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

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear 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}

. (i) Calculate the decay constant of

^{14}\text C

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

\pm5\%

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