In an unweathered sample of igneous rock, the ratio of an unstable isotope to its stable daughter isotope is 1:15. If no daughters were present at the time the rock cooled below closure temperature, and the half-life of the isotope is 50 million years, how old is the rock?

200 million years

Explanation:

The equation that describes the decay of a radioactive isotope is

where

is the amount of radioactive isotope left at time t

is the initial amount of isotope

is the half-life of the sample

In this problem, the ratio between unstable isotope and daughter isotope is 1:15; this means that

Because the "total proportion" of original sample was 1+15=16.

Also we know that the half-life is

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

So, 200 million years.

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explanation: