year ∴t=0.69312.303(0.6060−0.4771)5760=2391.20years
