half-life

(hăf'līf', häf'-)
n.

Physics. The time required for half the nuclei in a sample of a specific isotopic species to undergo radioactive decay.
Biology.
1. The time required for half the quantity of a drug or other substance deposited in a living organism to be metabolized or eliminated by normal biological processes. Also called biological half-life.
2. The time required for the radioactivity of material taken in by a living organism to be reduced to half its initial value by a combination of biological elimination processes and radioactive decay.

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half-life

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Interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or the time required for the number of disintegrations per second of a radioactive material to decrease by one-half. Half-lives are characteristic properties of the various unstable atomic nuclei and the particular way in which they decay. Alpha decay and beta decay are generally slower processes than gamma decay.

For more information on half-life, visit Britannica.com.

McGraw-Hill Science & Technology Encyclopedia:

Half-life

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The time required for one-half of a given material to undergo chemical reactions; also, the average time interval required for one-half of any quantity of identical radioactive atoms to undergo radioactive decay.

The concept of the time required for all of the material to react is meaningless, because the reaction goes very slowly when only a small amount of the reacting material is left and theoretically an infinite time would be required. The time for half completion of the reaction is a definite and useful way of describing the rate of a reaction.

The specific rate constant k provides another way of describing the rate of a chemical reaction. This is shown in a first-order reaction, Eq. (1),
1. $k=\frac{2.303}{t}\log\frac{c_0}{c}$
where c₀ is the initial concentration and c is the concentration at time t. The relation between specific rate constant and period of half-life, t_1/2, in a first-order reaction is given by Eq. (2).
2. $t_{1/2}=\frac{2.303}{k}\log\frac{1}{1/2}=\frac{0.693}{k}$
See also Chemical dynamics.

The activity of a source of any single radioactive substance decreases to one-half in 1 half-period, because the activity is always proportional to the number of radioactive atoms present. For example, the half-period of ⁶⁰Co (cobalt-60) is t_½, = 5.3 years. Then a ⁶⁰Co source whose initial activity was 100 curies will decrease to 50 curies in 5.3 years. In 1 additional half-period this activity will be further reduced by the factor ½. Thus, the fraction of the initial activity which remains is ½ after one half-period, ¼ after two half-periods, ⅛ after three half-periods, &frac116;, after four half-periods, and so on. The half-period is sometimes also called the half-value time or, with less justification, the half-life.

Oxford Dictionary of Units & Measures:

half-life

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time The period over which an amount or other value of decaying substance is reduced to half. The term is used most notably for the spontaneous disintegration and transformation of one radionuclide into another. It is used similarly for the transformation of elementary particles and, by parallelism, to the elimination of drugs from the body and similar circumstances. The significance of half-life depends on the rate of transformation or elimination being proportional to the amount present, i.e. on the graph of substance remaining being an exponential curve (called first-order decay in kinematics). Has also been called half-value period.

Barron's Accounting Dictionary:

half-life

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Estimated useful-life expectancy of a depreciable group of assets.
See also depreciation ; economic life ; useful life .

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Next:	Avoidable Cost, BIT, BUG

Oxford Food & Nutrition Dictionary:

half-life

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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.

Oxford Dictionary of the US Military:

half-life

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n.the time required for the activity of a given radioactive species to decrease to half of its initial value due to radioactive decay. The half-life is a characteristic property of each radioactive species and is independent of its amount or condition. The effective half-life of a given isotope is the time in which the quantity in the body will decrease to half as a result of both radioactive decay and biological elimination.

See the Introduction, Abbreviations and Pronunciation for further details.

Oxford Dictionary of Archaeology:

half-life

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[Ge]

The time taken for one half of a radioactive isotope to decay into a stable element. Different isotopes have different half-lives, ranging from a few seconds to many thousands of years. The most visible application in archaeology is in relation to radiocarbon dating and other radiometric dating techniques.

Columbia Encyclopedia:

half-life

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half-life, measure of the average lifetime of a radioactive substance (see radioactivity) or an unstable subatomic particle. One half-life is the time required for one half of any given quantity of the substance to decay. For example, the half-life of a particular radioactive isotope of thorium is 8 minutes. If 100 grams of the isotope are originally present, then only 50 grams will remain after 8 minutes, 25 grams after 16 minutes (2 half-lives), 12.5 grams after 24 minutes (3 half-lives), and so on. Of course the 87.5 grams that are no longer present as the original substance after 24 minutes have not disappeared but remain in the form of one or more other substances in the isotope's radioactive decay series. Individual decays are random and cannot be predicted, but this statistical measure of the great number of atoms in the sample is very accurate. The half-life of a radioactive isotope is a characteristic of that isotope and is not affected by any change in physical or chemical conditions.

Science Q&A:

What does half-life mean?

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Half-life is the time it takes for the number of radioactive nuclei originally present in a sample to decrease to one-half of their original number. Thus, if a sample has a half-life of one year, its radioactivity will be reduced to half its original amount at the end of a year and to one quarter at the end of two years. The half-life of a particular radionuclide is always the same, independent of temperature, chemical combination, or any other condition. Natural radiation was discovered in 1896 by the French physicist Antoine Henri Becquerel (1852-1908). His discovery initiated the science of nuclear physics.

Previous question:	Why is liquid water more dense than ice?
Next question:	Who made the first organic compound to be synthesized from inorganic ingredients?

Cosmic Lexicon:

Half-life

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The amount of time required for half of the mass of a radioactive isotope to decay.

Dictionary of Cultural Literacy: Science:

half-life

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In physics, a fixed time required for half the radioactive nuclei in a substance to decay. Half-lives of radioactive substances can range from fractions of a second to billions of years, and they are always the same for a given nucleus, regardless of temperature or other conditions. If an object contains a pound of a radioactive substance with a half-life of fifty years, at the end of that time there will be half a pound of the radioactive substance left undecayed in the object. After another fifty years, a quarter-pound will be left undecayed, and so on.

Scientists can estimate the age of an object, such as a rock, by carefully measuring the amounts of decayed and undecayed nuclei in the object. Comparing that to the half-life of the nuclei tells when they started to decay and, therefore, how old the object is. (See radioactive dating.)

Wiley Dictionary of Flavors:

Half-Life

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The time it takes for at least half of an isotope to lose neutrons and convert to a lesser atomic weight form. It is the half-life effect of carbon isotopes that enable the confirmation of natural sourcing. Ratios of degradation to non-degraded material assure the proper 'natural state.' See Carbon 12, Carbon 13, Carbon 14, Isotopic Analysis (Isotopic Ratio), Natural (Flavors).

Oxford Dictionary of Biochemistry:

half-life

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symbol: t_¹/₂ or T_¹/₂; the time for one half of the atoms of an amount of radionuclide to undergo radioactive decay.
a similar measure of the stability (i.e. rate of decay) of an excited atom or molecule, a radical, an unstable elementary particle, etc.
the time for one half of the amount of an administered substance to be metabolized or excreted. If the substance is radioactive, the time required for one half of the dose to be eliminated biochemically or physiologically is termed the biological half-life and that required for one half to disappear by radioactive decay as well as by the elimination is the effective half-life.
or (sometimes) half-time symbol: t_¹/₂; the time required for the concentration of a reactant in a chemical reaction to reach a value that is the arithmetic mean of its initial and final (equilibrium) values.
the time for one half of the number of cells in a tissue or organ to be replaced by new cells.

Previous:	half-ester, half-cystyl, half-cystine
Next:	half-of-the-sites reactivity, half-reaction, half-site reactivity

Saunders Veterinary Dictionary:

half-life

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The time in which the radioactivity usually associated with a particular isotope is reduced by half through radioactive decay.

Mosby's Dental Dictionary:

half-life

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The time in which a radioactive substance will lose half of its activity through disintegration.

Random House Word Menu:

categories related to 'half-life'

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Random House Word Menu by Stephen Glazier

For a list of words related to half-life, see:

Nuclear and Particle Physics - half-life: length of time during which one half of a sample of radioactive nuclides decays
PHARMACOLOGY - half-life: time required for body to reduce initial peak concentration of drug in blood by one half

Wikipedia on Answers.com:

Half-life

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This article is about the scientific and mathematical term. For other uses, see Half-life (disambiguation).

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2009)

Number of half-lives elapsed	Fraction remaining	Percentage remaining
0	¹/₁	100
1	¹/₂	50
2	¹/₄	25
3	¹/₈	12	.5
4	¹/₁₆	6	.25
5	¹/₃₂	3	.125
6	¹/₆₄	1	.563
7	¹/₁₂₈	0	.781
...	...	...
n	1/(2ⁿ)	100/(2ⁿ)

Half-life, abbreviated t_½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms (radioactive decay), but it may apply to any quantity which follows a set-rate decay.

The original term, dating to 1907, was "half-life period", which was later shortened to "half-life" in the early 1950s.^[1]

Half-lives are used to describe quantities undergoing exponential decay—for example, radioactive decay—where the half-life is constant over the whole life of the decay, and is a characteristic unit (a natural unit of scale) for the exponential decay equation. However, a half-life can also be defined for non-exponential decay processes, although in these cases the half-life varies throughout the decay process. For a general introduction and description of exponential decay, see the article exponential decay. For a general introduction and description of non-exponential decay, see the article rate law. Corresponding to sediments in environmental processes, if the half-life is greater than the residence time, then the radioactive nuclide will have enough time to significantly alter the concentration. The converse of half-life is doubling time.

The table on the right shows the reduction of a quantity in terms of the number of half-lives elapsed.

Contents

1 Probabilistic nature of half-life
2 Formulas for half-life in exponential decay
- 2.1 Decay by two or more processes
- 2.2 Examples
3 Half-life in non-exponential decay
4 Half-life in biology and pharmacology
5 See also
6 References
7 External links

Probabilistic nature of half-life

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is more regular and more predictable.

A half-life describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom with a half-life of 1 second, there will not be "half of an atom" left after 1 second. There will be either zero atoms left or one atom left, depending on whether or not the atom happens to decay.

Instead, the half-life is defined in terms of probability. It is the time when the expected value of the number of entities that have decayed is equal to half the original number. For example, one can start with a single radioactive atom, wait its half-life, and measure whether or not it decays in that period of time. Perhaps it will and perhaps it will not. But if this experiment is repeated again and again, it will be seen that - on average - it decays within the half-life 50% of the time.

In some experiments (such as the synthesis of a superheavy element), there is in fact only one radioactive atom produced at a time, with its lifetime individually measured. In this case, statistical analysis is required to infer the half-life. In other cases, a very large number of identical radioactive atoms decay in the time-range measured. In this case, the law of large numbers ensures that the number of atoms that actually decay is essentially equal to the number of atoms that are expected to decay. In other words, with a large enough number of decaying atoms, the probabilistic aspects of the process can be ignored.

There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a computer program.^[2]^[3]^[4] For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, due to random variation in the process. However, with more atoms (right boxes), the overall decay is smoother and less random than with fewer atoms (left boxes), in accordance with the law of large numbers.

Formulas for half-life in exponential decay

Main article: Exponential decay

An exponential decay process can be described by any of the following three equivalent formulas:

$N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}}$

$N(t) = N_0 e^{-t/\tau} \,$

$N(t) = N_0 e^{-\lambda t} \,$

where

$N 0$ is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
$N (t)$ is the quantity that still remains and has not yet decayed after a time t,
$t 1 / 2$ is the half-life of the decaying quantity,
$τ$ is a positive number called the mean lifetime of the decaying quantity,
λ is a positive number called the decay constant of the decaying quantity.

The three parameters $t 1 / 2$ , $τ$ , and λ are all directly related in the following way:

$t_{1/2} = \frac{\ln (2)}{\lambda} = \tau \ln(2)$

where ln(2) is the natural logarithm of 2 (approximately 0.693).

Click "show" to see a detailed derivation of the relationship between half-life, decay time, and decay constant.

Start with the three equations

$N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}}$

N (t) = N 0 e - t / τ

N (t) = N 0 e - λ t

We want to find a relationship between $t 1 / 2$ , $τ$ , and λ, such that these three equations describe exactly the same exponential decay process. Comparing the equations, we find the following condition:

$\left(\frac {1}{2}\right)^{t/t_{1/2}} = e^{-t/\tau} = e^{-\lambda t}$

Next, we'll take the natural logarithm of each of these quantities.

$\ln(\left(\frac {1}{2}\right)^{t/t_{1/2}}) = \ln(e^{-t/\tau}) = \ln(e^{-\lambda t})$

Using the properties of logarithms, this simplifies to the following:

$(t/t_{1/2})\ln \left(\frac {1}{2}\right) = (-t/\tau)\ln(e) = (-\lambda t)\ln(e)$

Since the natural logarithm of e is 1, we get:

$(t/t_{1/2})\ln \left(\frac {1}{2}\right) = -t/\tau = -\lambda t$

Canceling the factor of t and plugging in $\ln\left(\frac {1}{2}\right)=-\ln 2$ , the eventual result is:

$t_{1/2} = \tau \ln 2 = \frac{\ln 2}{\lambda}.$

By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:

$N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}} = N_0 2^{-t/t_{1/2}} = N_0 e^{-t\ln(2)/t_{1/2}}$

$t_{1/2} = t/\log_2(N_0/N(t)) = t/(\log_2(N_0)-\log_2(N(t))) = (\log_{2^t}(N_0/N(t)))^{-1} = t\ln(2)/\ln(N_0/N(t))$

Regardless of how it's written, we can plug into the formula to get

$N (0) = N 0$ as expected (this is the definition of "initial quantity")
$N(t_{1/2})=\left(\frac {1}{2}\right)N_0$ as expected (this is the definition of half-life)
$\lim_{t\to \infty} N(t) = 0$ , i.e. amount approaches zero as t approaches infinity as expected (the longer we wait, the less remains).

Decay by two or more processes

Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T_1/2 can be related to the half-lives t₁ and t₂ that the quantity would have if each of the decay processes acted in isolation:

$\frac{1}{T_{1/2}} = \frac{1}{t_1} + \frac{1}{t_2}$

For three or more processes, the analogous formula is:

$\frac{1}{T_{1/2}} = \frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + \cdots$

For a proof of these formulas, see Decay by two or more processes.

Examples

Main article: Exponential decay--Applications and examples

There is a half-life describing any exponential-decay process. For example:

The current flowing through an RC circuit or RL circuit decays with a half-life of $R C ln(2)$ or $ln(2) L / R$ , respectively.
In a first-order chemical reaction, the half-life of the reactant is $ln(2) / λ$ , where λ is the reaction rate constant.
In radioactive decay, the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, and is usually determined experimentally.

Half-life in non-exponential decay

Main article: Rate equation

The decay of many physical quantities is not exponential—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays.

As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5730 years. A quantity of carbon-14 will decay to half of its original amount after 5730 years, regardless of how big or small the original quantity was. After another 5730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But on the second day, there is no reason to expect that one-quarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the half-life reduces as time goes on. (In other non-exponential decays, it can increase instead.)

The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential. Mathematically, the sum of two exponential functions is not a single exponential function. A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives. Consider a sample containing a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of one year. After a few seconds, almost all atoms of the element A have decayed after repeated halving of the initial total number of atoms; but very few of the atoms of element B will have decayed yet as only a tiny fraction of a half-life has elapsed. Thus, the mixture taken as a whole does not decay by halves.

Half-life in biology and pharmacology

Main article: Biological half-life

A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose half of its pharmacologic, physiologic, or radiological activity. In a medical context, half-life may also describe the time it takes for the blood plasma concentration of a substance to halve ("plasma half-life") its steady-state. The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in tissues, active metabolites, and receptor interactions.^[5]

While a radioactive isotope decays perfectly according to first order kinetics where the rate constant is fixed, the elimination of a substance from a living organism follows more complex kinetics.

For example, the biological half-life of water in a human is about 7 to 14 days, though this can be altered by behavior. The biological half-life of caesium in humans is between one and four months. This can be shortened by feeding the person Prussian blue, which acts as a solid ion exchanger which absorbs the caesium while releasing potassium ions.

References

^ John Ayto, "20th Century Words" (1989), Cambridge University Press.
^ MADSCI.org
^ Exploratorium.edu
^ Astro.GLU.edu
^ Lin VW; Cardenas DD (2003). Spinal cord medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1888799617. http://books.google.co.uk/books?id=3anl3G4No_oC&pg=PA251&lpg=PA251.

External links

Look up half-life in Wiktionary, the free dictionary.

Nucleonica.net, Nuclear Science Portal
Nucleonica.net, wiki: Decay Engine
Bucknell.edu, System Dynamics - Time Constants
Subotex.com, Half-Life elimination of drugs in blood plasma - Simple Charting Tool

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Translations:

Half-life

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Dansk (Danish)
n. - halveringstid

Nederlands (Dutch)
halveringstijd (bij radioactiviteit)

Français (French)
n. - demi-vie

Deutsch (German)
n. - (Phys.) Halbwertszeit

Ελληνική (Greek)
n. - (φυσ.) ημιζωή, (μτφ.) αδράνεια, σκούριασμα

Italiano (Italian)
tempo in cui materiale radioattivo perde metà della sua radioattività, emivita

Português (Portuguese)
n. - meia-vida (f) (Fís.)

Русский (Russian)
период полураспада

Español (Spanish)
n. - media vida

Svenska (Swedish)
n. - halveringstid (fys.)

中文（简体）(Chinese (Simplified))
半衰期

中文（繁體）(Chinese (Traditional))
n. - 半衰期

한국어 (Korean)
n. - 반감기

日本語 (Japanese)
n. - 半減期

العربيه (Arabic)
‏(الاسم) العمر النصفي, الزمن الضروري لتفكيك نصف ذرات مادة ذات نشاط إشعاعي‏

עברית (Hebrew)
n. - ‮מחצית חיים (פיזיקה), הזמן שלוקח לרדיו-אקטיביות או לתכונה אחרת של חומר להיחלש ב-%05‬

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