Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: C ratio of 0.795 times that found in plants living today. Solution The half-life of carbon-14 is known to be 5720 years. Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation: is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay.Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.The key is to measure an isotope that has had time to decay a measurable amount, but not so much as to only leave a trace remaining.Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.After study and discussion of this question, I now believe that the claimed accuracy of radiometric dating methods is a result of a great misunderstanding of the data, and that the various methods hardly ever agree with each other, and often do not agree with the assumed ages of the rocks in which they are found.Radiometric dating is a means of determining the "age" of a mineral specimen by determining the relative amounts present of certain radioactive elements. Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old.
If we knew the fraction of a radioactive element still remaining in a mineral, it would be a simple matter to calculate its age by the formula To determine the fraction still remaining, we must know both the amount now present and also the amount present when the mineral was formed.
We are told that these methods are accurate to a few percent, and that there are many different methods.
We are told that of all the radiometric dates that are measured, only a few percent are anomalous.
If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.
In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.