Nd ratios on several minerals with a mass spectrometer and then from the slope determine the age of the rock. If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped.
The initial ratio has particular importance for studying the chemical evolution of the Earth's mantle and crust, as we discussed in the section on igneous rocks. If this happens, then the date obtained will be older than the date at which the magma erupted.
Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left.
After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.
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: ).
The best estimate from this dating technique says the man lived between 33 BC. From the ratio, the time since the formation of the rock can be calculated.
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.
The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e.
The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.