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| {{About|the scientific and mathematical term|the video game series|Half-Life (series)|other uses|Half-Life (disambiguation)}}
| | == fierce storm from the jungle 'shot' out == |
| {{Refimprove|date=July 2009}}
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| <!-- DO NOT add a link to the [[Half-Life]] (computer-game) page here. It's already listed in the disambiguation page. -->
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| {| class="wikitable" align=right
| | Xiao Yan Yi Deng feet ground, the body is turned into a shadow, rapid inroads that faint black forest.<br><br>With the departure of Xiao Yan, here is slowly fell into silence, it lasts ten minutes after the last ten road shadow, fierce [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html 電波時計 カシオ] storm from the jungle 'shot' out, holding a sword, face 'color' dignified glance a look around, saw no movement after that just light relief, as one another, are all with a wry smile [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-4.html カシオ 腕時計 ソーラー] and shook his head, 一枚 flares ready to go on the right hand clenched, and it was stuffed pregnant , for that can repel [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html 時計 メンズ カシオ] even the old sovereign Yunshan terrorist figures who these people are naturally afraid of God to be incomplete.<br><br>a leading cloud-lan apprentice slowly out, waving a sword, Jianguang flashing, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ 時計 電波 ソーラー] on a tree stem, leaving an obscure sigil, done it afterwards, he just turned around and whispered: ' here has been the search is completed, if then down, then, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-4.html カシオ ソーラー電波腕時計] is to be entered |
| ! Number of<br />half-lives<br />elapsed !! Fraction<br />remaining !! colspan=2| Percentage<br />remaining
| | 相关的主题文章： |
| |-
| | <ul> |
| | 0 || <sup>1</sup>/<sub>1</sub> ||align=right style="border-right-width: 0; padding-right:0"| 100||style="border-left-width: 0"|
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| | <li>[http://www.nmmxc.com/bbs/forum.php?mod=viewthread&tid=869475 http://www.nmmxc.com/bbs/forum.php?mod=viewthread&tid=869475]</li> |
| | 1 || <sup>1</sup>/<sub>2</sub> ||align=right style="border-right-width: 0; padding-right:0"| 50||style="border-left-width: 0"|
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| |-
| | <li>[http://scottalanciolek.com/Main_Page http://scottalanciolek.com/Main_Page]</li> |
| | 2 || <sup>1</sup>/<sub>4</sub> ||align=right style="border-right-width: 0; padding-right:0"| 25||style="border-left-width: 0"|
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| |-
| | <li>[http://www.goldshopmall.com/plus/feedback.php?aid=26 http://www.goldshopmall.com/plus/feedback.php?aid=26]</li> |
| | 3 || <sup>1</sup>/<sub>8</sub> ||align=right style="padding-right:0; border-right-width: 0"| 12||style="border-left-width: 0; padding-left:0"|.5
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| | </ul> |
| | 4 || <sup>1</sup>/<sub>16</sub> ||align=right style="border-right-width: 0; padding-right:0"| 6||style="border-left-width: 0; padding-left:0"|.25
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| | 5 || <sup>1</sup>/<sub>32</sub> || align=right style="border-right-width: 0; padding-right:0"|3||style="border-left-width: 0; padding-left:0"|.125
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| | 6 || <sup>1</sup>/<sub>64</sub> || align=right style="border-right-width: 0; padding-right:0"|1||style="border-left-width: 0; padding-left:0"|.563
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| | 7 || <sup>1</sup>/<sub>128</sub> ||align=right style="border-right-width: 0; padding-right:0"| 0||style="border-left-width: 0; padding-left:0"|.781
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| | ... || ... ||colspan=2| ...
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| | ''n'' ||<sup>1</sup>/<sub>2<sup>''n''</sup></sub> || colspan=2|100/(2<sup>''n''</sup>)
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| |}
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| '''Half-life''' ('''t<sub>½</sub>''') is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period. While the term "half-life" can be used to describe any quantity which follows an [[exponential decay]], it is most often used within the context of [[nuclear physics]] and [[nuclear chemistry]]—that is, the time required, probabilistically, for half of the unstable, radioactive [[atom]]s in a sample to undergo [[radioactive decay]].
| | == his right hand clenched into a fist == |
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| The original term, dating to [[Ernest Rutherford]]'s discovery of the principle in 1907, was "half-life period", which was shortened to "half-life" in the early 1950s.<ref>John Ayto, "20th Century Words" (1989), Cambridge University Press.</ref> Rutherford applied the principle of a radioactive [[chemical elements|elements]]' half-life to studies of age determination of [[Rock (geology)|rock]]s by measuring the decay period of [[radium]] to [[Isotopes of lead#Lead-206|lead-206]].
| | Who, in the eyes Hanmang suddenly flash, and its stature, unexpected disappearance in situ, when again, impressively been to that man behind the lead lizard!<br>With the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html カシオ 腕時計 チタン] right lava flow<br>special induction, when Xiao Yan [http://www.nnyagdev.org/sitemap.xml http://www.nnyagdev.org/sitemap.xml] appeared behind the leader after it is to be aware of, the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-12.html 電波腕時計 カシオ] moment [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html casio 腕時計] came a growl uncontrollably mouth, large palms clenched into a fist, fiercely against Behind Xiao Yan angrily smashing away.<br><br>'bang!'<br><br>large fist [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio 腕時計 データバンク] with one hand holding Xiao Yan, contact between the palm and fist attack, an outbreak of volatility forceful ripples out around the flame lizard man shook rapid retrogression.<br><br>'Well!'<br><br>one hand fall upon flame lizard people, Xiao Yan Leng Heng, body shoved forward, his right hand clenched into a fist, and then suddenly smacked!<br><br>'extreme collapse!'<br><br>deep self-Sheng Xiao Yan mouth spread, over fist, power suddenly soaring |
| | | 相关的主题文章： |
| Half-life is used to describe a quantity undergoing exponential decay, and is constant over the lifetime of the decaying quantity. It is a [[characteristic unit]] for the exponential decay equation. The term "half-life" may generically be used to refer to any period of time in which a quantity falls by half, even if the decay is not exponential. The table on the right shows the reduction of a quantity in terms of the number of half-lives elapsed. For a general introduction and description of exponential decay, see [[exponential decay]]. For a general introduction and description of non-exponential decay, see [[rate law]]. The converse of half-life is [[doubling time]].
| | <ul> |
| | | |
| == Probabilistic nature of half-life ==
| | <li>[http://www7b.biglobe.ne.jp/~miria/honey/honey.cgi http://www7b.biglobe.ne.jp/~miria/honey/honey.cgi]</li> |
| [[File:Halflife-sim.gif|thumb|right|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.]]
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| | | <li>[http://www.jitaweb.com/plus/feedback.php?aid=158 http://www.jitaweb.com/plus/feedback.php?aid=158]</li> |
| 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 "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.
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| | | <li>[http://98.126.169.156/home.php?mod=space&uid=2110688 http://98.126.169.156/home.php?mod=space&uid=2110688]</li> |
| Instead, the half-life is defined in terms of [[probability]]: "Half-life is the time required for exactly half of the entities to decay ''[[expected value|on average]]''". In other words, the ''probability'' of a radioactive atom decaying within its half-life is 50%.
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| | | </ul> |
| 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.
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| There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical [[computer program]].<ref>{{cite web
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| | url=http://www.madsci.org/posts/archives/Mar2003/1047912974.Ph.r.html | title=MADSCI.org | accessdate=2012-04-25}}
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| </ref><ref>
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| {{cite web | url=http://www.exploratorium.edu/snacks/radioactive_decay/index.html | title=Exploratorium.edu | accessdate=2012-04-25}}
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| </ref><ref>
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| {{cite web | url=http://astro.gmu.edu/classes/c80196/hw2.html | title=Astro.GLU.edu | accessdate=2012-04-25}}</ref>
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| == Formulas for half-life in exponential decay ==
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| {{Main|Exponential decay}}
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| An exponential decay process can be described by any of the following three equivalent formulas:
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| :<math>N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}}</math>
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| :<math>N(t) = N_0 e^{-t/\tau} \,</math>
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| :<math>N(t) = N_0 e^{-\lambda t} \,</math>
| |
| where
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| :* ''N''<sub>0</sub> is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
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| :* ''N''(''t'') is the quantity that still remains and has not yet decayed after a time ''t'',
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| :* ''t''<sub>1/2</sub> is the half-life of the decaying quantity,
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| :* τ is a [[positive number|positive]] number called the [[mean lifetime]] of the decaying quantity,
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| :* λ is a positive number called the [[decay constant]] of the decaying quantity.
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| The three parameters <math>t_{1/2}</math>, <math>\tau</math>, and λ are all directly related in the following way:
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| :<math>t_{1/2} = \frac{\ln (2)}{\lambda} = \tau \ln(2)</math> | |
| where ln(2) is the [[natural logarithm]] of 2 (approximately 0.693).
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| :{| class="toccolours collapsible collapsed" width="80%" style="text-align:left"
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| !Click "show" to see a detailed derivation of the relationship between half-life, decay time, and decay constant.
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| |-
| |
| |Start with the three equations
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| :<math>N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}}</math>
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| :<math>N(t) = N_0 e^{-t/\tau}</math>
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| :<math>N(t) = N_0 e^{-\lambda t}</math>
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| We want to find a relationship between <math>t_{1/2}</math>, <math>\tau</math>, and λ, such that these three equations describe exactly the same exponential decay process. Comparing the equations, we find the following condition:
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| :<math>\left(\frac {1}{2}\right)^{t/t_{1/2}} = e^{-t/\tau} = e^{-\lambda t}</math>
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| Next, we'll take the [[natural logarithm]] of each of these quantities.
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| :<math>\ln\left(\left(\frac {1}{2}\right)^{t/t_{1/2}}\right) = \ln(e^{-t/\tau}) = \ln(e^{-\lambda t})</math>
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| Using the properties of logarithms, this simplifies to the following:
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| :<math> (t/t_{1/2})\ln \left(\frac {1}{2}\right) = (-t/\tau)\ln(e) = (-\lambda t)\ln(e)</math>
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| Since the natural logarithm of ''e'' is 1, we get:
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| :<math> (t/t_{1/2})\ln \left(\frac {1}{2}\right) = -t/\tau = -\lambda t</math>
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| Canceling the factor of ''t'' and plugging in <math>\ln\left(\frac {1}{2}\right)=-\ln 2</math>, the eventual result is:
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| :<math>t_{1/2} = \tau \ln 2 = \frac{\ln 2}{\lambda}.</math>
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| |}
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| By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:
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| :<math>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}}</math>
| |
| :<math>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))</math>
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| Regardless of how it's written, we can plug into the formula to get
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| *<math>N(0)=N_0</math> as expected (this is the definition of "initial quantity")
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| *<math>N(t_{1/2})=\left(\frac {1}{2}\right)N_0</math> as expected (this is the definition of half-life)
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| *<math>\lim_{t\to \infty} N(t) = 0</math>, i.e. amount approaches zero as ''t'' [[Limit of a function|approaches infinity]] as expected (the longer we wait, the less remains).
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| | |
| === Decay by two or more processes ===
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| Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life ''T''<sub>1/2</sub> can be related to the half-lives ''t''<sub>1</sub> and ''t''<sub>2</sub> that the quantity would have if each of the decay processes acted in isolation:
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| :<math>\frac{1}{T_{1/2}} = \frac{1}{t_1} + \frac{1}{t_2}</math>
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| For three or more processes, the analogous formula is:
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| :<math>\frac{1}{T_{1/2}} = \frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + \cdots</math>
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| For a proof of these formulas, see [[Exponential decay#Decay by two or more processes]].
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| === Examples ===
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| {{further|Exponential decay#Applications and examples}}
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| There is a half-life describing any exponential-decay process. For example:
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| * The current flowing through an [[RC circuit]] or [[RL circuit]] decays with a half-life of <math>RC\ln(2)</math> or <math>\ln(2)L/R</math>, respectively. For this example, the term [[half time (physics)|half time]] might be used instead of "half life", but they mean the same thing.
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| * In a first-order [[chemical reaction]], the half-life of the reactant is <math>\ln(2)/\lambda</math>, where λ is the [[reaction rate constant]].
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| * In [[radioactive decay]], the half-life is the length of time after which there is a 50% chance that an atom will have undergone [[Atomic nucleus|nuclear]] decay. It varies depending on the atom type and [[isotope]], and is usually determined experimentally. See [[List of nuclides]].
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| 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.
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| == Half-life in non-exponential decay ==
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| {{Main|Rate equation}}
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| 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.
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| 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 ([[#Probabilistic nature of half-life|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 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.)
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| 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.
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| == Half-life in biology and pharmacology ==
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| {{Main|Biological half-life}}
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| 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 in [[blood plasma]] of a substance to reach one-half of its steady-state value (the "plasma half-life").
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| The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in [[tissue (biology)|tissues]], active [[metabolite]]s, and [[Receptor (biochemistry)|receptor]] interactions.<ref name="SCM">{{cite book|title=Spinal cord medicine|author1=Lin VW|author2=Cardenas DD|publisher=Demos Medical Publishing, LLC|page=251|url=http://books.google.co.uk/books?id=3anl3G4No_oC&pg=PA251&lpg=PA251|year=2003|ISBN=1-888799-61-7}}</ref>
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| 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.
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| For example, the biological half-life of water in a [[human being]] is about 7 to 14 days, though this can be altered by his/her behavior. The biological half-life of [[cesium]] in human beings is between one and four months. This can be shortened by feeding the person [[prussian blue]], which acts as a solid [[ion exchange]]r that absorbs the cesium while releasing [[potassium]] ions in their place.
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| == See also ==
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| * [[Half time (physics)]]
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| * [[List of isotopes by half-life]]
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| * [[Mean lifetime]]
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| == References ==
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| <div class="references-small">
| |
| <!--See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
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| <references/>
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| </div> | |
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| == External links ==
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| {{Wiktionary|half-life}}
| |
| * [http://www.nucleonica.net Nucleonica.net], Nuclear Science Portal
| |
| * [http://www.nucleonica.net/wiki/index.php/Help:Decay_Engine Nucleonica.net], wiki: Decay Engine
| |
| * [http://www.facstaff.bucknell.edu/mastascu/elessonshtml/SysDyn/SysDyn3TCBasic.htm Bucknell.edu], System Dynamics - Time Constants
| |
| * [http://www.subotex.com/SuboxoneTaperChart.aspx Subotex.com], Half-Life elimination of drugs in blood plasma - Simple Charting Tool
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| {{Radiation}}
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| {{DEFAULTSORT:Half-Life}}
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| [[Category:Radioactivity]]
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| [[Category:Exponentials]]
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| [[Category:Chemical kinetics]]
| |
fierce storm from the jungle 'shot' out
Xiao Yan Yi Deng feet ground, the body is turned into a shadow, rapid inroads that faint black forest.
With the departure of Xiao Yan, here is slowly fell into silence, it lasts ten minutes after the last ten road shadow, fierce 電波時計 カシオ storm from the jungle 'shot' out, holding a sword, face 'color' dignified glance a look around, saw no movement after that just light relief, as one another, are all with a wry smile カシオ 腕時計 ソーラー and shook his head, 一枚 flares ready to go on the right hand clenched, and it was stuffed pregnant , for that can repel 時計 メンズ カシオ even the old sovereign Yunshan terrorist figures who these people are naturally afraid of God to be incomplete.
a leading cloud-lan apprentice slowly out, waving a sword, Jianguang flashing, カシオ 時計 電波 ソーラー on a tree stem, leaving an obscure sigil, done it afterwards, he just turned around and whispered: ' here has been the search is completed, if then down, then, カシオ ソーラー電波腕時計 is to be entered
相关的主题文章：
his right hand clenched into a fist
Who, in the eyes Hanmang suddenly flash, and its stature, unexpected disappearance in situ, when again, impressively been to that man behind the lead lizard!
With the カシオ 腕時計 チタン right lava flow
special induction, when Xiao Yan http://www.nnyagdev.org/sitemap.xml appeared behind the leader after it is to be aware of, the 電波腕時計 カシオ moment casio 腕時計 came a growl uncontrollably mouth, large palms clenched into a fist, fiercely against Behind Xiao Yan angrily smashing away.
'bang!'
large fist casio 腕時計 データバンク with one hand holding Xiao Yan, contact between the palm and fist attack, an outbreak of volatility forceful ripples out around the flame lizard man shook rapid retrogression.
'Well!'
one hand fall upon flame lizard people, Xiao Yan Leng Heng, body shoved forward, his right hand clenched into a fist, and then suddenly smacked!
'extreme collapse!'
deep self-Sheng Xiao Yan mouth spread, over fist, power suddenly soaring
相关的主题文章：