Applications and ExamplesThe mean life of a radioactive

Chapter 7, Problem 39E

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Problem 39E

Applications and Examples

The mean life of a radioactive nucleus Physicists using the radioactivity equation  y = y0e -kt call the number 1 /k the mean life of a radioactive nucleus. The mean life of a radon nucleus is about 1/0.18 = 5.6 days. The mean life of a carbon-14 nucleus is more than 8000 years. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t = 3/k. Thus, the mean life of a nucleus gives a quick way to estimate how long the radioactivity of a sample will last.

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