I.  DEFINITIONS:

element: The smallest division of matter that still retains its chemical properties. The chemical properties are determined by the number of electrons in the neutral atom which in turn is determined by the number of protons in the nucleus of the atom.

isotope: An isotope of an element has the same number of protons but a different number of neutrons in its nucleus and therefore differs in atomic mass but has the same chemical properties.

radioactive atom: An unstable isotope that spontaneously changes into another form by emitting a particle from its nucleus. The other form will be an isotope of a new element with a different number of protons.

parent isotope: The term for the original radioactive atoms which decay at a known rate. In some cases the parent isotopes decay through a series of radioactive isotopes before reaching a stable isotope.

daughter (radiogenic) isotope: The term for the isotopes that result from the decay of the parent isotopes. For the purpose of radiometric dating of rocks, it is the final stable daughter isotope that is of interest.

half-life: The time required for half the original parent isotope to decay into its daughter isotope. For example: If the half-life of the parent isotope was 500 years and the original number of atoms was 1 billion, after 1 half-life (500 years) there would be 500 million (1/2 billion) atoms of the original parent isotope left. After another half-life (1000 years = 2 half-lives) there would be 1/2 of the 1/2 billion atoms left, or 1/4 billion (250 million) atoms. See figure.
 
 
 
 
 
 
 
 
 

II.  RADIOMETRIC DATING PROCEDURE FOR ROCKS:

Many minerals contain radioactive atoms which can be used to determine the age of the mineral and therefore the age of the rock containing the mineral. The age that is measured is the time since the rock began to retain the daughter isotope. This is usually the time since the rock solidified so that the daughter isotope atoms could be trapped in the solid mineral structure. Since sedimentary rocks are composed of previously formed igneous and metamorphic rocks and minerals, their formation ages cannot be determined by most of the radiometric dating techniques. Igneous rocks are the best candidates for these techniques and metamorphic rocks can be dated to their last episode of metamorphism.

In order to date the formation age of a rock, the original number of parent and daughter isotope atoms must be determined. It is also necessary to assume that there has been no addition or loss of either parent or daughter isotope since the minerals solidified. In most cases, it is actually the rate of decay (activity) that is measured rather than the total number of atoms. The activity is proportional to the total number of radioactive atoms in the sample. In some cases the original ratio of parent to daughter isotope can be measured by comparing different mineral grains in the same rock. In some cases the original number of parent isotope atoms can be determined by measuring the numbers of stable daughter isotope atoms which usually occur in certain proportions to the unstable parent isotope atoms in a given fresh material. (eg: A recently solidified lava rock with the same minerals.) Then by counting the present number of parent and daughter isotope atoms in the mineral, we can determine how many parent atoms have decayed into daughter atoms and hence determine the time since the rock solidified. For example, if it is determined that one half the original parent isotopes have decayed, then the rock is one half-life old. The formula for determining the age of a mineral given T_½ (half-life of the parent isotope), N (present number of parent isotopes), and N_o (original number of parent isotopes) follows:

Some of the parent isotopes most widely used to date rocks are: