Half-Life
Half-life, in general terms, is the time required for half of something to undergo a process. The term has several uses but in all of those uses it means essentially the same thing. In dealing with radioactive isotopes, the term refers to the time required for half of the atoms of a radioactive substance to disintegrate. It can also be used in conjunction with ecological systems such as drug or radioactive tracer dissipation in the human body. In these circumstances it is the time required for half of the drug or tracer to be removed from the body. Half-life is also commonly used in the study of chemical kinetics. Here it is defined to be the time required for the reactant concentration to decay to one-half its initial value.
The half-life of radioactive isotopes is as varied as the number of isotopes known. Astatine, the heaviest known halogen and a radioactive element, has a half-life of 7.21 hours. It is often used as a radioactive tracer because it collects in the thyroid gland. Americium, a radioactive element discovered by Glenn T. Seaborg (1912-1999) in 1944 during bombardment of plutonium, is part of the actinide series.
Many isotopes of this element have half-lives that range from 1.3 hours to over 7,000 years and are used in smoke detectors. It is clear from the use of this element that although some elements are radioactive they can still be effectively used in everyday functions for relatively long periods. The most stable isotope of actinium, a radioactive element discovered in 1899 by André Debierne in uranium residues from pitchblende and the first member of the actinide series, has a half-life of 21.6 years. So it is evident that there is a wide range of half-lives associated with radioactive decay. It should also be noted that the half-life of the shortest living elementary particles can be about the time for light to travel one nuclear diameter (these particles are better called resonances).
Half-life is also used in conjunction with chemical kinetics. In this situation the term usually refers to the time it takes for half of a substance to undergo a chemical reaction and be converted into aproduct, that is the time required for the reactant concentration to decay to one-half its initial value. In the mathematical analysis of such reactions the half-life is an important factor. If the reaction is first order, meaning simply that a reactant A goes to product B, the half-life is constant and depends only on the rate constant, k, that describes the reaction. So for a first order reaction, t1/2 = ln2/k = 0.693/k, where k is the rate constant for the reaction. This illustrates that the half-life of the reaction is independent of concentration for a first-order reaction. For a zero order reaction the half-life is found to be equal to the initial concentration of reactant divided by two times the rate constant for that reaction. For a second order reaction, one in which two molecules collide and form a product, the half-life is known to be equal to one divided by the initial concentration of reactant molecules times the rate constant for the reaction. It can be seen from this that the half-life of a chemical reaction depends upon the type of reaction being described.
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