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Half-Life:  Full Game Walkthrough 【NO Commentary】
Half-Life: Full Game Walkthrough 【NO Commentary】
Published: 2012/03/05
Channel: Bolloxed
World Record Progression: Half Life 2
World Record Progression: Half Life 2
Published: 2017/09/18
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[Vinesauce] Joel - Half Life Marathon: Half Life
[Vinesauce] Joel - Half Life Marathon: Half Life
Published: 2017/08/30
Channel: Vargskelethor Uncut: Full Joel Streams
Why was Half-Life so good?
Why was Half-Life so good?
Published: 2016/02/28
Channel: jackfrags
Game Theory: Gaming
Game Theory: Gaming's Biggest Mystery SOLVED! | Half Life G MAN Theory
Published: 2017/08/15
Channel: The Game Theorists
Half-Life: Blue Shift - Dreamcast vs. PC Soundtrack Comparison
Half-Life: Blue Shift - Dreamcast vs. PC Soundtrack Comparison
Published: 2017/09/22
Channel: MarphitimusBlackimus
UNLOST ile AYKUT HALF LIFE KAPIŞIYOR (YENİLEN BURGER ISMARLAYACAK)
UNLOST ile AYKUT HALF LIFE KAPIŞIYOR (YENİLEN BURGER ISMARLAYACAK)
Published: 2017/09/21
Channel: Furkan Burak 'Ehrmantraut' Bayrak
The Half-Life 3 Beta Prototype Map Leak
The Half-Life 3 Beta Prototype Map Leak
Published: 2017/08/27
Channel: Valve News Network
Страшные тайны: Вортигонты [Half Life]
Страшные тайны: Вортигонты [Half Life]
Published: 2017/09/21
Channel: Valaybalalay
THE END of Half-life - The Know Game News
THE END of Half-life - The Know Game News
Published: 2017/08/25
Channel: The Know
Half-Life 2: Episode 3
Half-Life 2: Episode 3's Story Released By Marc Laidlaw
Published: 2017/08/25
Channel: Valve News Network
UNLOST EKİPLE  HALF LİFE OYNUYOR EKİP ÖĞRENMİŞ
UNLOST EKİPLE HALF LİFE OYNUYOR EKİP ÖĞRENMİŞ
Published: 2017/09/22
Channel: DexoNn
Half-Life
Half-Life
Published: 2017/02/08
Channel: videogamedunkey
Half-Life - Female Assassin Overview
Half-Life - Female Assassin Overview
Published: 2017/09/10
Channel: MarphitimusBlackimus
ПЕРВЫЙ УРОВЕНЬ HALF LIFE 3 И БИТВЫ ГЕЙМЕРОВ 2 СЕЗОН - #HyperXNEWS
ПЕРВЫЙ УРОВЕНЬ HALF LIFE 3 И БИТВЫ ГЕЙМЕРОВ 2 СЕЗОН - #HyperXNEWS
Published: 2017/09/21
Channel: HyperX RU
Top 10 Facts - Half-Life
Top 10 Facts - Half-Life
Published: 2015/03/30
Channel: LEMMiNO
Half-Life 2 НА ДВИЖКЕ Half-Life 1! 0_o
Half-Life 2 НА ДВИЖКЕ Half-Life 1! 0_o
Published: 2017/09/20
Channel: ALLAN
Half-Life - Random Tiling Textures
Half-Life - Random Tiling Textures
Published: 2017/09/18
Channel: MarphitimusBlackimus
Discussing Half-Life’s Surprise Episode 3 Ending
Discussing Half-Life’s Surprise Episode 3 Ending
Published: 2017/08/25
Channel: Game Informer
Is It Time To Stop Caring About Half-Life 3?
Is It Time To Stop Caring About Half-Life 3?
Published: 2017/07/27
Channel: gameranx
Half-Life 2: Episode 3 Plot Revealed!
Half-Life 2: Episode 3 Plot Revealed!
Published: 2017/08/25
Channel: WhatCulture Gaming
Half-Life 2 - Full Game Walkthrough in HD【NO Commentary】
Half-Life 2 - Full Game Walkthrough in HD【NO Commentary】
Published: 2012/03/10
Channel: Bolloxed
The Lost Episodes of Half-Life 2
The Lost Episodes of Half-Life 2
Published: 2017/07/21
Channel: GVMERS
Half-Life Duncan Sheik with lyrics
Half-Life Duncan Sheik with lyrics
Published: 2009/12/28
Channel: TheCheesecake333
RetroAhoy: Half-Life
RetroAhoy: Half-Life
Published: 2014/10/19
Channel: Ahoy
Half - Life - Скоростное прохождение за 20:41 (Мировой рекорд)
Half - Life - Скоростное прохождение за 20:41 (Мировой рекорд)
Published: 2014/04/15
Channel: GaminG - Новости, обзоры, летсплеи, стримы, трейлеры игр и кино, юмор и многое другое
COD NOOB Tries Half Life...
COD NOOB Tries Half Life...
Published: 2017/02/16
Channel: M3RKMUS1C
Half Life 2 Gun Sounds vs Half Life 1
Half Life 2 Gun Sounds vs Half Life 1
Published: 2017/08/04
Channel: PC Gaming Videos
Half-Life 2 на движке GoldSrc! (Half-Life 2 Classic DEMO)
Half-Life 2 на движке GoldSrc! (Half-Life 2 Classic DEMO)
Published: 2017/09/18
Channel: STALKEROS
Half-Life 2: Epistle3Ville - Full Walkthrough 【NO Commentary】
Half-Life 2: Epistle3Ville - Full Walkthrough 【NO Commentary】
Published: 2017/09/17
Channel: Bolloxed
Half-Life X | The A.S.M.R. of Gordon Freeman
Half-Life X | The A.S.M.R. of Gordon Freeman
Published: 2017/09/14
Channel: Ephemeral Rift
Half Life VS Black Mesa Comparison - Snark
Half Life VS Black Mesa Comparison - Snark
Published: 2017/06/24
Channel: Jarek4GamingDragon
Half-Life Movie - The Freeman Chronicles: Episode 2: Part 1 - Directed by Ian James Duncan
Half-Life Movie - The Freeman Chronicles: Episode 2: Part 1 - Directed by Ian James Duncan
Published: 2017/07/20
Channel: Chariotdrive
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Трудности перевода. Half-Life 2
Published: 2017/05/26
Channel: StopGame.Ru
Half-Life 2 (Все эпизоды) "Баги, Приколы, Фейлы"
Half-Life 2 (Все эпизоды) "Баги, Приколы, Фейлы"
Published: 2016/12/16
Channel: Mr. Marmok
"Half Life 2" Walkthrough (Hard) Chapter 13 - Our Benefactors
"Half Life 2" Walkthrough (Hard) Chapter 13 - Our Benefactors
Published: 2017/09/22
Channel: Zevik
REKOR! Göğsümde Fare Tek El ile Crosshairsiz Half-Life Oynadım
REKOR! Göğsümde Fare Tek El ile Crosshairsiz Half-Life Oynadım
Published: 2016/05/22
Channel: Unlostv
HALF-LİFE 20 DAKİKA DA BİTİRMEK! (DÜNYA REKORU)
HALF-LİFE 20 DAKİKA DA BİTİRMEK! (DÜNYA REKORU)
Published: 2017/08/26
Channel: Metin Boz
ОФИЦИАЛЬНЫЙ CЮЖЕТ HALF-LIFE 3, ОБЪЯСНЕНИЕ КОНЦОВКИ
ОФИЦИАЛЬНЫЙ CЮЖЕТ HALF-LIFE 3, ОБЪЯСНЕНИЕ КОНЦОВКИ
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Half Life Trailer by James Benson
Half Life Trailer by James Benson
Published: 2011/05/29
Channel: James Benson
Half-Life 2: Classic POINT INSERTION Demo Gameplay
Half-Life 2: Classic POINT INSERTION Demo Gameplay
Published: 2017/09/17
Channel: Kinko
Duncan Sheik - Half-life
Duncan Sheik - Half-life
Published: 2011/09/30
Channel: Jonah A.
Half-Life 2: Classic POINT INSERTION Alpha Demo Teaser
Half-Life 2: Classic POINT INSERTION Alpha Demo Teaser
Published: 2017/09/16
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Half-Life 2 : Half-Mind "Войди в Меня ;)" [МОДА-ТРЕШ]
Half-Life 2 : Half-Mind "Войди в Меня ;)" [МОДА-ТРЕШ]
Published: 2017/05/16
Channel: MLCGAMING
Half-Life 2: Episode 3 - The Closure 【Live Stream Recording】
Half-Life 2: Episode 3 - The Closure 【Live Stream Recording】
Published: 2017/09/13
Channel: Bolloxed
MURATABİGF vs UNLOST +18 / Half Life Crossfire Günlükleri #7 [Allah Belanı Versin!]
MURATABİGF vs UNLOST +18 / Half Life Crossfire Günlükleri #7 [Allah Belanı Versin!]
Published: 2016/10/23
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История вселенной Half-Life (Режиссерская версия) [FULL] [RUS]
История вселенной Half-Life (Режиссерская версия) [FULL] [RUS]
Published: 2011/04/27
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Другая сторона конфликта [Half-Life 2: Combine Combat]
Другая сторона конфликта [Half-Life 2: Combine Combat]
Published: 2016/09/15
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A Thorough Look at Half-Life
A Thorough Look at Half-Life
Published: 2013/06/29
Channel: Noah Caldwell-Gervais
Why We Never Got To Play Half-Life 3
Why We Never Got To Play Half-Life 3
Published: 2017/02/27
Channel: Looper
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WIKIPEDIA ARTICLE

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Number of
half-lives
elapsed
Fraction
remaining
Percentage
remaining
0 11 100
1 12 50
2 14 25
3 18 12 .5
4 116 6 .25
5 132 3 .125
6 164 1 .563
7 1128 0 .781
... ... ...
n 1/2n 100⁄(2n)

Half-life (symbol t1⁄2) 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 human 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.[1] 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[edit]

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 is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" 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.[2][3][4]

Formulas for half-life in exponential decay[edit]

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

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,
  • t1⁄2 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 t1⁄2, τ, and λ are all directly related in the following way:

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

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

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

  • as expected (this is the definition of "initial quantity")
  • as expected (this is the definition of half-life)
  • ; i.e., amount approaches zero as t approaches infinity as expected (the longer we wait, the less remains).

Decay by two or more processes[edit]

Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1⁄2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation:

For three or more processes, the analogous formula is:

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

Examples[edit]

Half life demonstrated using dice in a classroom experiment

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.

In non-exponential decay[edit]

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.

In biology and pharmacology[edit]

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.[5]

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,[citation needed] 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[edit]

References[edit]

  1. ^ John Ayto, "20th Century Words" (1989), Cambridge University Press.
  2. ^ Chivers, Sidney (March 16, 2003). "Re: What happens durring half lifes [sic] when there is only one atom left?". MADSCI.org. 
  3. ^ "Radioactive-Decay Model". Exploratorium.edu. Retrieved 2012-04-25. 
  4. ^ Wallin, John (September 1996). "Assignment #2: Data, Simulations, and Analytic Science in Decay". Astro.GLU.edu. 
  5. ^ Lin VW; Cardenas DD (2003). Spinal cord medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1-888799-61-7. 

External links[edit]

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