Question

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)

Answer 1

t = 2212 years

Step-by-step explanation:

In radioactive decay processes it is described by the equation

N = N₀
`e^(-\lambda t)`

to calculate the activity

`T_(1/2)` = 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