Carbon from the remains of an extinct Australian marsupial, called Diprotodon, has a specific activity of 0.61 pCi/g. Modern carbon has a specific activity of 6.89 pCi/g. How long ago did the Diprotodon apparently become extinct?

This question is in reference to the use of carbon 14 dating. We know the specific activity of a Australian marsupial. Based on the carbon 14 present. It's .61 PICO curie program. Modern carbon has a specific activity of 6.89 PICO curie program. So all we need to do then is use the first order integrated rate law to solve for the time that has elapsed with Both of these activities as part of the equation.

But before we can do that we need the decay constant for carbon 14, which we can get by dividing the half life Of carbon 14 into natural log of two. And we get 1.21 times 10 to give 14, 1 over years. So using the first order integrated rate law, the natural log of the activity at time, T divided by the activity Um at time zero represented by present day Will be equal to negative K. multiplied by T.

Little Algebraic rearrangement gives us an age of 20,000 years.

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