Question

You have a rock sample and analyze it for the presence of radioactive isotopes in order to determine when it was formed. You find an isotope that has a half-life of 100 million years. After you analyze it, you determine that it has equal amounts of radioactive parent isotope and stable daughter product.
A. How many half lives have gone by.
B. How old is it?

Answer 1

Answer:

the decay of half of the nuclei only a half-life has passed ,  b) in rock time it is 1 108 years

Explanation:

The radioactive decay is given by

         N = N₀ $e^{\lambda t}$

If half of the atoms have decayed

       ½ N₀ = N₀ $e^{\lambda t}$

       ½ = $e^{\lambda t}$ ₀

       Ln 0.5 = - λ t

       t = - ln 0.5 /λ

The definition of average life time is

      $T_{1/2}$= ln 2 / λ

       λ = ln 2 /  $T_{1/2}$

       λ = 0.693 / 100 10⁶

       λ = 0.693 10⁻⁸ years

We replace

       t = -ln 0.5 / 0.693 10⁻⁸

       t = 10⁸ years

We see that for the decay of half of the nuclei only a half-life has passed

b) in rock time it is 1 108 years