Question

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?

Answer 1

The answer should be 450,000 years. The answer below (or above) had it right, just needs to check arithmetic.

Answer 2

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