Earth’s atomsphere is constantly being bombarded by cosmic rays of extremely high penetrating power. these rays, which originat in outer space, consist of electrons, neutrons, and atomic nuclei. One of the important reactions between the atmosphere and cosmic rays is the capture of neutrons by atmospheric nitrogen (nitrogen-14 isotope) to produce the radioactive carbon-14 isotope and hydrogen. The unstable carbon atoms eventually form 14CO2, which mixes with the ordinary carbon dioxide (12CO2) in the air. As carbon-14 isotope decays, it emits β particles (electrons). The rate of decay (as measured by the number of electrons emitted per second) obeys first-order kinetics. It is customary in the study of radioactive decay to write the rate law as:

rate = kN

where k is the first-order rate constant and N the number of 14 C nuclei present.

The carbon-14 isotopes enter the biosphere when carbon dioxide is taken up in plant photosynthesis. Plants are eaten by animals, which exhale carbon-14 in CO 2 . Eventually, carbon-14 participates in many aspects of the carbon cycle. The 14C lost by radioactive decay is constantly replenished by the production of new isotopes in the atmosphere. In this decay-

replenishment process, a dynamic equilibrium is

established whereby the ratio of 14 C to 12 C remains constant in living mater. But when an individual plant or an animal dies, the carbon-14 isotope in it is no longer replenished, so the ratio decreases as 14 C decays. This same change occurs when carbon atoms are trapped in coal, petroleum, or wood preserved undergound and of course, in Egyptian mummies. After a number of years, there are proportionately fewer 14 C nuclei in, say, a mummy than in a living person.

(i) Rock (geological dating) is based on the–