half-life

Dictionary: half-life (hăf'līf', häf'-)

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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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.

Food and Nutrition: 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.

Dental Dictionary: half-life

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

US Military Dictionary: 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.

Measures and Units: 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.

Britannica Concise Encyclopedia: 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.

Archaeology Dictionary: 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.

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Science Dictionary: 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.)

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.

Cosmic Lexicon: Half-life

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

Wikipedia: 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 reliable references. 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 is the period of time, for a substance undergoing decay, to decrease by half. The name originally was used to describe a characteristic of unstable atoms (radioactive decay), but 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" sometime in the early 1950s.^[1]

Half-lives are very often 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.

The converse of half-life is doubling time.

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

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 See also
5 References
6 External links

Probabilistic nature of half-life

A half-life often 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 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 central limit theorem 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. See the following websites: [1], [2], [3].

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 formulae:

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

$N_t = N_0 e^{-t/\tau} \,$

$N_t = N_0 e^{-\lambda t} \,$

where

$N 0$ is the initial quantity of the thing 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

$N t = N 0$ at t=0 (as expected—this is the definition of "initial quantity")
$N_t=\left(\frac {1}{2}\right)N_0$ at $t = t 1 / 2$ (as expected—this is the definition of half-life)
$N t$ approaches zero when 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 formulae, 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

Many quantities decay in a way not described by exponential decay—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In this case, the half-life is defined the same way as before: 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 changes 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 orginal amount (on average) 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 by waiting a second day, there is no reason to expect that precisely 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.)

A biological half-life is also a type of half-life associated with a non-exponential decay, namely the decay of the activity of a drug or other substance after it is introduced into the body.

The decay of a mixture of two or more materials that each have different half-lives is not a simple exponential, as each material decays at a rate independent of the other. 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 of slowly decaying element B, with a half-life of one year. After a few seconds, almost all atoms of element A have decayed after repeated halving of the initial total number of atoms but very few atoms of element B will have decayed yet as not even one half-life has elapsed. Thus, the mixture taken as a whole does not decay by halves.

References

^ John Ayto, "20th Century Words" (1989), Cambridge University Press.

External links

Radiation (Physics)

Main articles

Radiation health effects

Radiation therapy · Radiation poisoning · Skin depth · Radioactivity in biological research · List of civilian radiation accidents
Mobile phone radiation and health · Wireless electronic devices and health · Health physics

Radiation hardening · Half-life · Radiobiology · Nuclear physics

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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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