Kinetics of Chemical and Radioactive Processes

The rate of change of concentration of some species A (e.g., d A /dt ) is a measure of the rate of chemical reaction. Most of the equations in chemical kinetics are differential equations meaning they involve at least one derivative. In addition, nuclear disintegrations (such as 14C— 14N+ - ) use the same rate equations as do many unimolecular decompositions (suchas CU — 2NO2). 

In the nuclear case, one electron is emitted for each 14C that disintegrates. The total number of emitted electrons per unit time is proportional to the number of 14C present at that time (N(t), as we defined it in Section 1.4). 

Note the minus sign. Each disintegration decreases the total number of carbons. One solution to this differential equation is apparent from Equation 2.8, which shows that the derivative of an exponential is proportional to itself. You can readily use Equation 2.8 to verify that 

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