# Half life and radioactive dating

The only problem is that we only know the number of daughter atoms now present, and some of those may have been present prior to the start of our clock. The reason for this is that Rb has become distributed unequally through the Earth over time.

We can see how do deal with this if we take a particular case. For example the amount of Rb in mantle rocks is generally low, i.e. The mantle thus has a low If these two independent dates are the same, we say they are concordant.

For example, if there were \(100 \: \text\) of \(\ce\)-251 in a sample at some time, after 800 years, there would be \(50 \: \text\) of \(\ce\)-251 remaining and after another 800 years (1600 years total), there would only be \(25 \: \text\) remaining.

The only difference is the length of time it takes for half of a sample to decay.An event like metamorphism could heat the crystal to the point where Pb will become mobile.Another possible scenario involves U leakage, again possibly as a result of a metamorphic event.We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates.The Concordia curve can be calculated by defining the following: ).

To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.