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As we saw in Section 3.8, a radioactive substance decays exponentially: The mass at time $ t $ is $ m(t) = m(0)e^{kt} $, where $ m(0) $ is the initial mass and $ k $ is a negative constant. The mean life $ M $ of an atom in the substance is

$$ M = -k \int_0^\infty te^{kt}\ dt $$

For the radioactive carbon isotope, $ ^{14} C $, used in radiocarbon dating, the value of $ k $ is $ -0.000121 $. Find the mean life of a $ ^{14} C $ atom.

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Integration Techniques

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Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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