Question

Show all work: A rock contains 125g of a radioactive isotope with a half-life of 150,000 years and 875g of its daughter material. How old is the rock according to radioactive dating ?

Answer 1

`t = 500000\,years`

Step-by-step explanation:

The time constant of the radioactive isotope is:

`\tau = (150000\,years)/(\ln 2)`

`\tau = 216404.256\,years`

The isotope decay is predicted by the following model:

`(m)/(m_(o)) = e^{-(t)/(\tau) }`

`(125\,g)/(125\,g + 875\,g) = e^{-(t)/(216404.256\,years) }`

`0.125 = e^{-(t)/(216404.256) }`

The age of the rock is determined after algebraic handling:

`\ln 0.125 = -(t)/(216404.256)`

`t = 500000\,years`