Nuclear Disintegrations and Reaction Kinetics

2 Applications of Exponentials and Logarithms Nuclear Disintegrations and Reaction Kinetics 

Exponentials play a useful role in understanding nuclear disintegrations and half-lives. For example, 14C, a radioactive isotope of carbon used for carbon dating, has a half-life / /2 = 5730 years before it converts into stable 147V. This means that the number 

N of carbon-14 atoms in a sample will satisfy the following relationships  

Half of the sample will be left after t /2 = 5730 years half of what is left will decay in another 5730 years (in other words, one-quarter will be left after 21 /2 = 11460 years), and so forth. More generally, 

Written in this form, k is called the rate constant. Rate constants also appear in chemical kinetics. For instance, in Chapter 4 we will show that the rate of a unimolecu-lar reaction (such as an internal rearrangement of some atoms within a single molecule) changes with temperature according to the equation 

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