Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.

The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.

Furthermore, Parentium and Daughterium are so different in chemical properties that they don't otherwise occur together.

If there were such a pair of isotopes, radiometric dating would be very simple.

It is one of the simplest examples of a differential equation.his document discusses the way radiometric dating and stratigraphic principles are used to establish the conventional geological time scale.It is not about the theory behind radiometric dating methods, it is about their , and it therefore assumes the reader has some familiarity with the technique already (refer to "Other Sources" for more information).In fact, radiometric dating can be used to determine the age of the Earth, (5.54 billion years old) other planets, and celestial objects.Radiometric dating is often referred to as “radioactive dating” and “carbon dating,” though many different types of isotopes can be used to identify an object’s age.While not all objects have the same isotopes, both living and nonliving objects have some sort of decaying, radioactive isotope that can be used based on known decay rates. An isotope of some sort is located and isolated within an object.That isotope is then compared to its decaying product and scientists are able to use known decay rates to determine how old the initial isotope is.Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.This is the only way Parentium-123 decays, and there is no other source of Daughterium-123.Because this new element (decay product) remains on or within the object, scientists can easily determine how old the object is. A mass spectrometer is a fundamental device in any radiometric dating experiment.Mass spectrometers can be used to measure isotopic samples as small as one 1 nanogram.

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