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? Make sure to share the math of how you came up with your answer…

450,000 years

Explanation:

The equation that describes the decay of a radioactive isotope is:

where

is the mass of the isotope at time t = 0

is the mass of the isotope at time t

is the half-life of the isotope, which is the time it takes for the isotope to halve its mass

In this problem:

is the half-life of the radioisotope

m(t) = 125 g is the mass of radioisotope left after time t

is the initial mass of the radioisotope (the sum of the mass of the final radioisotope + the mass of the daughter nuclei, since mass is conserved)

So, we can re-arrange the equation to find t:

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explanation: