Question

How old is the dinosaur fossil footprint based on the following information?Consider the following scenario: I am a famous paleontologist and an expert in radioactive-dating techniques. I examine a dinosaur fossil footprint and discover that the fresh mud the dinosaur stepped in had just been covered with a thin layer of volcanic ash. I study the amount of potassium-40 and argon-40 in the ash. The ratio shows that 1/10 of one potassium-40 half-life has passed since the footprint was made. I know that the half-life of potassium-40 is 1.3 billion years. So,

Accepted Answer

Well, a half-life is the amount of time it takes for a radioactive substance to decay by half (mass decays into another, more stable substance in series).  So if 1/10 (or 0.1) of the half-life of 1.3 billion years has passed, that's 1.3 X 0.1 = .13 billion years, or 130 million years since the ash was deposited.

Answer

Since the ratio of potassium-40 and argon-40 in the ash covering the dinosaur foot print shows that 1/10th of one potassium-40 half life has passed since deposition of the ash. Since the ash was deposited on the footprint immediately after it was made, it is clear that the time elapsed since formation of the foot print is also 1/10th of one potassium-40 half life.
The half life of potassium is 1.3 billion years. that is, 1300 million years. Therefor the footprint is 1/10th of 1300 million years old. This comes to 130 million years.

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