Talk:Half-life/Archive 2

Archive 1

Archive 2

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. ManInStone

Probability of decay - decays per time - is directly related to half-life. --Vuo 10:00, 18 May 2007 (UTC)

Regularity

I believe the concept of half-life is only useful if there is some regularity in the decline. If a stench is half as powerful after one day, but takes another week to again be half as powerful, it is useless to talk about its half-life. Similarly if the same stench sometimes takes a week for the first halving --JimWae 00:03, 28 October 2007 (UTC)

You are entitled to YHO (your humble opinion), but we must use the terms as defined and standardized. One point is that we don't know what is regular? A continuous function? A monotonic function? BTW, your example is not too different of how pharmacologic agents behave, however they are characterized by a "half life" that can be qualified "biologic", etc, as you can find even in the Wikipedia. Read also the articles about reaction rates, reactions of different order, etc, and you'll find their corresponding half life. Only in the case of exponential decay the same proportion decays for each successive half-life. You can also look up the past histories of all half life related articles and see that your POV has already been argued in the past. Jclerman 02:45, 28 October 2007 (UTC)

I am well aware of all that. Perhaps a better example would help. Does a snow-melt also have a half-life? We certainly caould measure the height as 4 metres one day & 2 metres 2 weeks later. Are we justified in any expectation that 2 weeks hence it would be 1 metre? Would we also say snow-melt has a half-life just because we once determined how long it took to decrease by half? Regularity is any regularity in which the rate of "decay" is constant - not fluctuating --JimWae 03:16, 28 October 2007 (UTC)

It doesn't appear you are aware of the article rate equation. Four half-lives follow, for different rates of decay. Only the second one shows a half-life constant, i.e., independent of the initial value Ao. That is what you imply with your definition and examples of regularity. That only for an exponential decay the half-life is constant, doesn't imply that half-lives which vary with time can't be defined and accordingly measured. And the definition is general, not only valid for chemical reactions of different order, but for processes not defined by those rate equations. That you don't find such a non-constant half-life useful, doesn't mean that it's incorrect.

From the article rate equation (see the article to identify the rate orders and more info):

• $t_{1/2}={\frac {[A]_{0}}{2k}}$
• $t_{1/2}={\frac {\ln(2)}{k}}$
• $t_{1/2}={\frac {1}{[A]_{0}k}}$
• $t_{1/2}={\frac {2^{n-1}-1}{(n-1)k[A_{0}]^{n-1}}}$

Jclerman 07:16, 28 October 2007 (UTC)

Alright, not "constant" then. I will return to my original choice of word: regularity (describable over some period of time by some equation or other) - not completely haphazard (o/w there'd be no predictive value). Unless we are prepared to say that ALL "decreases in value" are describable by some law. As the article stands ("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") it would seem to be OK to apply the term half-life the first time the price of something is halved - but there'd be no predictive value and no reasonable person would be prepared to defend the claim that something HAS a half life, unless there is an expectation of SOME kind of regularity that can be used to predict a future value. --JimWae 20:51, 4 November 2007 (UTC)

again the table?

The table, as of today, is the result of natural selection. See the previous discussions. And don't repeat entries like 1/8, don't supress the ... row (a good high-school teacher should have taught you why such a row). Etc. If you have reasonable reasons to modify the table, read the preceding discussions and propose changes here. Jclerman (talk) 18:42, 20 January 2008 (UTC)

There was no ... row before my edit and I have no objection to a ... row. The row I added for 10 was mistakenly left with 8 in the left column, and that should just be corrected to 10. I think my additions were very reasonable. After reading the preceding discussions, there seems to be a lot of arguing, much of which does not make sense, as well as some extreme positions like refusing to allow any table or having a table with 1000 rows. I'm not sure what you mean by "natural selection". Do you have any specific objection to the rows I added? --JWB (talk) 04:34, 21 January 2008 (UTC)

I like the idea of having some powers-of-ten fraction-remaining entries, but I don't think it should be in the same table as the powers-of-two. Both are useful ways of looking at the effect, but both are different ways. Having them interleaved (both sets of entries in order in a unified table) makes it hard to see either trend clearly and putting one after the other in the same table gives an out-of-order list. DMacks (talk) 21:42, 21 January 2008 (UTC)

I don't object to having separate tables, although I don't think it makes much difference. I'll try doing separate tables now. --JWB (talk) 22:00, 21 January 2008 (UTC)

• The reason the (now 1st) table only went up to 7th HL was that it showed that there was less than 1% then (or did when percentages were still displayed). The new table omits the 1% mark (a mark many find remarkable) & probably has too much precision for a process that can be a bit "uneven"
• I also still think the definition given is now too broad - there needs to be some mention that the decay follows some kind of regular (& thus predictable) pattern -- otherwise we could claim to talk sensibly about the half-life of some shares on the stock market --JimWae (talk) 23:40, 21 January 2008 (UTC)

Reverted 2nd table. Seems to just add clutter and the indicated precision was over the top. The decay curve fits the power of two (or 1/2) and is much simpler, more elegant and easier to explain and develop for people learning about the subject. The powers of ten table is quite redundant and 9.96578428 half lives(??) nine significant figures - no way. Seems the % column has vanished - it was illustrative and sufficient as a decimal comparison. And yes the ... row was essential. Also replaced N with n as representative of the nth half-life, more consistent with math nth term and N has other uses or meanings in science. Vsmith (talk) 00:25, 22 January 2008 (UTC)

Powers of 10 and percentages are what are used in real-world applications, and it is good to provide a few example conversions to them. Of course it does not come out to an exact power of 2, but the 2¹⁰≈10³ and 2^3.33≈10 estimates are very useful, and should be demonstrated, and the Avogadro's number example is also relevant to physical examples. If anything, this is actual data which is informative, while repeated entries of k halflives: 2^-k are predictable and trivial. The number of significant digits can be whatever consensus determines and is not a valid excuse for deletion of the table. --JWB (talk) 09:47, 22 January 2008 (UTC)

Trivial? all is trivial :-) Actual data - no again, just trivial calculator punching. I would see no problem with an added percentage or decimal fraction column added to the table.

If you want to add a referenced section on real world applications that should be acceptable - and please explain the use/relevance of 1/N (Avogadro's number) beyond the triviality(?) of approaching zero. As for significant figures, if we have real measured data significant figures show the precision of the measurements - but for simple calculator playing, as we seem to be doing here, 3-4 decimal places should be adequate. Again please enlighten us on the published real world data/applications. Cheers, Vsmith (talk) 12:54, 22 January 2008 (UTC)

The previous commenter wanted the decimal entries to not be interleaved with the binary ones, so I changed to a separate table, now you insist that they be interleaved. Please come to some consensus on interleaved vs. separate and I'll be glad to go along, but it is no excuse for deletion of the data itself.

Again, I have no objection to 3-4 digits of precision, but is somebody else going to complain about that now? This time I would like some consensus first before changing. The only difference between a computation and physical data is that the error term is zero in this case and does not need to be listed. There is no difference that dictates leaving off precision in the mathematical case and not the physical case; if one had to make a distinction, it would be the opposite, as physical data does have some error. There is no shortage of column width in the table to hold the previously given number of digits since the column heading is already that wide, so you have no rational grounds for objection.

It is disingenuous to claim that knowing a particular logarithm with arbitrary precision is as trivial as knowing the number 2. One requires looking up, one does not. However, if one accepts your contention that they are equivalent, there should be no objection to presenting both. --JWB (talk) 18:20, 22 January 2008 (UTC)

Are we talking past each other here? Disingenuous? They both simply require using and reading a calculator display.

I've added a column for percentage representation (digital) for comparison and to show the rapidity in reaching values <1% as suggested above.

I'm still waiting for the real world applications - especially for N. As for the only difference between a computation and physical data is that the error term is zero in this case and does not need to be listed, we do have a different view of what's going on...

Again, to me the function of the table serves to illustrate the simplicity of exponential decay and it works for my students - some of whom have no exposure to the concept and wouldn't know a log if it bit 'em. Vsmith (talk) 19:13, 22 January 2008 (UTC)

Deja vu, in fact "deja said". Sometime ago I said that Vsmith's sound understanding and exposure of the issues discussed and how to convey them to his students reflects that he is an outstanding teacher and IMHO his classes should be broadcast for the benefit of many. "Less is more": his approaches to logs, powers of 2, and number of significant figures remind me of the approaches of Evans (British physicist, ca 1960) and Tukey (US statistician and mathematician, ca 1980). Please, leave the table as it is as of today at 4 pm MST. Saludos, Jclerman (talk) 23:33, 22 January 2008 (UTC)

Decay to nonbinary fractions

Such a new section should have been discussed here before inserting in the article. In fact, the topic it has been extensively discussed above. It doesn't add meaning and it's not perceptually functional. More than 3 significant figures appear as chaos to human brains. In fact, both Evans and Tukey (a physicist and a mathematician-statistician, see above) have done significant research using 2 significant figures. 'Less is more' Jclerman (talk) 14:19, 1 February 2008 (UTC)

Are you really suggesting that all data in Wikipedia be truncated to 3 significant figures? Please feel free to propose such a policy. In any case, I've already said above that I'm flexible on the precision issue.

I think you are missing the difference between exposition of a mathematical concept like exponential decay, where any actual numbers used may as well be as simple as possible for clarity, and specific applications where quantities are very much relevant. The article is not limited to the former; if anything, some of the abstract material might better belong in the Exponential decay article (in fact, looking there, much of the content of this article is duplicating that article, and could be removed from this article), and Half-life should have the specific applications. --JWB (talk) 08:44, 2 February 2008 (UTC)

Any more objections? --JWB (talk) 08:44, 13 February 2008 (UTC)

As stated previously: If you want to add a referenced section on real world applications that should be acceptable... However, that does not mean the re-addition of original research/calculator playing in the form of tabulated nonbinary fractions.

Also, we're still waiting for an explanation of the use/relevance of 1/N (Avogadro's number) beyond the triviality(?) of approaching zero. Please provide an explanation based on published reference.

Vsmith (talk) 16:08, 15 February 2008 (UTC)

Several sections of the current article are composed of calculations that are not only unreferenced, but duplicates from the Exponential decay article where they are more appropriate. By your standard of requiring references even for mathematical discussion of uncontroversial facts, they are even less worthy of inclusion in the article. As above, I suggest that they be removed and replaced with a link to Exponential decay and that the article be reoriented towards applications. Also, please cease using pejorative terms like "triviality" and "playing" which would apply equally to these sections.

Question 10 of [1] is one source mentioning decay from one mole to one atom.

I would be glad to add examples for decay of well-known radioisotopes like Cs-137. Are you also going to object to these, saying that the phrasing is not identical to published sources or the number of halflives in examples are not identical to published sources? --JWB (talk) 17:04, 15 February 2008 (UTC)

Your source is a quiz or worksheet from a high school class. Sorry but, www.pkwy.k12.mo.us is not a reliable source. This is getting quite absurd. How about some published sources? Vsmith (talk) 19:02, 15 February 2008 (UTC)

I can keep looking, but the source shows it is a topic of interest. Are you saying that no calculations are allowed in Wikipedia unless they are taken verbatim from a scientific publication? That would be plagiarism, not writing an encyclopedia article. That is absurd, plus you are not complaining about all the other unreferenced equations in the article. --JWB (talk) 20:00, 15 February 2008 (UTC)

Lambda

The frequency response for electronic circuits is tau, not lambda. The article suggests that lambda is the variable used. However it could mention that lambda is the one used for wavelengths. I am not familiar with wiki rules of edition, so I thought I'll just discuss that here and see if the modification is needed or if the note was justified. 88.169.112.155 (talk) 21:07, 29 May 2008 (UTC)

At least three incorrect and/or not relevant statements above. Jclerman (talk) 09:01, 30 May 2008 (UTC)

-Is there any talk about half life of non 1st order reactions? I can't seem to find them maybe under a different heading

Yes. There is a full article with different reaction rates in their own article, rate law? Jclerman (talk) 03:14, 26 June 2008 (UTC)

Verbatim, from the article: * For non-exponential decays, see half-life in the article Rate equation".

Jclerman (talk) 03:21, 26 June 2008 (UTC)

Decay width

Hi, it is difficult to find an explanation of "decay width" on the Wikipedia.--Mr Accountable (talk) 13:41, 20 July 2008 (UTC)

Restructured for novices

I restructured this page - no content was added or removed. I simply re-ordered the sections so that the least technical sections now come first. This will be a great improvement for novices and non-math whizzes like me. I also believe that this is wikipedia policy (that is, non-technical sections first).

216.57.220.87 (talk) 23:00, 25 August 2008 (UTC)

Add section: Calculate Half-life From Test Data

I came looking for a formula or algorithm for calculating half-life (or doubling-time) from two pair of lab test data.

Wiki "Doubling-time" provides the following:

Given two measurements of a growing quantity, q1 at time t1 and q2 at time t2, and assuming a constant growth rate, you can calculate the doubling time as

   T_{d} = (t_{2} - t_{1}) * \frac{\log(2)}{\log(\frac{q_{2}}{q_{1}})}. 

Someone better than I, please add the equivalent inverse for Half-life = f( n1,n2,t1,t2) here. Thanks HalFonts (talk) 16:46, 19 May 2009 (UTC)

Usage In Practical Applications

This is a request - sorry I cannot contribute myself on this topic. I have children who want to understand Half-Life, but they cannot relate to the content on this page easily. A small section on the practical applications of using Half-Life measurements would go a long way in helping them learn this facinating topic, and others in future. Jcmeredith (talk) 07:42, 20 June 2009 (UTC)

This is a great idea, but I ran into strong resistance from other editors when trying to add anything other than mathematical definitions redundant with the Exponential decay article. --JWB (talk) 23:22, 21 June 2009 (UTC)

Thank you for trying anyway! Jcmeredith (talk) 11:02, 26 June 2009 (UTC)

Why half-life? Why not whole-life?

Can I suggest that the page does not answer the basic, very simple, question that I'm certain is in the minds of a huge percentage of readers when they come to this page:

Why half-life? Why not whole-life?

Why do scientists not refer simply to the life-time, or decay-time, of things, rather than to the half of those values?

Could someone in the know please answer this question in lay terms. Right at the top of the page!

Cricobr (talk) 00:17, 1 January 2010 (UTC)

'Cause there ain't no "whole life". OK, it's math, an exponential function approaches zero - but never gets there - just closer and closer .... So whole life is undefined in such a system. Realistically for a finite number of items, after about ten or so half lives there is too little left to measure, but there's still some there - just gets lost in the background noise. Yeah, that probably wasn't what you were looking for, but for things undergoing an exponential decay it's what happens. Happy New Year! (still 3.5 hours to go here - and it'll get here 'cause it's not an exponential function :-) Vsmith (talk) 02:38, 1 January 2010 (UTC)

Half life is a hard concept to understand. —Preceding unsigned comment added by 64.38.92.21 (talk) 05:51, 27 January 2010 (UTC)

No it isn't. Half-life is the time needed for half of a sample to decay. What's hard to understand about that?

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