Carbon dating for archeological materials is based on the fact that a plant, after its death, stops absorbing radioactive C-14 as CO2 from the atmosphere. This radioactive carbon accounts for 0.10% of the total carbon content at death. After death, the C-14 decays at its characteristic rate. A piece of straw from a brick excavated from within an ancient ruin shows a C-14 content of 0.089%. Estimate the age of the ruin. (For C-14, T1/2 =5715 years)

 t = 2212 years

Explanation:

In radioactive decay processes it is described by the equation

         N = N₀

to calculate the activity

        = log 2 /λ

        λ = log 2 / T_{1/2}

        λ = log 2 /5715

        λ = 5.267 10⁻⁵

now the amount of carbon 14 is N₀ = 0.1%, the sample contains an amount of N = 0.089%

          N / N₀ = e^{-\lambda t}

          -λ t = ln N / N₀

           t = - 1 /λ  ln N /N₀

           t = 1 / 5.267 10⁻⁵   ln (0.089 / 0.1)

           t = 2,212 10³ years

           t = 2212 years