# Carbon dating and half life calculations

Carbon 14 occurs naturally, and is absorbed by all living things when we eat and drink.

When we die, we no longer ingest C14, and it begins to decay and turn into N14.

The half-lives of several isotopes are listed in In our earlier discussion, we used the half-life of a first-order reaction to calculate how long the reaction had been occurring.

Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.

Using Activity is usually measured in disintegrations per second (dps) or disintegrations per minute (dpm).

The techniques that have been developed for this application are known as radioisotope dating techniques.

The most common method for measuring the age of ancient objects is carbon-14 dating.

The activity of a sample is directly proportional to the number of atoms of the radioactive isotope in the sample: $A = k N \label$ Here, the symbol is the same as the equation for the reaction rate of a first-order reaction, except that it uses numbers of atoms instead of concentrations.

In fact, radioactive decay is a first-order process and can be described in terms of either the differential rate law () or the integrated rate law: $N = N_0e^$ $\ln \dfrac=-kt \label$ Because radioactive decay is a first-order process, the time required for half of the nuclei in any sample of a radioactive isotope to decay is a constant, called the half-life of the isotope.