Half-life

The half-life (abbreviated half-life, symbols usually) is the time in which a halved with time exponentially decreasing value. In exponential growth we speak according to a doubling time or ( in biology ) generation time.

The remaining after a half-life amount of a substance is halved over the next half-life again, that is, it remains 1/4; after 3 half-lives of 1/8, then 1 /16, 1 /32, 1/64 and so on.

Radioactive half-life

The radioactive decay half-life is the time period in which the quantity, and thus the activity of a given radionuclide is decreased by decomposition to one-half. 50 % of the nuclei have been converted into a different nuclide by emitting ionizing radiation; this in turn may also be radioactive or not. For each nuclide, the half-life is a fixed size that can not be influenced ( very slightly only in exceptional cases ).

However, the halving applies only as a statistical average. You can find them all the more confirmed accurate the more non-decayed atoms containing the sample under consideration yet. The conversion of a single nucleus can not be predicted in time, but can only be given a chance of the conversion per unit time ( decay constant, see below). The probability that a considered one single core is converted within the first half-life is 50%, that he converts within two half-lives, 50 % 25 % = 75 %, at 3 half-lives of 50 % 25 % 12.5 % = 87.5 %, etc.

There are radioactive half-life over the entire range of less than 1 micro second to several years quadrillion. Polonium -212, for example, has 0.3 microseconds half-life, tellurium -128, however, about 7.1024 (7 quadrillion ) years.

Closely related to the half-life of a radionuclide is its specific activity, ie the activity per unit mass, expressed for example in becquerels per milligram, Bq / mg. The relationship between the specific activity and the half-life is inversely proportional to the shorter the half-life is the greater, for a given amount of substance, the type and vice versa.

The following table shows some examples. In the numerical values ​​here only the mass of the radionuclide itself is taken into account; In practice, more specific activity based on the particular natural isotopic mixture or the entire material of the sample.

In recent years, some nuclides previously considered stable have been " exposed " to be extremely long-lived radionuclides, such as 149Sm, 152Gd, 174Hf, 180W and 209Bi with half-lives of up to a few trillion years. Because of this very long half -lives of the corresponding low radioactivity is detectable only with great effort.

For some practical purposes, for example when considering the total radioactivity inventory of a laboratory or a nuclear plant, you can see a rule of thumb, the activity of a particular radiation source after 10 half-lives to be negligible, because it then has to be 2 to 10 times (= 1 / 1024), which is less removed than one thousandth of the initial value.

Measuring radioactive half-lives

To measure the half-life are due to the different orders of magnitude different methods necessary. In a central region, for half-lives of about from seconds to days, one can directly follow the decrease up to half the activity. Very long half-life is measured by counting of decays per unit time at a known mass of the substance; So you can not determine, but the decay constant ( see below). For a very short half-lives, there are techniques to determine, for example, the location of the decay, where the atom or molecule of known speed flies past a series of detectors, and other methods.

Data collections

The half-lives of all radionuclides can be found in the list of isotopes. Generally, they are given as well as other data in Nuklidkarten. A printed collection very much used is the Karlsruhe Nuclide Chart. As an online chart of nuclides, for example, a representation of the Korean Atomic Energy Research Institute available.

Biological half-life

The biological half-life or elimination half-life (see also plasma half-life) is the period in which an organism (human, animal, plant, single-celled organisms ), the content of the incorporated substance by the action of all the involved biological processes ( metabolism, excretion, etc.) to half has fallen.

In pharmacokinetics half-life is the time in which half of the absorbed drug metabolized and / or excreted. Pharmacokinetic half-lives may be very different. In adults, 0.5 hours are specified, for example, penicillin G, phenobarbital for 120 hours. Since different processes are involved with partially different concentration dependencies of volume loss, the elimination half-life of many materials depends on the initial concentration; for phenytoin it is, for example at low concentrations seven hours at elevated up to 40 hours.

Effective half-life

The effective half -life of a radionuclide means the period of time within which half the amount of incorporated ( recorded in an organism ) radionuclide disappears. Here two processes are involved, the radioactive decay and regardless of the re- excretion by the metabolism. Both run exponentially with mostly different half-lives. The resulting function may be described by a single exponential function, and therefore also through a half-life.

The effective half -life is always smaller than the smaller of the two individual half-lives. The physical and biological half-life is very different, the effective half-life approximately equal to the shorter. At the same long half-lives effective half-life is the half of each of the original half-lives.

Bibliometric half-lives

In bibliometrics can be identified different half-lives in the study of publications. Brooks examined as one of the first half lives in this area.

The half-life of literature is about 5 years. This applies to both the reading and the number of citations. This means that a work on average each year by about 14% less often borrowed from a library or is cited as in the previous (aside from classics and the latest works ).

The half-life of hyperlinks on the WWW is about 51 months. This means that after one year, approximately 15% of all the links are no longer valid.

Mathematical definition

Preliminary remark: The decay law is as " quantity " a continuous, representable as a real number size ahead. But it is also to integer values, such as the number of atoms in the radioactive substance sample applicable, because it describes the metrological each expected value, that is averaged over many (imaginary ) individual measurements.

Be the time after which the output quantity has fallen to the times (for the half-life ):

(small Greek letter lambda) is the decay constant, ie, the probability per unit time of a single atom for the conversion.

Dividing by and taking the logarithm yields:

It follows in accordance with the Logarithmengesetze:

Especially for the half-life () applies:

As a result for the decay law:

This formulation of the decay law illustrates best that has halved the amount initially present after half- time: