# Half-life

# Half-life

The half-life of a diminishing substance is the time it takes for the amount of substance present to go halfway from some initial value to zero. It is thus an indication of how fast the diminishment process proceeds or of the rate or rapidity of that process. The faster the process, the shorter the substance’s half-life is.

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. In this process, 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 radio-isotope has a half-life of one hour, for example, then at 3 PM there will be only half as many of the original species of radioisotope atoms remaining as there were at 2 PM; at 4 PM, there will be only half as many as there were at 3 PM, 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

# Half-life

# Half-life

As defined by geophysicists, the half-life (or half-value period) of a substance is the time required for one-half of the atoms in any size sample to radioactively decay.

Radioactive elements have different isotopes that decay at different rates. As a result, half-life varies with regard to the particular isotope under consideration. Some isotopes have very short half-lives, for example oxygen-14 has a half-life of only 71 seconds, some are even shorter—with values measured in millionths of a second not being uncommon. Other elements' isotopes can have a much longer half-life, thallium-232 has a half-life of 1.4 × 10 ^{10} years and carbon-14 has a half-life of 5,730 years. This latter figure is used as the basis of radiocarbon dating.

While living, an organism takes in an amount of carbon-14 at a relatively constant rate. Once the organism dies no more carbon-14 is taken in and the amount of carbon-14 present overall starts to decrease, decreasing by half every 5,730 years. By measuring the ratio of carbon-12 to carbon-14 an estimate of the date when carbon-14 stopped being assimilated can be calculated. This figure can also be obtained by comparing the levels of **radioactivity** of the test material to that of a piece of identical material that is fresh. Other radioactive elements can be used to date older, inorganic materials (e.g., rocks).

Strontium-90 has a half-life of 29 years. If starting with a 2.2 lb (1 kg) mass of strontium-90, then after 29 years there will only be 1.11 lb (0.5 kg) of strontium-90 remaining. After a further 29 years there will only be 0.55 lb (0.25 kg). Strontium-90 decays to give yttrium-90 and one free electron. Half-life is independent of the mass of material present.

The half-life (t_{1/2}) of a material can be calculated by dividing 0.693 by the decay constant (which is different for different radionucleotides). The decay constant can be calculated by dividing the number of observed disintegrations per unit time by the number of radioactive nuclei in the sample. The decay constant is usually given the symbol k or λ.

The half-life of a material is a measure of how reactive it is either in terms of radioactive decay or in participation in specific reactions.

** See also ** Atomic mass and weight; Atomic number; Atomic theory; Cosmic microwave background radiation; Dating methods; Geologic time

# Half-Life

# 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/t12. In this equation, P is the percentage of the original atoms that still remain after a period of time t, and t12 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

# Half-Life

# Half-life

A term primarily used to describe the physical half-life, how **radioactive decay** processes cause unstable atoms to be transformed into another element, but can also refer to the biological half-life of substances that are not radioactive.

Specifically, the physical half-life is the time required for half of a given initial quantity to disappear (or be converted into something else). This description is useful because radioactive decay proceeds in such a way that a fixed percentage of the atoms present are transmuted during a given period of time (a second, a minute, a day, a year). This means that many atoms are removed from the population when the total number present is high, but the number removed per unit of time decreases quickly as the total number falls.

For all practical purposes, the number of radioactive atoms in a population never reaches zero because decay affects only a fraction of the number present. Some infinitesimal number will still be present even after an infinite number of half-lives because with each time period half of what was present before decays and is lost from the sample. Therefore, determining the point at which half of the original number disappears (the half-life) is usually the most accurate way of describing this process.

*See also* Radioactivity

# Half-Life

# Half-life

Half-life is a measurement of the time it takes for one-half of a radioactive substance to decay (in this sense, decay does not mean to rot, but to diminish in quantity).

The atoms of radioactive substances, such as uranium and radium, spontaneously break down over time, transforming themselves into atoms of another element. In the process, they give off radiation, or energy emitted in the form of waves. An important feature of the radioactive decay process is that each substance decays at its own rate. The half-life of a particular substance, therefore, is constant and is not affected by any physical conditions (temperature, pressure, etc.) that occur around it.

Because of this stable process, scientists are able to estimate when a particular substance was formed by measuring the amount of original and transformed atoms in that substance. For example, the amount of carbon in a fossil sample can be measured to determine the age of that fossil. It is known that the radioactive substance carbon-14 has a half-life of 5,570 years. The half-lives of other radioactive substances can range from tiny fractions of a second to quadrillions of years.

[*See also* **Dating techniques; Geologic time; Isotope; Radioactivity** ]

# half-life

**half-life** Time taken for one-half of the nuclei in a given amount of radioactive isotope to decay (change into another element or isotope). Only the half-life is measured because the decay is never considered to be total. Half-lives remain constant under any temperature or pressure, but there is a great variety among different isotopes. Oxygen-20 has a half-life of 14 seconds and uranium-234 of 250,000 years. A radioactive isotope disintegrates by giving off alpha or beta particles, and measurement of this rate of emission is the normal way of recording decay. The term ‘half-life’ also refers to particles that spontaneously decay into new particles, such as a free neutron being transformed into an electron. See also dating, radioactive; radioactivity

# half-life

**half‐life** **1.** The time taken for half the protein or tissue in question to be replaced. Proteins are continuously degraded and replaced even in the mature adult, and the half‐life is used as a quantitative measure of this ‘dynamic equilibrium’. The values of half‐life of different proteins range from a few minutes or hours for enzymes which control the rate of metabolic pathways, to almost a year for structural proteins such as collagen. The average half‐life of human liver and serum proteins is 10 days, and of the total body protein, 80 days.**2.** Of radioactive isotopes, the time in which half the original material undergoes radioactive decay.

# half-life

half-life • n. the time taken for the radioactivity of a specified isotope to fall to half its original value. ∎ the time required for any specified property (e.g., the concentration of a substance in the body) to decrease by half.

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