# What is half of frac 62 16

The **Half-life** (Abbreviation **HWZ**) is the time in which a value that decreases exponentially over time has halved. In the case of exponential growth, one speaks accordingly of one *Doubling time*.

Exponential behavior occurs when the change in a quantity over time is proportional to the quantity itself, as is the case with radioactive nuclides (quantity decrease) or in the case of many biological growth processes (quantity increase).

### To visualize

The amount of a substance remaining after one half-life is halved in the course of the next half-life, i.e. H. it remains ^{1}/_{2}·^{1}/_{2}=^{1}/_{4}; after 3 half-lives ^{1}/_{8}, then ^{1}/_{16}, ^{1}/_{32}, ^{1}/_{64} and so on. However, this is only valid as a statistical mean value, i.e. when the sample under consideration contains a large number of molecules or atoms. The conversion z. B. of an individual atomic nucleus cannot be predicted, only a probability for this transformation within a given time can be given (decay probability λ, see below). The probability that a considered nucleus transforms within the first half-life is 50%, that it transforms within 2 half-lives, 50% + 25% = 75%, with 3 half-lives the value is 50% + 25% + 12, 5% = 87.5%, etc.

### Law of decay

It was a radioactive preparation with *N*_{0}Cores and activity*A.*. Then applies to the number d*N* who in the time d*t* disintegrated cores:

After the time *t* are therefore from *N*_{0} Output cores still *N*(*t*) left.

Here is the rate of decrease by the **Decay constant***λ* (Lambda) determined. It is the reciprocal of the mean lifetime τ = 1 / λ, i.e. the time after which the number of atoms increases by the factor *e* has decreased. τ differs from the half-life *T*_{1/2} only by the constant factor ln (2): *T*_{1/2} = τ ln (2) ≈ 0.693 τ.

### Radioactive decay statistics

The radioactive decay rate, the activity, is the mean value of the number of decays per unit of time. The actual number of decays in a fixed unit of time follows the Poisson distribution, which can be approximated by a Gauss distribution if the average number is large.

### Mathematical definition of half-life

Be the time after which the initial quantity *N*_{0} on the 1 /*n*-fold has fallen (for the half-life applies *n*=2):

After that it is done on both sides *N*_{0} divided and logarithmized.

From this it follows, taking into account the logarithmic laws:

The following applies especially to the half-life (*n*=2):

This results for the law of decay:

- (Exponential laws)

This formulation of the law of decay best illustrates that after the half-life *T*_{1 / 2} halved the number of not yet disintegrated nuclei.

### Examples

### Radioactive half-life

The **Half-life** in nuclear physics is the period of time in which the amount of a certain radioactive nuclide has fallen by half, i.e. has been converted into other atoms. The half-life is a constant for every nuclide.

The number of remaining nuclei at a certain time is given by the law of decay (see above).

Half-lives of some radioactive nuclides:

element Formula symbol Half-life Tellurium ^{128}Teapprox. 7 10 ^{24}Years (7 quadrillion years)Bismuth ^{209}Biapprox. 1.9 · 10 ^{19}Years (19 trillion years)Thorium ^{232}Th14.05 billion years uranium ^{238}U4.468 billion years uranium ^{235}U704 million years plutonium ^{239}Pooh24,110 years carbon ^{14}C.5,730 years radium ^{226}Ra1,602 years plutonium ^{238}Pooh87.74 years Cesium ^{137}Cs30.2 years Tritium ^{3}H12.36 years Cobalt ^{60Co }5.3 years sulfur ^{35}S.87.5 days radon ^{222}Marg3.8 days Francium ^{223}Fr.22 minutes Thorium ^{223}Th0.6 seconds polonium ^{212}Po0.3 µs beryllium ^{8}Be9 · 10 ^{-17}s (90 quintillionths of a second)

From a purely mathematical point of view, the radioactive substance never disappears, physically, of course, a limit is set with the conversion of the last atom (the substance has completely disappeared). Often ten times the half-life is used as an estimate for the time until a radioactive radiation becomes insignificant, which corresponds to a decrease to the 2nd^{-10}times (= 1/1024).

With the practically important problem of the absorption of radioactive substances in the body, not only the half-life in the physical sense plays a role, but also the re-excretion of the substance through the biological metabolism. In some cases, this can also be done according to an exponential law, i.e. it can be described by a half-life. In these cases, the *physical* and the *biological half-life* can be distinguished (see below).

See also: Lifespan (physics)

### Radiocarbon method

*See also radiocarbon dating*

The radioactive carbon nuclide ^{14}C is contained in a fixed proportion in the carbon dioxide in our atmosphere. Due to the proportionate incorporation of the nuclide into the biomass of plants during photosynthesis and further via the food chain, there is also an approximately fixed ratio between stable in the body of all living things ^{12}C and radioactive ^{14}C. When a living being dies, it stops photosynthesis or ingesting food. As a result, the proportion of ^{14}From exactly this point in time, C decreases exponentially with a half-life of 5730 years, corresponding to the radioactive decay. On the basis of the ionizing residual radiation emanating from a dead living being, this radiocarbon method can be used to determine what percentage of the original ^{14}C proportion are still present and subsequently determine the time of death of the living being and thus the age of the find.

#### Application example

The beam of a historic building still has 90% of its original equilibrium portion ^{14}C in fresh plant matter. Then the following applies to the elapsed decay time:

This means that the tree from which the beam was made was felled about 871 years ago.

The dating is not accurate to the year. The possible accuracy depends on the amount of sample material available, the counting time used and the calibration for the corresponding period. Much smaller amounts of the sample material are sufficient for measurements using accelerator mass spectrometry. In addition, investigations have become more complicated in recent times, since the C-14 content has been increased for a short time by aboveground nuclear weapons tests. On the other hand, the C-12 content also increases due to the massive combustion of fossil fuels, which makes dating finds more difficult, especially near motorways.

For subtleties, see the main article: Radiocarbon Dating

### Biological half-life

The **biological half-life** also called the elimination half-life, specifically designates the period of time *t*_{1/2}, in which in a biological organism (human, animal, plant, single cell) the content of an incorporated radioactive, toxic or pharmaceutical substance has fallen by half due to the effect of all biological and physical processes involved (metabolism, excretion, radioactive decay, etc.) is.

In pharmacokinetics, the half-life is the time in which half of the ingested drug is metabolized and / or excreted. Since the biological half-life is made up of different processes, some of which have different concentration dependencies, it is not always independent of the initial concentration of the substance being investigated. Cf. Plasma half-life.

*See also:* Context-sensitive half-life

### Effective half-life

The effective half-life takes into account both the physical and biological half-life.

### Bibliometric half-lives

In bibliometrics, various half-lives can be determined when examining publications. *Brooks* studied as one of the earliest half-lives in the field.

The **Half-life of literature** is about 5 years. This applies to both the reading and the number of citations. That is, a work *average* is borrowed or cited from a library about 14% less often than in the previous year (apart from classics and the latest works).

The **Half-life of hyperlinks** is about 51 months. This means that after one year around 15% of all hyperlinks are no longer valid.

### Half-lives of cars (with regard to price)

The resale value of a car decreases almost exponentially with age, with a half-life of approx. 4–5 years. For example, the price of a new VW Beetle car today (2006) is around € 20,000, the 2002 model costs around € 10,000, that of 1998 around € 5,000 and that of 1995 around € 2,500.

### Related terms

Half value thickness, tenth value time, tenth value thickness

Category: radioactivity

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