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##### 1/5/2019

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Radiometric dating is a means of determining the "age" of a mineral specimen by determining the relative amounts present of certain radioactive elements. By "age" we mean the elapsed time from when the mineral specimen was formed. Radioactive elements "decay" that is, change into other elements by "half lives. The formula for the fraction remaining is one-half raised to the power given by the number of years divided by the half-life in other words raised to a power equal to the number of half-lives. To determine the fraction still remaining, we must know both the amount now present and also the amount present when the mineral was formed.

The Radiometric Decay Equation A constant-rate process such as radioactive decay is described by the simple equation: In order to use this equation for decay over a given time period, we will need the solution of a first-order differential equation. Obtaining such a solution is beyond the scope and requirements of this class, though with years of calculus, you to could do the impossible. The equation above is known as the decay equation. It shows that at any time t, the number of parent atoms, N, is equal to the number of original parent atoms at time zero N0 gives the number of parent atoms at time zero , multiplied by the natural exponent raised to the negative power of the decay constant l multiplied by the time t.

The J factor relates to the fluence of the neutron bombardment during the irradiation process; a denser flow of neutron particles will convert more atoms of 40K to 40Ar than a less dense one. However, in a metamorphic rock that has not exceeded its closure temperature the age likely dates the crystallization of the mineral. Thus, a granite containing all three minerals will record three different "ages" of emplacement as it cools down through these closure temperatures.

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