# Half-Life

The half-life of a process is an indication of how fast that process proceeds—a measure of the **rate** or rapidity of the process. Specifically, the half-life is the length of **time** that it takes for a substance involved in that process to diminish to one-half of its initial amount. The faster the process, the less time it will take to use up one-half of the substance, so the shorter the half-life will be.

The rates of some biological processes, such as the elimination of drugs from the body, can be characterized by their half-lives, because it takes the same amount of time for half of the drug to disappear no matter how much there was to begin with. Processes of this kind are called first-order processes. On the other hand, the speeds of many **chemical reactions** depend on the amounts of the various substances that are present, so their rates cannot be expressed in terms of half-lives; more complicated mathematical descriptions are necessary.

Half-lives are most often heard of in connection with radioactive decay—a first-order process in which the number of **atoms** of a radioisotope (a radioactive **isotope**) is constantly diminishing because the atoms are transforming themselves into other kinds of atoms. (In this sense, the word "decay" does not mean to rot; it means to diminish in amount.) If a particular radioisotope has a half-life of one hour, for example, then at 3 P.M. there will be only half as many of the original species of radioisotope atoms remaining as there were at 2 P.M.; at 4 P.M., there will be only half as many as there were at 3 P.M., and so on. The amount of the radioactive material thus gets smaller and smaller, but it never disappears entirely. This is an example of what is known as exponential decay.

The half-life of a radioisotope is a characteristic of its nuclear instability, and it cannot be changed by ordinary chemical or physical means. Known radioisotopes have half-lives that range from tiny fractions of a second to quadrillions of years. Waste from the reprocessing of **nuclear reactor** fuel contains radioisotopes of many different half-lives, and can still be at a dangerously high level after hundreds of years.

The mathematical equation which describes how the number of atoms, and hence the amount of radioactivity, in a **sample** of a pure radioisotope decreases as time goes by, is called the **radioactive decay** law. It can be expressed in several forms, but the simplest is this: log P = 2 - 0.301 t/t_{12}. In this equation, P is the percentage of the original atoms that still remain after a period of time t, and t_{12} is the half-life of the radioisotope, expressed in the same units as t. In other words: To get the logarithm of the percentage remaining, divide t by the half-life, multiply the result by 0.301, and subtract that result from 2.

See also Radioactive waste.

Robert L. Wolke

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