15. The Rates of Chemical Reactions   Previous PageNext Page
       Exponential First Order Decay

After another equal time interval the concentration will be at an eighth its starting value, then a sixteenth, and so on. The time required for any beginning quantity of material to decay by a first-order process to half its starting is known as the "half-life" for the decay.

The faster the decay the shorter the half-life. For carbon-14 the half-life is 5570 years, which means that if an experiment is begun with one gram of pure carbon-14, only a half gram will be left after 5570 years.

In 11,140 years only a quarter gram will remain, and after 16,710 years, one eighth gram will remain. Unstable nuclei vary widely in their decay rates or half-lives: uranium-238 has a half-life of 4,510,000,000 years, whereas the elusive polonium-213 nucleus has a half-life of only 4.2 millionths of a second.

Since the half-life, t is the time required for the ratio [C-14]/[C-14]o to decrease to 0.5 , the half-life and the decay rate constant, k, are related by the expression

  0.5 = e-kt
  ln2 = +kt1/2


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