Question

How can radioactive half-life be used to date fossils?

Answer 1

`A=A_0e^(-lambdat)`, where:
`A` = current activity (`s^-1`)
`A_0` = original activity (`s^-1`)
`lambda` = decay constant `(ln(2)/t_(1/2))` (`s^-1`)
`t` = time (`s`, though sometimes uses different units like `year^-1` when `lambda` is given in terms of years)

`A/A_0=e^(-lambdat)`

`ln(A/A_0)=-lambdat`

`t=-ln(A/A_0)/lambda`

`t=-(t_(1/2)ln(A/A_0))/ln(2)`

`t` `(text(years))=-(5730ln(A/A_0))/ln(2)`

If we know the current activity of the decay of `""^14"C"` and use living material for a rough estimate for the original activity of `""^14"C"`, then we can put them into this equation to find its age in years.