Talk:Half-life/Archive 1

Measuring the half lifes
Given that the half-life of Tungsten is so long and that decay is therefore a very rare event I would like to ask how it is possible to accurately measure its half life? For example if a reasonable mass of Tungsten only has one theoretical atomic decay a year there is a real statistical chance (by random variation) that none or more may occur and so one would surely need to measure over an unfeasible period of time (of unfeasible mass)? Also such a low rate would surely be masked by contamination and background radiation or re-absorption of emitted particles? Could an explanation of the method be added as a link? [ManInStone].

I think Bismuth has an even longer half-life that Tungsten. —The preceding unsigned comment was added by 194.176.105.39 (talk) 13:48, 5 April 2007 (UTC).


 * Right heres a problem to put all this into context. The half life of bismuth is 19*10^18 years. Its molecular mass is 208.98040g•mol−1. Accordingly there are about 2.87108E+27 atoms in a ton of bismuth. How long would I have to observe the one ton mass in order to be 95% sure that I would observe a single disintigration (assuming there were no technical problems to observation of every event)? --ManInStone 08:21, 18 May 2007 (UTC)


 * I had a go at this but soon got bogged down in the maths. According to my rough and long winded calculations you would have a fifty percent chance of seeing one decay on the first day.  Can anyone shed any light on this problem?


 * From the question on the exponential decay page: the equation is dN/dt = γN = [ln2/t(1/2)]N. If t(1/2) is 1.9e19 years = 6e26 sec and N is 2.9e27, then dN/dt is 3.35 disintigrations per sec. From here, you have to know that you need to calculate from the Poisson distribution the 0.05 probability time for 0 events, when gamma (expected event rate) is 3.35/sec, is exp-(γ*t), where the lamba here is the total expected event rate for our entire mass, not the one for each atom. So 0.05 = exp-(3.35*t). Solve for t and you get a time about 0.893 sec. You have to wait that long for a 95% chance to see a single disintigration with an expected rate of 3.35/sec. SBHarris 02:07, 28 July 2007 (UTC)

yeah... seriously most half lives are older than chemistry —Preceding unsigned comment added by 141.149.13.22 (talk) 20:08, 22 April 2008 (UTC)

Misleading 'a'
To say that the constant 'a' is negative in the case of exponential decay leads to a very confusing developement (imho): the standard is to use the decay constant $$\lambda$$, which is positive: $$\lambda = \frac{ln(2)}{t_{1/2}}$$. One should write the exponential law as $$x(t) = x(0) e^{-a t}$$, and so there is no need to talk about the constant being able to absorb the minus sign, which is actually incorrect! (if $$a$$ absorbs the minus sign, it becomes positive, that's indeed what we see in the last formula: $$t_{1/2} = \frac{ln(2)}{a}$$ since ln(2) and $$a$$ are positive. And since $$a$$ is positive, there should be a minus signe in the exponent of the decay law). To make things even easier to understand, one may use N instead of x, it's probably a more natural way to represent the population of radioactive isotope which is an integer. (I leave it to other people to make the changes: my English is not very good).

I agreed with the above point, but the whole article needs some work IMO. I have flagged it as needing attention. The discussion on the half-life usage in physics seems to talk about lots of points that don't belong here. Perhaps these bits should be integrated into the radioactive decay article? The structure doesn't seem that great either - there are lots of major headings containing only a sentence or two of description. I don't understand the section on its usage in population calculation. Could someone clarify this or else remove this section. There are probably other problems that I have forgotten... Bobbis 18:52, 26 Oct 2004 (UTC)

Of "particles", "substances", "radioactivity" and the like
People like to use these words in this article, but strictly speaking, none of them have anything to do with half-life. Half-life is a purely mathematical (theoretical) property of the likewise mathematical phenomenon of exponential decay. The differential equation that describes exponential decay crops up in a bunch of places; see Exponential decay for a list (which I'm sure is less than complete). --Smack 05:02, 10 Nov 2004 (UTC)

A little more simplicity might be in order
Imagine a high-school student -- or anyone who did not take more than first year college math. Do you think they would get anything from this page or the one on exponential decay?

I think the table is needed on BOTH pages, but even more so on the half-life page -- as it is more likely anyone who was not mathematically advanced would go there first.

Anyone who was able to understand what has appeared on these pages would NOT need to look up the terms.

No? --JimWae 04:35, 2004 Dec 20 (UTC)


 * I see two viable options: a) leave this article as it is, or b) put a thorough discussion of exponential and radioactive decay here. (I disregard any intermediate compromise solution, as it would frustrate both your goals and mine to an equally great extent.)
 * I rewrote this article with Option A in mind, by purposely stripping it of everything not related to this narrow subject. My hope is that the references to Exponential decay and Radioactive decay are prominent enough that people who see this article and wonder where all of the information is will go there.  Option B would involve simple duplication of material presented elsewhere, which encourages divergent evolution. --Smack 18:07, 20 Dec 2004 (UTC)
 * P.S: If you want to make this subject more clear to those with weak mathematical skills (or even short attention spans for math), I see no reason why you shouldn't. I just have concerns about the way it's done. --Smack 18:12, 20 Dec 2004 (UTC)


 * I still think the simple table would make this a much more useful article for the overwhelming majority of readers. Those who understand the math here, would never need to look up the meaning.--JimWae 20:55, 2004 Dec 31 (UTC)


 * What meaning?
 * I agree that this article is not very helpful. I don't intend it to be helpful for most people.  It does not stand alone, except for narrow purposes.  People who come here with general questions are better off at Exponential decay, and I think we should do our best to make sure they go there. The more general content we put here, the less likely that is to happen.  --Smack 18:45, 3 Jan 2005 (UTC)


 * Encyclopedia articles should be accessible to those who might open the page, not just be technically correct. Most people will more likely go to half-life first than exponential decay. Even if they manage to click on exponential decay after going to half-life (but why that link rather than any other there?), they are first going to see stuff way too technical for them there too. There is no real danger of significantly different versions with that table. If somebody understands either page, they already know what half-life means--JimWae 07:03, 2005 Feb 18 (UTC)


 * You're right, exponential decay is not referenced prominently enough for inexperienced readers. I'll tweak the intro paragraph a bit.
 * You're also right that that article is not very accessible to the non-mathematical. IMO, the way to resolve that problem is not to slap half-hearted stand-in explanations of exponential decay onto other articles, but to write a qualitative treatment of the topic into the main article's introduction. If you consider yourself capable of doing that, please do so.  I wouldn't trust myself with the task. --Smack (talk) 03:45, 20 Feb 2005 (UTC)

half-life decay to infinity
So in theory radioactive substances cannot complete decompose, as it constantly halving, in practice though i doubt this as one single atom will obviuosly become another substance after some time and none will be left, so what do we believe? 19:50, 10 December 2005 (UTC)


 * Why do you think it will "obviously" decompose? An unstable atom can, in principle, go on indefinitely without falling apart.  It's very unlikely to do this, but it can. --Smack (talk) 22:21, 14 December 2005 (UTC)

Hey High School Student Here...This is mind bogoling....Slayerx675 19:16, 1 May 2006 (UTC)

Just to make sure this is clear. The maths is talking about probability. In one half-life, roughly half the atoms will decompose. The most likely result is half of them decomposing. Once you get down to one atom, it has a 50/50 chance of decomposing every half-life. Think of it like throwing 100 coins in the air, and every coin that lands face-up has 'decomposed'. Each time you do it, about half the coins should 'decompose'. When you only have one coin, it obviously doesn't land as half-heads each time, it is either heads or tails. You have a 50/50 chance of it landing heads. Skittle 15:04, 13 June 2006 (UTC)

Request for Mediation
Removed old mediation tag - it died two months +/- ago. Vsmith 22:35, 1 May 2006 (UTC)


 * Well, I'm just a kid and checked this out because I'm a fan of the videogame. Anyway, I think that an atom could decompose by 1/2 again and again and again. what I am wondering about is that if it could completly compose to nothing what would happen to the empty space? My guess is that it continues the curved path by halving itself on the X axis every time it goes down one unit on the Y. I think it will do this forever and to infinity. (Based on junior high science and pre-algebra).


 * An unstable (radioactive) isotope will decay along a decay pathway until it become a stable atom (such as lead) at which point the decay stops. I think you are confusing theoretical probability theory with the actual mechanics of radioactive decay.  This appears to be a common point of confusion judging by other posts on this general topic.

--ManInStone 08:34, 18 May 2007 (UTC)

Table of values
I move to remove the table. --Smack (talk) 03:25, 21 March 2006 (UTC)
 * Keep the table and maybe expand to show the pattern in fractional form (1/2)n. This needs to be aimed at the general reader rather than just catering to the math geeks :-) Vsmith 22:35, 1 May 2006 (UTC)


 * The contributor who originally added the table intended precisely to cater to the general reader. If I understand it correctly, your proposed version would cater only to the profoundly stupid.  I think that very few readers would find a table of this form to be helpful at all. --Smack (talk) 18 May, 2006

I like the current table in the article. It doesn't help me, but I think it illustrates the basic principle of half-life, to people who do not understand it, better than any accurate, encyclopedic words possibly could. Skittle 15:06, 13 June 2006 (UTC)

Derivation
Hi,

You (fresheneesz) remarked in an edit comment at Half-life that you're moving the derivation to the talk page, but the talk page's edit history shows no edits by you. Where did it go, and why did you remove it at all?

P.S: You can use the five-tilde feature for the timestamp at the top of this talk page. --Smack (talk) 02:43, 9 June 2006 (UTC)


 * Hmm, yea I guess I never did end up pasting the derivation to the talk page. Whoops.. I did it now. I removed the derivation because it wasn't clear, and I guess I didn't think it was very helpful. I can't remember my reasoning, but I didn't think it derserved the space it took up.


 * Do you think the derivation should stay? Sometimes, its better if derivations like that appear at the bottom of a page, or if they appear on a separate page all together. Oh and thanks for the five-tilde tip. Fresheneesz 03:30, 9 June 2006 (UTC)


 * I think that a section at the end of the page would give it the right amount of prominence. I originally put it in the beginning because I needed it for the formulas, but that point is moot now that we have a whole section just to define the term.  I'll put the derivation back, then. --Smack (talk) 03:48, 9 June 2006 (UTC)


 * Sounds good, I'll copy this discussion to the talk page of half-life. Fresheneesz 03:56, 9 June 2006 (UTC)

Here is the derivation:

Quantities that are subject to exponential decay are commonly denoted by the symbol N. (This convention suggests a decaying number of discrete items. This interpretation is valid in many, but not all, cases of exponential decay.)  If the quantity is denoted by the symbol N, the value of N at a time t is given by the formula:


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

where


 * $$N_0$$ is the initial value of N (at t=0)
 * &lambda; is the decay constant, a positive constant.

When t=0, the exponential is equal to 1, and N(t) is equal to $$N_0$$. As t approaches infinity, the exponential approaches zero.

In particular, there is a time $$t_{1/2} \,$$ such that:


 * $$N(t_{1/2}) = N_0\cdot\frac{1}{2} $$

Substituting into the formula above, we have:


 * $$N_0\cdot\frac{1}{2} = N_0 e^{-\lambda t_{1/2}} \,$$


 * $$e^{-\lambda t_{1/2}} = \frac{1}{2} \,$$


 * $$- \lambda t_{1/2} = \ln \frac{1}{2} = - \ln{2} \,$$


 * $$t_{1/2} = \frac{\ln 2}{\lambda} \,$$

Thus the half-life is 69.3% of the mean lifetime.

Definition
This is not the definition of half-life:
 * $$ t_{1/2} = \frac{\ln (2)}{\lambda} $$

It's a correct relationship but not the definition of half-life. Jclerman 04:56, 9 June 2006 (UTC)


 * Do you care to mention what the "definition" is? 71.238.35.126 23:47, 12 November 2007 (UTC)
 * After you care to read the article's first sentence: "The half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value." Jclerman 11:10, 13 November 2007 (UTC)

Opinions unsourced
These opinions need to be verifiable from peer-reviewed sources: ''Most people understand the concept of half-life quickly and are usually first introduced to it in an introductory chemistry or biology course. The extra logarithmic factor, however, is often considered mathematically unpleasant because it leaves room for an additional source of computational error. Nearly all textbooks beyond the introductory level, especially in physics, consider half-life to be archaic and use mean lifetime instead.'' Jclerman 00:17, 11 June 2006 (UTC)
 * The rationale for the deletion of the quoted statements (unsourced and subjective) follows the discusion of the terminology given in


 * Jclerman 00:13, 18 June 2006 (UTC)

Verification requested...
How old is an archeological site according Carbon 14 dating where the half life of Carbon 14 is equal to 5,730 years and there is only 25% as much Carbon 14 in an archeological sample as a recent sample?


 * $$ h=5,730 $$
 * Where h is the half life of Carbon 14
 * $$ p=.25 $$
 * where p is the percent or portion and is defined by:
 * $$ p= 1/{2^n}$$
 * and n is defined as the number of half lives
 * $$ n = \frac{\lg \left(\frac{1}{p}\right)}{\lg \left({2}\right)}$$
 * and age is defined as
 * $$ age=h*n $$


 * 1) Option Explicit
 * 2) Dim h As Double, p As Double, n As Double, age As Double
 * 3) Private Sub Form_Load
 * 4) h = 5730
 * 5) 'Where h is the half life of Carbon 14
 * 6) p = 0.25
 * 7) '(where p is the percent or portion) and defined by'
 * 8) 'p = 1 / (2 ^ n)
 * 9) 'and n is defined as the number of half lives
 * 10) n = Log(p) / Log(.5) (or n = log(1/p) / log(2))
 * 11) 'and age is defined as
 * 12) age = h * n
 * 13) Debug.Print "Half-life", "Percent", "Half-lives", "Age"
 * 14) Debug.Print h, p, n, age
 * 15) End Sub

Can anyone verify the accuracy of this conclusion and method so that it may be posted to the article page? Thanks.

...IMHO (Talk) 19:57, 12 June 2006 (UTC)


 * That's not necessary. See Radiocarbon_dating. --Smack (talk) 23:47, 12 June 2006 (UTC)


 * Its necessary for readers (especially young readers) who have learned how to write a computer program but not yet learned fancy mathematical symbols which ar only meant to awe strike and confuse them them instead of helping them get on with the business of learning science and saving higher mathematics for higher mathematics. ...IMHO (Talk) 01:35, 13 June 2006 (UTC)
 * Then forget all formula for your example: 50% ~ 5730yrs x 1 = 5730yrs; 25% ~5730yrs x 2 = 11460 yrs. Keep adding 5730yrs and halving the activity for each half-life. Jclerman 02:04, 13 June 2006 (UTC)


 * By whatever method is used kids still need a variety of optional methods for comparision before then can grasp what the symbols are all about and before they reach middle age. ...IMHO (Talk) 02:12, 13 June 2006 (UTC)


 * ...and that is what teachers are paid for. However, an encyclopedia is not a teacher - rather it is a source of information and the article provides valid information. Now, I'll agree that the calculation method presented in the article is a bit much for those without some background in math manipulations, logarithms and rate laws. But, as I said up front, that's why we have textbooks and teachers.
 * Now for your calculations. The general approach works, but it seems you have an error:
 * p = (1/2)n
 * log p= n&middot;log 0.5
 * n = (log p) /(log 0.5) ... (not log 1/p)
 * That's my simplified approach for easing students into the concept. If they can find the calculator log button they can do it.
 * However, all that does not belong in the article. Wikipedia is not a how to... Vsmith 02:48, 13 June 2006 (UTC)

There are two entirely different "how to" reasons. The first is to offer a means of simplifying and softening the explanation of a concept and thereby reducing the learning curve. The second is far more detailed an is for the purpose of actually doing the task over and over again in the real world. A reputable online encyclopedia embraces both kinds of “how to” explanations by including the first kind within the article and by providing a link to the second, which in the case of the Wikipedia would be to the Wikibooks and the How-tos_bookshelf. ...IMHO (Talk) 03:10, 13 June 2006 (UTC)
 * Thanks for the reference to the Wikibooks. However, don't rely too much on them. They have a misleading module on the application of logs to radiocarbon dating. I just entered my comments (see below) on a module written, without teacher assistance, by a high-school student. Jclerman 03:42, 13 June 2006 (UTC)


 * And likewise for the change from log(2) to log(.5) above. Computer wise it gets rid of a division which as I recall from my computer classes of many years ago is far slower than a floating point multiplication. The important issue here, however, is to mold the Wikipedia to the variety of minds out there versus trying to get them to mold to the Wikipedia. Symbolic math is great but once math markup becomes functional and an actual programming language on its own there is no way that it can compete except perhaps for display of math in the form it has taken over the past centuries. What is especially important to realize is that most people have been seduced by the power of a computer to do math and would rather have formulas provided to them in a form that they can plug into their personal computers and get answers with right away so its important to use the universal, all inclusive, comprehensive approach and provide formulas as if all of these were but different languages so that all will be accommodated according to there individual leanings. While Log(1/p)/log(2) might work for me and Log(p)/log(.5) might work for you they both work for the computer. BTW I had previously run a "simplify equation" command under Mathcad 12 and it did not do the conversion to log(p) and Mathcad 12 has made a lot more money than me. ...IMHO (Talk) 08:10, 13 June 2006 (UTC)

Please correct the following in the math module of the Wikibook
<>
 * The half-life is a quantity, not an application.

<>
 * A sample of 100 gram is not reduced to 20 grams. You won't be able to notice any change in mass.

Please, don't teach erroneous concepts. Jclerman 03:42, 13 June 2006 (UTC)

Sounds like the student did not do any proof reading in the first sentence and has a complete misunderstanding of how little carbon-14 is actually involved. Atoms would be a far more appropriate measure than grams since there are approximately one trillion carbon-12 atoms for every carbon-14 atom. To do grams you would need a carbon object weighing 100 trillion grams before you could extract 100 grams of carbon-14. However, if you start off with 100 trillion atoms of carbon-12 and 100 atoms of carbon-14 then after 5,730 years you would still have 100 trillion atoms of carbon-12 but only 50 atoms of carbon-14 and 50 atoms of nitrogen-14. So even though weight is not an appropriate unit the student's idea may be correct. It would take 13,305 years for 80 atoms of carbon-14 to be converted to nitrogen-14, leaving only 20 atoms of carbon-14. After 38,069 years all of the carbon-14 would be gone and converted back into into nitrogen-14 from whence it came. ...IMHO (Talk) 09:38, 13 June 2006 (UTC)
 * Nice try. But,


 * Carbon-14 is never completely gone. It decays exponentially ad infinitum.
 * How come we date samples as old as 60,000 yrs if all C-14 is gone after 38,069 yrs?
 * Jclerman 10:57, 13 June 2006 (UTC)


 * Huh? Are you sure you should be editing any of these pages??? Sorry to tell you this but...


 * There are only a finite number of carbon-14 atoms in any living organism when it stops breathing.
 * Some samples start off with more than 100 atoms of carbon-14. In other words it depends upon sample size. However, even though all atoms of carbon-14 will in any sample eventually be converted into nitrogen-14 by the process of Beta decay the generally accepted reliability limits for measuring any of the residual atoms of carbon-14 left in any reasonable maximum size sample taken from an organism that was once living is about 8 half-life cycles or around 50,000 years max. You can reverse the calculation and do a growth analysis to find out just how big an organism would have to be to start off with in order to extend the number of cycles beyond 8.

Think about it this way. If you only have one atom of carbon-14 and another 5,730 years goes by (plus or minus 40 years) how many atoms of carbon-14 will you have left? As soon as carbon-14 replacement stops in an organism (as the result of the organism no longer breathing) replacement of carbon-14 atoms taken in from the atmosphere stops and there is nothing to counteract the decay process. Since carbon-14 atoms (or any atom for that matter) can only be divided in number down to the number of one eventually no matter how many atoms you start with you will end up with only one atom and in another 5,730 years in the case of carbon-14 (plus or minus 40 years) that last atom of carbon-14 will be gone - converted back into nitrogen-14 from where it came. ...IMHO (Talk) 15:32, 13 June 2006 (UTC)
 * Since you hinted that I shouldn't be editing, you probably do not see me fit to discuss your comments. So, I won't discuss them. However, for the sake of others that could be misled, I will point out the more important areas of misunderstanding and let the readers resolve them if they wish so in the literature about the relevant topics. As somebody else said, wikipedia is neither a classroom nor a manual, but just a pointer to topics and to related references.

This is the partial list:
 * No organism incorporates carbon-14 by breathing.
 * The counting statistics needed for dating is based on exponential statistics of random decays, not valid for small number of atoms.


 * This is the article on half-life, thus dating methods consist of counting radioactive decays, not C-14 atoms.
 * A single atom can decay at ANY time, irrespective of the isotope's half-life.
 * The age limit can be extended not only by increasing the sample size but also the counting time.
 * Certain amount of decays per second (specific [radio]activity) are needed to be detectable above the background.

Jclerman 20:42, 13 June 2006 (UTC)


 * Item 1 above. Plants breath c02 with some of the c atoms being c-14 and animals eat plants. Item 2 above. I will leave it to you to determine the probability of transformation in respect to half-life for only a few atoms. C-14 decay for even only a few atoms will happen eventually because it is an unstable isotope. Item 3 above. Radioactive decay results in a decrease of c-14 atoms and an increase in n-14 atoms. While only the names and characteristics change the total number of atoms stays the same. The only way to understand why there is less radioactive emission is to understand why there are fewer atoms of c-14. Item 4 above. True. If you have only one atom of c-14 it might transform into n-14 immediately or wait awhile but eventually it will decay. I'll leave it to you to determine the probability of it not transforming within 2 of its half-lives. Item 5 above. we probably agree on sample size and counting but without your definition of both terms I can't comment. Item 6 above. True. But this number appears to be arbitrary and dependent upon equipment calibration, sensitivity, proximity, components of the surronding environment, etc. To be an editor you not only have to understand a topic but understand why others do not and how to bridge the gap for their benefit rather than your own. ...IMHO (Talk) 03:32, 14 June 2006 (UTC)

Half-life comprehension and computation...
The following discussion moved from Reference desk/Science. Arbitrary username 19:47, 13 June 2006 (UTC)

Improper deletions
This article can not be used to prevent other users from obtaining a complete comprehension of half-life in the same manner as a member of a trade or artisan guild might try to hide techniques or methods of performing some function. An explanation of half-life can not be limited to only a very technical or mathematical version or explanation of the process. Half-life decay can not be presented here in the same way as a tradesman or artisan would withhold a simple explanation from a patron for the sole purpose of mystifying the topic and keeping the ordinary user from comprehending the topic fully. Such censorship can not be permitted. For this reason deletion of example data, compute code, and simple arithmetic intended to clarify the process and results of Carbon-14 to Nitrogen-14 half-life decay for other users is not acceptable. If such deletions continue then they must be assessed as vandalism an pursued accordingly. ...IMHO (Talk) 04:54, 19 June 2006 (UTC)


 * User:GangofOne added this comment within the text of your table: (This example isn't very realistic. 1E+308 atoms of C14 has a mass of 2E+282 kilograms. The Earth's mass is only 5E+24 kilograms.)
 * The physics is unrealistic for this and other reasons, and the numbers you post do not appear to reflect your description of the table.


 * Both the physics and the mathematics are relevant and important here in response to Jclerman's statement that the process of half-life decay in a sample never ends but rather proceeds ad infinitium. This table is verification that no matter how large a sample of Carbon-14 one starts with that the process of half-life decay will eventually terminate. ...IMHO (Talk) 14:26, 19 June 2006 (UTC)


 * IMHO the whole matter belongs to this discussion page, and sans personal atttacks so I've transferred the table to the following section.
 * Jclerman 07:34, 19 June 2006 (UTC)


 * Nice try to prevent inclusion and clarification of the topic. Recognition that your actions are vandalism does not mean that it is a personal attack. However you are the one who must be held accountable for any act of vandalism thus necessitating the use of personal pronouns. My fault is in warning of an impending complaint rather than making the complaint outright. ...IMHO (Talk) 14:19, 19 June 2006 (UTC)


 * User:Pce3@ij.net aka IMHO, the absurdly long table you added was quite innappropriate as well as OR. Its removal was not vandalism and Jclerman is not trying to hide anything.
 * A teacher often has to simplify concepts to help students understand, however, simplifying requires an understanding of the concept to avoid introducing errors. Your posts above illustrate a lack of basic understanding of the concept of radioactive half life and basic biochemistry. Your attempted clarifications, though well meaning I'm sure, had the opposite effect by adding incorrect information and flooding the article with absurd calculations. Now, I'd suggest that you be cautious with your accusations of vandalism and other personal attacks and carefully consider related Wikipedia policies. Vsmith 14:53, 19 June 2006 (UTC)

Computational Data (demonstration of half-life results)
(Note: This chart is limited to a maximum value of1E+308 using Microsoft Excel Spreadsheet.)

Beginning with a total sample size of 1E+308 atoms of Carbon-14 and zero atoms of Nitrogen-14 we can track the progress of decay (or transition of Carbon-14 to Nitrogen-14) over 1025 half-life cycles of 5,730 years each or 5,873,250 years. (Notice that the process of Beta decay which results in the transition of Carbon-14 to Nitrogen-14 is not the same as the process of fission and the change involves only a decrease in whole Carbon-14 atoms to whole Nitrogen-14 atoms. Thus an end point is reached in 1024 cycles with a starting sample size of 1E+308 at the point their continued division results in less than one Carbon-14 atom.) Also please note that the total number of relevant cycles we can investigate is limited by 1.) sample size (which is in this case 1E+308) and the threshhold of distinction between sample emmissions and background radiation.

(This example isn't very realistic. 1E+308 atoms of C14 has a mass of 2E+282 kilograms. The Earth's mass is only 5E+24 kilograms.)


 * The purpose of this example is not only to show computational or mathematical results of half-life computation but to show the basis for refuting Jclerman's claim that half-life is an infinite rather than a finite process. ...IMHO (Talk) 15:17, 19 June 2006 (UTC)

The personal attack was transferred here
This is not a personal attack but rather being labeled as such in an effort to diminish the truth of what is being said. ...IMHO (Talk) 14:31, 19 June 2006 (UTC)


 * Accusations of lying or deception are personal attacks - please refrain from using such language. Vsmith 15:18, 19 June 2006 (UTC)


 * As with a charge of slander in the real world they are not unless false. ...IMHO (Talk) 02:27, 20 June 2006 (UTC)

You do not own the Half-life article.
''You can not use this article to prevent other users from obtaining a complete comprehension of half-life in the same manner as a member of a trade or artisan guild might try to hide techniques or methods of performing some function. You can not limit an explanation of half-life to only a very technical or mathematical version or explanation of the process. You are presenting half-life decay here in the same way as a tradesman or artisan would withhold a simple explanation from a patron for the sole purpose of mystifying the topic and keeping the ordinary user from comprehending the topic fully. Such censorship can not be permitted. For this reason deletion of example data, compute code, and simple arithmetic, such as the data you have deleted which clarifies the process and results of Carbon-14 to Nitrogen-14 half-life decay is not acceptable. If you continue to practice such vandalism an official complaint will be pursued against you. ...IMHO (Talk) 04:49, 19 June 2006 (UTC)'' See a long discussion of the computations, above,  which had already been moved from elswhere, with contributions from other users. Jclerman 08:03, 19 June 2006 (UTC)

suggestion :
I suggest that, if there are no new arguments and/or facts, we conclude here the current discussion. REMINDER: The fate of the table is being decided together with the fork article, at Articles for deletion/Half-life computation.

I have no objection to deletion of the "fork" article or exclusion of a table based on integer variables so long as the difference between the use of integers and the use of decimal variables and their results in terms of termination versus continuation ad infinitum is acknowledged and explained and that unstable radioactive isotopes are admitted to be mortal on behalf of future readers. ...IMHO (Talk) 15:28, 21 June 2006 (UTC)


 * The problem is that a given atom of an unstable radioactive material can last for an arbitrary length of time. A half-life indicates the probability that an atom may decay within a given period of time; it does not compel the atom to decay&mdash;ever.  The half-life (and associated exponential decay theory) are models and nothing more.  Using an integer representation to imply that it actually is some sort of count is misleading; all that the half-life calculation gives you is an expectation value.  The very small decimal value generated after many half-lives have elapsed represents the small probability that the atom has not yet decayed.  By all means emphasize this fact in the article, but it is flatly incorrect to imply that the use of integers in the calculation will give a result in some way superior, more accurate, or more 'real'.  TenOfAllTrades(talk) 01:33, 22 June 2006 (UTC)

"Validation" section
I think that a practical discussion of how half-lives work in late generations is a great idea; however, this section as it presently stands is pretty rough. Since it appears fairly contentious, I'll post thoughts here for now and hold off on the boldness. In short, this section is better suited to radioactive decay; specifically, as addenda to Radioactive_decay where the distinction between predicted and observed (and the necessity of integral) quantities of substance is already discussed. &mdash; Lomn | Talk 20:54, 21 June 2006 (UTC)
 * 1) The present content simply looks bad. WP:MoS is needed regardless.  Specifically, italics and bold text are overused.
 * 2) Several external references appear superfluous. Most notably, the "this site shows how to program..." is a homework assignment, not an explanation.  I feel the pennies/m&ms links are sufficient for the purpose
 * 3) The soliloquy on "physics is nature, formulas do things, other stuff happens" is far outside the scope of the article
 * 4) Perhaps most importantly, the section fixates on atomic decay and its implications, far more specific than the subject of half-lives at large.

This is the talk page and not the article page. It is inapproriate to apply the rules which apply to articles to discussions of those articles. The fact that half-life may be computed using integer variables to represent discrete decay and decimal variables to represent continuous decay are highly relevant to the article. You need to spend less time in your Ivory tower and more time down here on Earth. ...IMHO (Talk) 02:40, 22 June 2006 (UTC)
 * Please try to remain civil. Snide comments about "ivory towers" and "being on earth" do not help improve the article.  I intentionally did not check authorship of this section so as to avoid possible bias -- it's simply a bad section, in my opinion, as it stands currently.  Because it's contentious, I'm discussing my problems with it here first.
 * As for relevance, I feel an in-depth discussion of the particulars of calculations for integral decay are better suited to articles that focus on integral decay; that is, radioactive decay. Continuous decay isn't particularly interesting (from an expansion standpoint) because it simply mirrors the mathematical definition in all particulars. &mdash; Lomn | Talk 03:01, 22 June 2006 (UTC)


 * There's nothing wrong with the ideas that the section expresses, per se. The trouble is that the text rambles disjointedly and makes little sense.  Furthermore, some of these ideas, such as the one about "validation of physics-math models" don't belong in a specialized article like this one (because it really should keep a narrow scope, even though people keep stuffing it with extraneous goodies).  In fact, it may even be good to write a separate article on validation of physics-math models or something like that, if we don't already have one. --Smack (talk) 18:41, 25 June 2006 (UTC)

Schroedinger's cat
Mentioning it in the "see also" without any pointer within the text of the article and without any "half-life" being mentioned in the cat's article, puzzles readers like myself who wondered what the relationship and purpose of the link was. The proponent should edit the article as to make the "connection" obvious to the reader. BTW, consider that this article is about half-life as the time to reach half of an initial quantity that decreases with time. It was never intended to discuss the timing of the last element because in origin it dealt with decays of very large number of elements. Perhaps a reference to the cat would be more suitable in a more general article about decay. Anyhow, the proponent could try drafting/editing one or both of these approaches, then re-insert the link. Jclerman 19:54, 24 June 2006 (UTC)

major revisions complete
The Half-life computation article has undergone substantial revision which has hopefully addressed everyone's concerns. If you have any further comments after looking at the article again, please list the items you do not like, make whatever comment you have and please be specific and allow time for further revision. If there is any reason I can not comply with your wishes then I will let you know the reason why. ...IMHO (Talk) 12:18, 25 June 2006 (UTC)

Proposed merge
I can see no reason for four articles on this subject. As it stands, we have
 * 1) Exponential decay
 * 2) Half-life
 * 3) Elimination half-life
 * 4) Biological half-life

All four describe the same mathematical process with small variations that could be covered in sections. All the material in #2 is also in #1, except for the "Validation" section and the dubious statement that half-life has a meaning for non-exponential decays. If what is meant is that the term is sometimes pressed into service for elimination processes above the point where the liver is saturated, that should be said more explicitly.

Is there an actual reason for so many virtually-identical articles? I don't see them as focused, just redundant. Robert A.West (Talk) 20:16, 25 June 2006 (UTC)


 * I think a merge of exponential decay and half-life would be okay, and perhaps a merge of biological half-life and elimination half-life. Although they are related, I think merging all four articles into one would not be a good idea. Biological half-life has a lot of content that is specific to it and it would be odd to include it in a combined article. Also, I think a single article might be confusing since there are subtle differences in the terms. I suggest that there be a single talk page for the discussion to take place at. -- Kjkolb 04:19, 26 June 2006 (UTC)

One advantage of a diversity of articles is that each may deviate just slightly enough from another to allow comparisons that make comprehension of half-life computations a lot easier than a single article with the methodology and mathematics condensed into a precise and yet virtually incomprehensible (at least for the layman) result. So long as such an article would include a grade school level explanation with examples for each application then I think it would be a great idea. Here is an example of what I would like to see:

Usage example for the laymen

 * Where p is the percent or portion of Carbon-14 in a sample:
 * $$ p= \frac {1}$$
 * and where n defines the number of Carbon-14 half lives in an archaeological sample:
 * $$ n = \frac{\ln \left(\frac{1}{p}\right)}{\ln \left({2}\right)}$$
 * and where age of an archaeological sample is defined as
 * $$ age=h*n\ $$

Specifically:


 * Where h is the half-life of Carbon 14:
 * $$ h=5730\ $$
 * and the percent or portion of Carbon-14 in the archaeological sample is 25%:
 * $$ p=.25\ $$
 * and the number of Carbon-14 half lives equal to:
 * $$ 2 = \frac{\ln \left(\frac{1}{.25}\right)}{\ln \left({2}\right)}$$
 * then the age of the archaeological sample will be:


 * $$ 11,460 =5730 * 2\ $$  years

...IMHO (Talk) 06:53, 26 June 2006 (UTC)

Also you may wish to look at the extremely wide variety of papers (1,340,000) regarding the application of half-life outside the Wikipedia starting with Google Scholar List of Google Scholar half-life application papers ...IMHO (Talk) 10:23, 26 June 2006 (UTC)

Actually, I think it might be better to keep biological half-life and elimination half-life separate or to name the combined article something like biological and elimination half-lives, so that the terms are not seen as equivalent. Anyway, a discussion about merging half-life and exponential decay was recently concluded at Talk:Exponential decay. The merge was clearly opposed. I think the tags should be removed unless there is something different about this merge proposal. The argument seems to be the same, so I don't know what that would be. -- Kjkolb 11:27, 26 June 2006 (UTC)

The problem is is that application of the concept of half-life is now so diverse that it would be impossible to merge every article that utilized the concept. The Google Scholar half-life list above references over one and a quater million papers. A far better idea would be to classify articles beginning with the basic divisions used for the reference desks maybe even going so far as to incorporate the Dewey Decimal System if not one of our own. Is what I am proposing to classify the entire Wikipedia? Yeah! ...IMHO (Talk) 11:45, 26 June 2006 (UTC)


 * I think that elimination half-life should be retained since it is the correct terminology in pharmacokinetics. Almost all drug-related articles (with Template:Drugbox) link to this page as an explanation of the half-life field in the infobox. I other disagree with the merger generally since, as others have said above, each of these half-life articles concern related, but distinct concepts. Perhaps part of the reason why a merger was proposed was because the biological half-life page is badly in need of a cleanup. -Techelf 11:35, 27 June 2006 (UTC)


 * Merge "biological" into "elimination" or vice versa, but keep the rest. If an article with 'half-life' in the title loses focus, it needs to be trimmed, not merged.  For instance, much of what people try to include into this article really belongs at Exponential decay.  Likewise, some of the content at Biological half-life should probably go under Clearance (medicine). --Smack (talk) 23:43, 27 June 2006 (UTC)

Single place to discuss: RfC?
I know that Request for Comment tends to be a place where people go when they are fighting, but I agree with Kjkolb that there should be a single place to discuss this, and I can't think of a better place to do it. What do others think? Robert A.West (Talk) 11:52, 26 June 2006 (UTC)

Seems like this is as good a place as any unless maybe it would be the science desk or villiage pump proposals. ...IMHO (Talk) 11:55, 26 June 2006 (UTC)

Per Robert A West, RfC is indeed the correct place to ask for additional comment on articles. Just put a short summary of the dispute (in terms as neutral as possible) on the appropriate article dispute page&mdash;in this case, Requests for comment/Maths, science, and technology. For discussing a merger to this article, or any other content issues, this talk page is as good a place as any for a centralized forum. TenOfAllTrades(talk) 12:33, 27 June 2006 (UTC)

I'm for merging Half-life and Exponential decay, tough there's really no reason to cram the others together. The two concepts share significant conceptual overlap, and it would be good for organizational purposes to more clearly destinguish between Half-life and Half-Life. 70.48.151.133 00:50, 28 June 2006 (UTC)

I agree that elimination half-life and biological half-life are similar concepts and could be merged. The inclusion of exponential decay and half-life would however be incorrect. The concepts may be the similar mathematically, they are distinctly different. The exponential decay is a strictly mathematical concept. The concept of half-life again, is a general concept, most widely know for describing radioactive decay, but should not be restrained to such. Finally the biological half-life, which is a mathematical model describing the passage of material through the body. It is not the same as radiological half-life and should not be confused as such. Although the three examples share a common mathematical formula the concepts are unique. Dav1s 75 00:41, 13 April 2007 (UTC)

Graph
A graph should accompany the chart in the intro. — Omegatron 23:07, 15 September 2006 (UTC)


 * There is a graph at Exponential decay, to which this article refers as prominently as it can without being unseemly. As for the chart, I still think that we should remove it. --Smack (talk) 03:25, 17 September 2006 (UTC)


 * By what logic? — Omegatron 17:01, 17 September 2006 (UTC)


 * Because the table actually tabulates exponential decay. This article is supposed to be narrowly focused on half-life, to avoid duplicating exponential decay more than necessary.  I'm partly inclined to resolve your objection backhandedly by moving the table to that article, which has a graph but no table. --Smack (talk) 00:20, 18 September 2006 (UTC)


 * I don't understand why you think that. Both should be in both. — Omegatron 00:42, 18 September 2006 (UTC)


 * Seems there's room for both in both, why the limitation? The graph 'tho seems a bit misleading as it shows the first two lines aparently zeroing out rather than approaching zero asymptotically (is that spelled right, looks wierd?) - may be a resolution problem. Vsmith 01:19, 18 September 2006 (UTC)


 * It's not a resolution problem; the lines do actually disappear when they hit the x-axis.
 * I don't like the idea of "both in both." We have "room" (Wiki is not paper) to put the entire Exponential decay article here.  But we don't – why? --Smack (talk) 03:55, 18 September 2006 (UTC)


 * Ok. After that, we'll also have to take the space shuttle pictures out the NASA article, the Arc de Triomphe pictures out of the Paris article, the lightning picture out of the electricity article, ... — Omegatron 04:44, 18 September 2006 (UTC)

What is the point of this article?
Pictures of the space shuttle belong in NASA, because NASA is a major topic that relates very closely to the space shuttle. Half-life, however, is not a major topic. It's a scrappy little topic, subsidiary to Exponential decay. However, someone casually familiar with scientific literature could easily fail to realize this. People tend to use the word 'half-life' without explicitly referring to exponential decay; the former has become a metonym for the latter. (If you doubt me, just compare the two articles' Whatlinkshere pages.) Noting this fact, let's consider how we can distribute content between the two articles.


 * 1) I find that this situation smacks of Category:Redirects from related words: the same way that we redirect Atheist to Atheism, we might consider redirecting Half-life to Exponential decay.  But the terms differ too much for us to do that.
 * 2) Discuss the topic extensively at Exponential decay.  Since half-life is a scrappy little topic, give it a scrappy little article, and send people to the longer article if they want to know more.
 * 3) Discuss the topic extensively at both places.  This would create the nightmare task of keeping information synchronized between two long articles.  I hope nobody actually espouses this option.
 * 4) Discuss the topic extensively here, and keep a stub at Exponential decay.  I abhor this option.  I believe that populistically substituting a commonly-used name for the correct name compromises our scientific integrity.

Each approach has its problems, of course, but I'll assume for the sake of argument that everyone agrees with me that option 2 has the fewest. That leaves us with the problem of how best to implement it. Note that, because of the metonymic usage, many people go looking for Half-life when they actually want to know about Exponential decay. Thus, we need to make it clear that there's more information outside this article. Which leads me to the point I've been trying to make all along: the more information we have here, the more likely people are to think that this is all we have. --Smack (talk) 16:52, 18 September 2006 (UTC)


 * Sure, there are related articles and some should be merged/changed into disambiguation pages. But which ones?:


 * Half-life
 * Half-life (disambiguation)
 * Radioactive decay
 * Exponential decay
 * Elimination half-life
 * Biological half-life
 * Effective half-life
 * Half-life of knowledge
 * Reaction half life
 * Context-sensitive half-life
 * Maybe merge Half-life's content into the appropriate articles, move Half-life (disambiguation) to Half-life, given a sentence or two of description, and then link to all the various field-specific meanings?
 * Otherwise, merge all the field-specific meanings into Half-life. We definitely shouldn't be duplicating content.  (But we should duplicate images and graphs where appropriate.) — Omegatron 17:50, 18 September 2006 (UTC)


 * RE: "the more information we have here, the more likely people are to think that this is all we have"
 * Using that line of reasoning, one should keep only the simplest explanation here - including the simple table - and remove all the complex math to the exponential decay article - rather than arguing for removal of the simplest material --JimWae 18:23, 18 September 2006 (UTC)


 * I think that all of the specific half-life articles represent the metonymic usage that I'm talking about. They should be dicdefs referring the reader elsewhere.  For instance, Biological half-life should point to Clearance (medicine).
 * JimWae: I have judged successive additions to this article by how much they relate specifically to half-life, as distinct from exponential decay. I have let the specifically half-lifey things stay, and tried to remove the others.  You have a point, but I can't say offhand which approach I like better. --Smack (talk) 18:40, 18 September 2006 (UTC)

Simplified Formula
The formula:

$$N = N_oe^{- \lambda t} \,$$

could be simplified to: $$N = \cfrac{N_o}{2^{(\cfrac{t}{t_\frac{1}{2}})}}$$ by substituting the value of lambda in terms of half-life:

$$\lambda = \cfrac{ln 2}{t_\frac{1}{2}}$$ Just wanted to know if you wanted to include it somehow.

—Preceding unsigned comment added by 69.223.47.102 (talk • contribs)


 * Why would we want to do that? I think that that version looks awful.  We could fix up the TeX markup like this:


 * $$N = \cfrac{N_o}{2^{\left(\cfrac{t}{t_\frac{1}{2}}\right)}}$$


 * but then it still look pretty wonky. --Smack (talk) 20:15, 1 December 2006 (UTC)
 * $$N(t) = N_0 2^{-t/t_{1/2}}. \,$$ in the article exponential decay where both formulae are shown, and their scaling is mentioned.
 * lambda has physical meaning. Don't change this article. --Jclerman 05:13, 2 December 2006 (UTC)
 * I don't think the way it looks matters, but if the formula works, it should be changed. --199.43.172.254 14:13, 19 March 2007 (UTC)
 * Nonsense. You are not a physicist, sure. Go change E = m.c.c; it's simpler because doesn't need superscripts and "it works". Jclerman 01:19, 21 March 2007 (UTC)