Half-life Guide, Meaning , Facts, Information and Description
- This article describes the scientific meaning. For the computer game, see Half-Life.
For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value.
For a quantity x subject to exponential decay, the value of x at a time t is given by the formula:
In particular, there is a time such that:
In physics, the half-life of a radioactive isotope is the time it takes for half of the atoms in a pure sample of the isotope to decay into another element. It is a measure of an atom's stability: the shorter the half-life, the less stable the atom.
The decay of an atom is said to be spontaneous as one can only determine the probability of decay and not predict when an individual atom will decay. All the atoms of a particular isotope have the same probability of disintegrating in a given time. Therefore, a sample of radioactive material containing many millions of atoms will, on average, always disintegrate at the same rate. This rate at which the material changes is expressed in terms of the half-life, the time required for one half the atoms initially present to disintegrate, which is constant for any particular isotope.
The half-life is shorter than the average lifetime. The half-life is ln 2 ≈ 0.693 times the average life. If this seems strange, note that the life of half of the particles is only somewhere between 0 and the half-life, while the life of the other half can be anywhere between the half-life and infinite.
Half-lives of radioactive materials range from fractions of a second for the most unstable to billions of years for those which are only slightly unstable. Decay is said to occur in the parent nucleus and produce a daughter nucleus. Decay from a parent to a daughter nucleus may produce alpha, beta particles, and neutrinos. Gamma radiation may be produced as the nucleus is de-excited but this is only after the alpha or beta decay has taken place. Radioactive decay results in a mass loss, which is converted to energy (the disintegration energy) according to the formula E = mc2. Often, the daughter nucleus is also radioactive, and so on down the line for several successive generations of nuclei until a stable one is finally reached. The three such naturally occurring series are shown in the following table:
Mathematical basis for half-life
where is the initial value of x (at t=0), and is a positive constant (the decay constant). When t=0, the exponential is equal to 1, and x(t) is equal to . As t approaches infinity, the exponential approaches zero. Applications
Physics
| Series | Starting Isotope | Half-life (years) | Stable end-product |
|---|---|---|---|
| Radium | U-238 | 4.47×109 | Pb-206 |
| Actinium | U-235 | 7.04×108 | Pb-207 |
| Thorium | Th-232 | 1.41×1010 | Pb-208 |
Note: there are naturally occurring radioactive isotopes (such as C-14) but they are not part of a series.
Chemistry
The concept of half-life is not restricted to the decay of radioactive nuclei. The law is also useful in many processes where the rate of change of some property of a system depends itself on this property. In some chemical reactions, the rate of reaction depends on the concentration of a particular reactant. During the course of the reaction this concentration decreases, causing the rate of reaction also to go down. It is found that the time taken for the rate of reaction to halve is constant, if the reactant is said to be first order with respect to the rate. Enzyme-catalyzed reactions fall into this category.
Accordingly, half-life is a common term in pharmacology, used to refer to the time it takes the body to metabolize or remove half the amount of an administered substance.
Half-life is also important in calculating populations, although it is only applicable where the resources available to the population remain surplus to the needs. In these situations the population and its demands increase rapidly, so in reality the resources are always a limiting factor.
The half-life of a radioactive substance denotes the length of time it takes that substance to emit half its potential radioactivity. The shelf-life of a manufacture denotes its expected timespan of marketability.
Thus a cultural half-life of six months means that in six months those open toed stilletto heels are only going to be half as fashionable as they were when you bought them. Cultural half-life can be vividly graphed by the theater attendance of extremely trendy movies.
This is an Article on Half-life. Page Contains Information, Facts Details or Explanation Guide About Half-life Pharmacology and medicine
Population calculation
Lexical half-life: glottochronology
In linguistics, the technique of glottochronology is used to estimate the time of divergence of two related languages. It is analogous to the use of carbon-14 dating of organic materials, in that a "lexical half-life" is estimated and used to extrapolate the time elapsed since two languages being compared originally diverged.Cultural half-life
The recognizable phenomenon that may be called cultural half-life assesses any recently-originated fashion or other cultural meme combining the term from physics with concepts from marketing. References
See also