What I am looking for is not when an isotope after initial set up will have only the quarter or initial amount left.
What I am looking for is the half time of a half life.
It is NOT the time after which 1/4 is gone.
Suppose 1/4 were the ratio (we are looking for an irrational proportion, really, I will be giving rational approximations). Then after another such time you would not again take away 1/4 of initial amount, but only 1/4 of new amount after first of it. So, 4*4 = 16. Take away 1/4 of 16, you are left with 12. Take away one quarter of that, this time it is three, you are left with 9. Instead of getting 8/16 after the halflife you would be getting 9/16 after the time, which in that case would not merit the name of halflife.
So, what is taken away after half of a halflife is perhaps 1/3? 3*3=9. First take away 3 of them, then 2 of them. You have taken away 5/9 and are left with 4/9. Which is not what a half life is supposed to land you with.
Now amount taken away after half a halflife must be between 1/4 and 1/3.
24*24 = 576
7/24 * 7/24 =
289 and 287 are far closer proportionally than 4 and 5 or 7 and 9.
We have taken away too much. But not so very much too much as previously. So, at half of a half life, a bit less than 7/24 is gone, a bit more than 17/24 is left. I thought until checking. Of course people dealing with radiometric dating known exactly what ratio would be left after the half of one halflife. Now, one way for an ordinary person to find out without asking them is using a calculator. If you push 0.5 and then the root sign, you get:
And if you multiply that by itself you get back to 0.5, whereas 17:24 gives:
Meaning that 17/24 is actually a bit too much for the half of a halflife. Here is the square of it:
Which, as you see, is a bit more than one half.
Now, the point is, when we deal with isotopes having very long half lives, we will not be measuring the half life directly. For C14 we might be measuring the half time of one halflife directly. Suppose C14 levels have not been rising, and - given the halflife usually given for it - the time for finding 7/24 as much as in today's atmosphere (or a bit more than that), would be around historically known material from say wood beams from one city built and soon after abandoned or a wooden statue of known origin or so around 500 BC / 1000 BC. Why? Because the half life is usually given for a measure between 5000 and 6000 years. That means that - supposing C14 levels are not rising but fluctuating and we ignore that for now - we can calibrate C14 method on known historical material.
Can we calibrate it on laboratory samples revisited after a few years? Hardly. Obviously still less possible for isotopes far longer in half life than C14.
Next half life is Americium-243 which is cancer hazardous - very lucky we do not have much of that clock around us - or Curium-245, which is artificial and was not present before. For 20.300 years we have Niobium-94.
The three largest producers of niobium ore are mining pyrochlore deposits. The largest deposit in Brazil is the CBMM mine located south of Araxá, Minas Gerais, followed by the deposit of the Catalão mine east of Catalão, Goiás. The third largest deposit of niobium ore is Niobec mine west of Saint-Honore near Chicoutimi, Quebec.
Pyrochlore ore typically contains greater than 0.05% of naturally occurring radioactive uranium and thorium.
Niobium is also present in columbite:
See map at the bottom. Click "show list of localities". I have not recognised any of the localities where fossil species are found on that list. Nor any locality with obviously datable archaeological import, where artefacts can be known from history. Even ignoring that 10.150 years ago is not exactly history either to a YEC or to an Evolutionist. To the one it is a false date pre-creation, to the other "pre-history". But I do not even know of carbon dated bones or trees from those areas which would give us a hint if 7/24 of original content of Niobium-94 was gone. So it is not a great idea to say the half life of even Niobium-94 has been measured by checking a sample old as half of its half life against some several halflives of Carbon 14.
This is even supposing the measurable halflives of Carbon 14 do not get us back beyond the time of its presence on an even level in earth's atmosphere.
You see, the even level of Carbon 14 depends mainly on the balance of two factors: the cosmic radiation which is building it up and the radioactive decay which is pulling the level down. Suppose at any point of time levels were above the balancing level, it would decay faster than getting renewed and approach the balancing level. Suppose on the other hand it were at any point lower than the balancing level, it would build up faster than it decayed and approach the balancing level. This is so because the level of decay is not a constant per se, but a percentage of the total amount.
This means that the Young Earth Creationist standpoint on Carbon 14 is that dates "older than creation" (like pretty obviously post-flood Göbekli Tepe being dated 15.000 years or something before present) only point to the fact that when organic material was alive, the Carbon 14 level was not yet completely up to the balancing level but still rising and still at a lower level.
That in its turn means that if you obtained 17/24 of present Carbon 14 level in a historically dated remain of organic material from the millennium before Christ, this could EITHER mean that the time from when it was alive to the present was half the time of a half life OR that if Carbon 14 was still building up (and historical dating is sure, like being the traditional date, not doubted by historians) the half life is longer.
But on the other hand if instead it is history that is reassessed according to Carbon 14, and it was in the buildup, that would imply that historical material would be carbondated as too old and the history unduly rewritten. I think the carbondated age of Troy VI (?) is one hundred years older than the historical date of the fall of Troy. But what if instead another one of the Troy cities on top of each other was the real one, then the carbondate would be even further off than 32:31. As late as 1000 BC.
Now this has consequences for our ability to calibrate longer halflives on carbondated material.
Now we come to a page quoted by David Palm, the one with the eight questions from 1909. In the bottom it linked to another page* with supposed evidence for an old earth. I refuse to quote Ratzinger and Wojtyla or even the slight misrepresentation of what Pius XII' Humani generis amounts to. We go to its main number of scientific argumentation, or what seemed to me to be the main number, and I will intersperse the quotes with my critical comments:
The half-life of an element (if you remember from your high school or college chemistry courses) is the time it takes for one-half of the atoms of an unstable element or nuclide to decay radioactively into another stable element or nuclide.
The other element need not per se be stable. It could be another isotope of radioactive material with another half life.
When we strike from the list every nuclide that is continually produced by natural processes,
Meaning obviously Carbon fourteen (14C). Plus any element formed by radioactive decay.
[When we strike from the list etc.] we are left only with those that persist from the date of the formation of our solar system (from Kenneth Miller, page 69-72). What does this list tell us?
... 244Pu 8.2 x 107 yes (and so on for all above)
146Sm 7.0 x 107 no (and so on for all below) ...
As seen above, every nuclide with a half-life less than 80 million years (8.0 x 107) is missing from our region of the solar system, and every nuclide with a half-life greater than 80 million years is present. That means the solar system is much older than 80 million years, since the shorter-lived nuclides have simply decayed themselves out of existence. Since a nuclide becomes undetectable after about 10 to 20 half-lives (Dalrymple, page 378), multiplying 80 million times 10 (or 20) gives us about 800 million years (or 1.6 billion years). The earth must be at least that old since these nuclides have disappeared from nature.
A very relevant question would of course be, whether they ever were present in nature. The Pink Unicorns must have reached a total of thirteen since they were able to form a coven and make themselves invisible ... which we know since we see no Pink Unicorns. Wait ... there might have been no Pink Unicorns there in the FIRST PLACE?
But if we get to the bottom of this list, we get to "154Dy 1.0 x 106 no".
Even the least of all these half lives is one million years.
How do you measure such a half life? The half lives of Zirconium 86, 88 and 89 are very short.** The half life of Zr-93 (which is on the no-part of the list above that I am not quoting in full) is 1,530,000.0 years. Isotopes 95 and 97 are also with short halflives. But five isoptopes of Zirconium are stable. So, if 93 has such a long halflife and does not form and is therefore absent from nature, how do we get at it having existed? Zirconium 87 is not enumerated among the isotopes. Thus we have no need to assume 93 must have gotten away because it is not there. It could like "Zirconium 87" not have been there in the first place.
And the same applies to the other ones on the list. We have thus no scientific ground in the number of isotopes present or absent or in their halflives to assume earth older than 800,000,000 years.
The long halflives are also relevant for other datings that contradict Genesis as taken literally as history - which according to questions 1 and 2 from 1909 we must do. They are not the only relevant factor for such datings, but they are one of the factors. I do not know how they were measured. I do know that of such long halflives not only is there no sample measured before and after a full halflife, as with Carbon 14 anyway, but not even a sample with calibration on half of a halflife or quarter of it.
Bpi, Georges Pompidou
St Tatiana of Rome, Martyr
[Appendix A:] Bill Nye*** when "answering" Marco Rubio claimed Rubidium Strontium transmutation has had its speed measured by watching it in laboratories for "sometmes as long as fifteen years just to get it exactly right". Obviously that gets nowhere near the kind of certainty we can have for Carbon dating the last two thousand years when it can be checked against historically certain objects.
Appendix [B]: By "Quarterlife," bad as the term is, I meant "when a quarter is gone and three quarters left" = half of a half-life, when one half is gone and one half is left. But half that time corresponds rather to the diminution of "71 %" on copy machines, like A3 > A4. Not to the 75% that two quarters are. Here is a little table, using also the calculator results, which will give the different approximations and show their respective exactness:
- (3/4)2 = 9/16 =
- (17/24)2 = 289/576 =
- (577/816)2 = 332,929/665,856
- (12/17)2 = 144/289 = 288/578 =
- 1/2 = 0.5 =
- 288/576 = 289/578 = 332,928/665,856
- 3/4 = 75%
- 17/24 = "71 %" =
- 577/816 = "71 %" =
- 12/17 = "71 %" =
- sqrt(1/2) = "71 %" =
* Evidence for Evolution and an Old Earth
subtitled: Evidence for Evolution and an Old Earth, a Catholic Perspective
** Bentor, Yinon. Chemical Element.com - Zirconium. Jan. 12, 2014
*** The video: CRUClEFICTION : Bill Nye: Creationism Is Just Wrong!