half-life is the length of time required for half of any
given amount of an element to decay into another element. For example,
if one begins with a gram of carbon-10, 20 seconds later only half
a gram will remain, after 40 seconds only a quarter gram will be
left, after 60 seconds an eighth of a gram, after 80 seconds one
sixteenth of a gram, and after 100 seconds have elapsed from the
beginning of the experiment, only one thirty-second of the original
carbon-10 will remain (left). Because it decays so fast carbon-10
is not found in nature, although it can be observed as the product
of some nuclear reactions.
The half-lives of the five unstable isotopes of carbon differ greatly.
Whereas half of any starting quantity of carbon-16 decays to nitrogen-16
in three quarters of a second, the same reaction for carbon-14 decaying
to nitrogen-14 takes nearly six thousand years. Even so, carbon-14
is not a stable isotope, and will disappear in time. This slow decay
of carbon-14 is the basis of a widely used dating method for archaeological
materials. As long as any organism is alive, its carbon atoms are
being exchanged continuously with the atmosphere. Plants and animals
into the atmosphere during respiration. Plants use atmospheric
during photosynthesis to make carbohydrates, and animals obtain
these carbon atoms by eating the plants. A constant ratio of carbon-14
to stable carbon-12 is maintained in the atmosphere because of the
continuous production of new carbon-14 by reactions with high -
energy neutrons in the upper atmosphere.