By measuring the amounts of parent isotope and daughter product in the minerals contained in a rock, and by knowing the half-life of the parent isotope, a geologist can calculate the absolute age of the rock. A rock contains 125 g of a radioisotope with a half-life of 150,000 years and 875 g of its daughter product. How old is the rock according to the radiometric dating method?

The total mass of the substance remains the same so the original amount can be calculated by adding the current amount and the amount of daughter isotope produced.

Original amount: 125 + 875 = 1000 g

Relationship between half life and decay constant (λ):

T (half) = ln (2) / λ

λ = ln (2) / 150,000

For radioactive decay:

N = N (0) exp (-λt)

[ln (N/N (0)) ] / - λ = t

t = [ln (125/1000) ] / - [ln (2) / 150,000]

t = 45,000 years