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

Answer:

$t = 500000\,years$

Explanation:

The time constant of the radioactive isotope is:

$\tau = \frac{150000\,years}{\ln 2}$

$\tau = 216404.256\,years$

The isotope decay is predicted by the following model:

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

$\frac{125\,g}{125\,g + 875\,g} = e^{-\frac{t}{216404.256\,years} }$

$0.125 = e^{-\frac{t}{216404.256} }$

The age of the rock is determined after algebraic handling:

$\ln 0.125 = -\frac{t}{216404.256}$

$t = 500000\,years$