Activity and Dating

A radioactive sample is not measured by its number of nuclei (invisible), but by its activity A: the number of decays per second. It is expressed in becquerels (Bq), where 1 Bq = 1 decay per second. The activity is proportional to the number of remaining nuclei:

   A = λ · N        (so A decreases exactly like N: A(t) = A₀ · e^(−λt))

Since the activity follows the same exponential, it is also halved with each half-life. Measuring the activity therefore means indirectly measuring N — and the elapsed time.

This is the principle of carbon-14 dating. A living being exchanges carbon with its environment: the proportion of (radioactive) carbon-14 in it is constant. When it dies, the exchange stops, and carbon-14 decays with its half-life of 5,730 years, without being replenished.

   measured activity      estimated age
   -------------------    -------------------------
   A₀ (like the living)   recent death
   A₀/2                   ~ 5,730 years
   A₀/4                   ~ 11,460 years
   A₀/8                   ~ 17,190 years

By comparing the activity of a bone or a piece of wood with that of a living organism, we can work back to the date of death. The method reaches up to about 50,000 years (beyond that, too little carbon-14 remains). Other pairs (uranium-lead, potassium-argon) date rocks over billions of years. Radioactivity has thus become the clock of archaeology and geology — a clock that nothing can speed up or slow down.