half life

• 半減期

関

half-life、halflife、T1/2

WordNet

1. the period during which something is functional (as between birth and death); "the battery had a short life"; "he lived a long and happy life" (同)lifetime, life-time, lifespan
2. a characteristic state or mode of living; "social life"; "city life"; "real life"
3. the course of existence of an individual; the actions and events that occur in living; "he hoped for a new life in Australia"; "he wanted to live his own life without interference from others"
4. the organic phenomenon that distinguishes living organisms from nonliving ones; "there is no life on the moon"
5. the period between birth and the present time; "I have known him all his life"
6. the period from the present until death; "he appointed himself emperor for life"
7. living things collectively; "the oceans are teeming with life"
8. the experience of being alive; the course of human events and activities; "he could no longer cope with the complexities of life" (同)living
9. a living person; "his heroism saved a life"
10. a motive for living; "pottery was his life"
11. partially or to the extent of a half; "he was half hidden by the bushes"
12. one of two divisions into which some games or performances are divided: the two divisions are separated by an interval
13. (of siblings) related through one parent only; "a half brother"; "half sister"
14. consisting of one of two equivalent parts in value or quantity; "a half chicken"; "lasted a half hour"
15. partial; "gave me a half smile"; "he did only a half job"
16. Chinese distance measure; approximately 0.5 kilometers

PrepTutorEJDIC

1. 〈U〉(無生物と区別して,生物が持っている)『生命』,命 / 〈U〉《集合的に》『生物』,生き物 / 〈U〉(死後の)霊,霊的存在 / 〈C〉人間(person) / 〈U〉『一生』,生涯 / 〈C〉『寿命』,活動(有効,耐久)期間 / 〈U〉『人生』,現世,世間 / 〈C〉〈U〉『生活』,暮らし,生き方,暮らし方 / 〈C〉『伝記』(biography) / 〈U〉『生気』,活気,元気(vitality)
2. 〈C〉〈U〉『半分』,2分の1;約半分 / 〈U〉《時刻を表す数詞と共に用いて》『半』,30分 / 〈C〉《おもに英》(2学期制の学校での)前(後)期 / 〈C〉(競技などの)前(後)半;(野球で1イニングの)表(裏) / 〈C〉=halfback / 『半分の』 / 不十分な,中途はんぱな / 『半ば』,半分[だけ] / 半時間だけ,30分だけ / 不完全に / かなり,ほとんど
3. おや,はああ,ああ(驚き・喜び・疑い・ためらいなどを表す声)
4. hectare; hectares

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/10/15 19:00:22」(JST)

wiki en

[Wiki en表示]

This article is about radioactive decay of isotopes. For other uses, see Half-Life (disambiguation).

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_1⁄2) is the time required for a quantity to reduce to half its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the body. The converse of half-life is doubling time.

The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.

Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.

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 consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.

A half-life usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". For example, if there are 3 radioactive atoms with a half-life of one second, there will not be "1.5 atoms" left after one second.

Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%.

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, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.

There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.

Formulas for half-life in exponential decay

Main article: Exponential decay

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

${\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}$

where

• N₀ 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 ${\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{t/t_{1/2}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}$ We want to find relationships among t1⁄2, τ, and λ such that these three equations describe exactly the same exponential decay process. Comparing the equations, we find the following conditions, $\left({\frac {1}{2}}\right)^{t/t_{1/2}}=e^{-{\frac {t}{\tau }}}=e^{-\lambda t}.$ Next, we'll take the natural logarithm of each of these quantities. $\ln \left(\left({\frac {1}{2}}\right)^{t/t_{1/2}}\right)=\ln \left(e^{-{\frac {t}{\tau }}}\right)=\ln \left(e^{-\lambda t}\right)$ Using the properties of logarithms, this simplifies to the following: ${\frac {t}{t_{1/2}}}\ln \left({\frac {1}{2}}\right)=\left(-{\frac {t}{\tau }}\right)\ln(e)=(-\lambda t)\ln(e)$ Since the natural logarithm of e is 1, we get: ${\frac {t}{t_{1/2}}}\ln \left({\frac {1}{2}}\right)=-{\frac {t}{\tau }}=-\lambda t$ Canceling the factor of t and plugging in $\ln \left({\frac {1}{2}}\right)=-\ln(2)$, the final 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:

${\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}=N_{0}2^{-t/t_{1/2}}\\&=N_{0}e^{-t\ln(2)/t_{1/2}}\\t_{1/2}&={\frac {t}{\log _{2}(N_{0}/N(t))}}={\frac {t}{\log _{2}(N_{0})-\log _{2}(N(t))}}\\&={\frac {1}{\log _{2^{t}}(N_{0})-\log _{2^{t}}(N(t))}}={\frac {t\ln(2)}{\ln(N_{0})-\ln(N(t))}}\end{aligned}}$

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")
• $N\left(t_{1/2}\right)={\frac {1}{2}}N_{0}$ 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 Exponential decay § Decay by two or more processes.

Examples

Half life demonstrated using dice in a classroom experiment

Further information: 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 RCln(2) or ln(2)L/R, respectively. For this example, the term half time might be used instead of "half life", but they mean the same thing.
• 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. See List of nuclides.

The half life of a species is the time it takes for the concentration of the substance to fall to half of its initial value.

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 5,730 years. A quantity of carbon-14 will decay to half of its original amount (on average) after 5,730 years, regardless of how big or small the original quantity was. After another 5,730 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 mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year. In a couple of minutes, almost all atoms of element A will have decayed after repeated halving of the initial number of atoms, but very few of the atoms of element B will have done so as only a tiny fraction of its half-life has elapsed. Thus, the mixture taken as a whole will 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 one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life").

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.

While a radioactive isotope decays almost perfectly according to so-called "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.

For example, the biological half-life of water in a human being is about 9 to 10 days, though this can be altered by behavior and various other conditions. The biological half-life of cesium in human beings is between one and four months.

See also

• Half time (physics)
• List of isotopes by half-life
• Mean lifetime

References

External links

• 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

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

• 1. 薬理ゲノム学の概要 overview of pharmacogenomics
• 2. 栄養の吸収および吸収不良の機序 mechanisms of nutrient absorption and malabsorption
• 3. 成人における抗癌剤の投与 dosing of anticancer agents in adults
• 4. 小児および思春期におけるイブプロフェン中毒の概要 overview of ibuprofen poisoning in children and adolescents
• 5. ビタミンDの概要 overview of vitamin d

English Journal

• Polyethylene glycols enhance the thermostability of β-cyclodextrin glycosyltransferase from Bacillus circulans.

• Li C1, Li W2, Holler TP3, Gu Z4, Li Z5.
• Food chemistry.Food Chem.2014 Dec 1;164:17-22. doi: 10.1016/j.foodchem.2014.05.013. Epub 2014 May 15.
• We investigated the ability of six polyethylene glycols (PEGs), with molecular weights ranging from 400 to 20,000Da, to enhance the thermostability of β-cyclodextrin glycosyltransferase (β-CGTase) from Bacillus circulans. We found that PEGs with different molecular weights could activate and stabi
• PMID 24996299

• Kinetic study and mechanism of Niclosamide degradation.

• Zaazaa HE1, Abdelrahman MM2, Ali NW2, Magdy MA3, Abdelkawy M1.
• Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.Spectrochim Acta A Mol Biomol Spectrosc.2014 Nov 11;132:655-62. doi: 10.1016/j.saa.2014.04.050. Epub 2014 Apr 20.
• A spectrophotometric kinetic study of Niclosamide alkaline degradation as a function of drug concentration, alkaline concentration and temperature has been established utilizing double divisor-ratio spectra spectrophotometric method. The developed method allowed determination of Niclosamide in prese
• PMID 24892546

• Expression and purification of optimized rolGLP-1, a novel GLP-1 analog, in Escherichia coli BL21(DE3) and its good glucoregulatory effect on type 2 diabetic mice.

• Ma B, Tu P, Zhao X, Zhang Y, Wang Y, Ma C, Ji Y, Li X, Abbas SA, Li M1.
• Current pharmaceutical biotechnology.Curr Pharm Biotechnol.2014 Nov;14(11):985-94.
• Glucagon-like peptide-1 (GLP-1) is an incretin hormone that decreases postprandial glycemic excursions by enhancing insulin secretion but with short half-life due to rapid inactivation by enzymatic N-terminal truncation. Therefore, efforts are being made to improve the stability of GLP-1 via modifyi
• PMID 24372241

Japanese Journal

• Terrestrial Half-life of Cesium on the Surface of the Ground

• Shimo Michikuni
• Radiation emergency medicine 3(2), 43-46, 2014-08
• NAID 40020173436

• 清水寺における雨量指標を用いた斜面崩壊警戒基準に関する研究

• 石田 優子,藤本 将光,平岡 伸隆 [他]
• 歴史都市防災論文集 8, 151-158, 2014-07-05
• NAID 40020174787

• 慢性期統合失調症患者の地域生活の定着に向けた意志決定過程

• 藤野 清美
• 日本精神保健看護学会誌 23(1), 81-90, 2014-06-20
• 研究目的は,地域生活へ移行し定着した慢性期統合失調症患者の,症状を調整するために自ら選択・決定した体験の語りから,地域生活の定着に向けた意志決定過程を明らかにすることである.研究対象者は,精神科デイケアへ1年間以上通所する成人期後期の患者9名である.研究方法は,半構造化面接によりデータを収集し,修正版グラウンデッド・セオリー法による質的帰納的研究を行った.慢性期統合失調症患者の地域生活の定着に向け …
• NAID 110009818786

---

★リンクテーブル★

リンク元	「half-life」「T1/2」「halflife」
関連記事	「life」「half」

「half-life」

　　[★]

• 半減期

関

half life、halflife、T1/2, t1/2

「T1/2」

　　[★]

• 半減期

関

half life、half-life、halflife

「halflife」

　　[★]

• 半減期

関

half life、half-life、T1/2

「life」

　　[★]

• n.

• 生命、生活、生涯、人生

関

lifelong、lifetime、vital

　 　 　 　 　 　 　 　 　 　 　

「half」

　　[★]

• 半分

関

halves