Question

The half life of carbon 14 is 5600 years. If charred logs from an old log cabin show only 69% of the carbon 14 expected in living matter, when did the cabin burn down? Assume that the cabin burned soon after it was built from freshly cut logs.

Answer 1

There is a logarithmatic relationship between the amount of activity left in the sample and the time since the element was created. Half is left after 5600 years, so log2 of half is -0.693. So after another half life you can plot another point on a graph: 11200 years, log2 of the radioactive element carbon 14 is -1.38 and so on. You should have a straight line onto which you can plot log2 of 0.69 and so get your answer. Post it and I can check you got the same. Best wishes,

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