Question

Each time you dumped the pennies, one half-life passed; it has been shown that the half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery. It is shown that 95% of the nuclei have decayed. Approximately how long ago was the pottery made?

Answer 1

this is about the idea of exponential decay ---> \( N(t) = N_o e^{- kt}\) with k as the decay constant .... you can work it all from there if you're comfy with the manupulation



for a half life you have \(\dfrac{N}{N_o} =\dfrac{1}{2} = e^{- k~~t_{1/2}}\) or \(\ln \dfrac{1}{2} = - k ~ t_{1/2} \implies \ln 2 = k ~ t_{1/2}\) so you know that \(k = \dfrac{\ln 2 }{ t_{1/2}}\) with \(t = 20\)

pattern match for \(\dfrac{N(T)}{N_o} = \dfrac{5}{100} = e^{-kT}\) and solve for T