Physics

Problem

A piece of charcoal recovered from an ancient hearth has a measured

\beta

activity of

3.5\,\text{Bq g}^{-1}

. The activity of living wood is

6.0\,\text{Bq g}^{-1}

. The half-life of

^{14}\text C

5730\,\text{y}

. a. (i) Calculate the decay constant of

^{14}\text C

. b. (ii) Determine the age of the charcoal sample. c. (iii) The measured ratio of activities has a relative uncertainty of

\pm5\%

. Estimate the corresponding maximum possible uncertainty in the age obtained above.

Intuitive explanation

This is a radiocarbon dating problem where you use the decay of $^{14}\text{C}$ to find how long ago the charcoal stopped exchanging carbon with the atmosphere. The key insight is that activity decays exponentially with time—by comparing the current activity to the initial activity of living wood, you can solve for the age using the half-life relationship. Think of it as a "clock" where the fading radioactivity tells you elapsed time.

Intuitive explanation

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