Atmospheric Argon-40 and the Total Radiogenic Decay Budget

"There is far too much Ar⁴⁰ in the earth for more than a small fraction of it to have been formed by radioactive decay of K⁴⁰.  This is true even if the earth were really 4.5 billion years old.  In the atmosphere of the earth, Ar⁴⁰ constitutes 99.6% of the total argon.  This is around 100 times the amount that would be generated by radioactive decay over the hypothetical 4.5 billion years." — Harold S. Slusher, Institute for Creation Research, 1973 and 1981¹

"The ⁴⁰Ar inventory of the atmosphere equals total ⁴⁰Ar outgassing during Earth history." — Michael Bender and colleagues, PNAS, 2008²

"To summarize the heat problem, we have several lines of physical evidence for volume cooling having occurred, and there is at least one promising theoretical approach we can try.  When we can devote more time to the problem, we may see good progress on it." — D. Russell Humphreys, RATE volume II, 2005³

Summary

Argon is 0.934% of dry air by volume.  Almost all of it is argon-40, and argon-40 is what potassium-40 turns into when it decays.  That makes the atmosphere a single, planet-sized collecting jar for one radioactive decay product.  Nothing resets it.  There is only one of it.  Count the argon and you have counted the decays.

This article concludes that the atmospheric argon inventory is the strongest quantitative argument against a six-thousand-year Earth that this project has assessed, and that the young-earth literature has no answer to it.  Four points carry that:

1. The number is a measurement, not a model. Multiply the mass of the dry atmosphere by the argon mass fraction by the argon-40 fraction and you get 1.649 x 10¹⁸ moles. Three independent published figures agree, the closest to within 0.06%. The arithmetic is worked in the open below.
2. It cannot be primordial. The Genesis spacecraft caught solar wind and brought it home. Its argon-40 to argon-36 ratio is at most 4.6 x 10^-4, against 298.56 in air. If every atom of atmospheric argon-36 arrived carrying that much argon-40, the primordial share of the air's argon-40 would be 0.00015%.
3. Six thousand years of present-rate decay cannot build it, and the cleanest version of that statement uses no Earth model at all. Bender and colleagues measured the modern argon-40 degassing flux from air trapped in Antarctic ice: 1.1 x 10⁸ moles per year. Run that for 6,000 years and you get one part in 2.5 million of what the air holds. Because the flux is measured rather than modelled, the one genuinely soft number in this subject, the Earth's bulk potassium content, cannot rescue the young-earth position.
4. The one young-earth engagement with this is a mis-transmission, and it can be traced to its source. Harold Slusher wrote in 1973, and again word for word in 1981, that the air holds about 100 times more argon-40 than 4.5 billion years of potassium decay can make. The true figure is about 0.47 times. His own reference note points at Melvin Cook, Prehistory and Earth Models (1966), p. 67 — and Cook says something different. Cook says the Earth's initial potassium-40 content would have to be 100 times greater than today's. That is a statement about potassium, not about argon. Cook's own arithmetic on the facing page gives a shortfall of 4.4, not an excess of 100. Henry Morris reprinted the claim for a popular audience in 1974 with the hedge "assuming Cook's calculations are right."⁴ Nobody checked. Brent Dalrymple corrected it from outside in 1984, and in the fifty-three years since Slusher first printed it, no young-earth publication has cited, repeated, or corrected it.

Where the young-earth side is right about something.  The Earth's bulk potassium content really is uncertain, from about 150 to 280 parts per million in the current literature, and the low end was proposed by mainstream geochemists precisely because the argon budget is awkward.  The mainstream degassing story also has an admitted hole: the missing half of the argon is usually parked in an undegassed lower mantle, and Bender's own paper says that position "is problematic to maintain" against the seismic evidence.²  Both are real.  Neither helps, because the gap to be closed is a factor of a million, not a factor of two.

Where accelerated decay does and does not bite.  Making the atmosphere's argon in one year releases about 2 x 10³⁰ joules of heat from potassium-40 alone.  That is a genuine problem, but it is not a new one.  RATE concedes the heat problem in print and treats it as unsolved.  The sharper problem is transport.  Speeding up decay speeds up production.  It does not speed up diffusion, melting, or volcanic degassing.  Argon made inside a feldspar crystal still has to get out of the crystal, out of the rock, out of the crust, and into the air.  Doing that for the whole silicate Earth in one year flatly contradicts the retention premise of RATE's own flagship Fenton Hill argument, which needs radiogenic gas to have stayed put.  No young-earth publication has been found that notices the tension.

Every source this article rests on is catalogued, with what it measured and which way it cuts, in a companion page: the literature.

What is actually in the air

Start with the measurement, because everything else is commentary on it.

Three numbers do the work, and all three come off instruments.

Both of the first two were re-fetched and read for this article rather than taken on trust, because the whole inventory rests on them.  Trenberth and Smith's abstract, read off the American Meteorological Society's own full-text page, states "the dry air mass as 5.1352 ± 0.0003 x 10¹⁸ kg."⁵  The 1976 standard atmosphere is a scanned government document whose text layer is unusable, so page 3 was rendered at 600 dpi and read.  The running head is "DEFINING CONSTANTS AND EQUATIONS | 3", the table is "TABLE 3.—Molecular weights and assumed fractional-volume composition of sea-level dry air", and the argon row reads "Ar 39.948 .00934".⁶  Summing molecular weight times fractional volume down all ten rows of that table gives 28.96443 g/mol, which is the standard mean molar mass of dry air to five figures.  So both constants check, and the second one checks against itself.

Now the arithmetic.

The argon mass fraction of dry air is the mole fraction times argon's molar mass over air's molar mass:

0.00934 x 39.948 / 28.9644 = 0.01288

So argon is 1.288% of the atmosphere by mass, and the total is

0.01288 x 5.1352 x 10^18 kg = 6.615 x 10^16 kg

Split that by isotope.  From ⁴⁰Ar/³⁶Ar = 298.56 and ³⁸Ar/³⁶Ar = 0.1885 the atom fractions are ⁴⁰Ar 0.996035, ³⁸Ar 0.0006289, ³⁶Ar 0.003336.  Weighting by atomic mass gives argon-40 as 0.996399 of the argon by mass, so

6.615 x 10^16 x 0.996399 = 6.591 x 10^16 kg = 1.649 x 10^18 mol

That is the whole calculation.  A hostile reader can redo it on a phone.  The script that produced it, with every constant carrying its source in a comment, is at research/argon-budget.ts.

Three independent confirmations, none of which was used to derive it.  Bender and colleagues give the atmosphere's argon content in Table 2 of their 2008 PNAS paper as 1.65 x 10¹⁸ mol, which agrees to 0.06%.²  Ozima and Podosek's standard graduate textbook⁸ gives 1.7 x 10¹⁸ moles, agreeing to 3%.⁸  Dalrymple, writing in 1984 with older decay constants, gives 6.6 x 10¹⁹ grams against the 6.591 x 10¹⁹ g computed here, agreeing to one part in a thousand.⁹

Four routes, four agreements, one number.  This is about as settled as a quantity in geochemistry gets.

Why that argon has to be radiogenic

The suspicion that atmospheric argon is a decay product is older than potassium-argon dating and is its historical foundation.  Carl von Weizsäcker proposed in 1937 that potassium-40 decays two ways, to calcium-40 and to argon-40, partly because there is far too much argon in Earth's air compared with the other noble gases.  Andrew Snelling, writing for Answers Research Journal, states the reasoning accurately in a creationist venue.¹⁰  His words: von Weizsäcker "concluded that ⁴⁰K undergoes branched decay to ⁴⁰Ca and to ⁴⁰Ar, based partly on the fact that the abundance of Ar in the earth's atmosphere is about 1000 times greater than expected when compared to the cosmic abundances of the other noble gases."¹⁰

Primordial solar-system argon is nearly pure argon-36 and argon-38.  Air is 99.6% argon-40.  That contrast is the whole argument, and until 2004 it rested on meteorites.  Then the Genesis spacecraft flew out past the Moon, exposed collector wafers to the solar wind for 27 months, and came back.

The Genesis team's report on the heavy noble gases¹¹ states the solar baseline plainly:

we know that the ⁴⁰Ar/³⁶Ar in the SW is small (an upper limit of 4.6 x 10⁻⁴ has been suggested from analyses of urelites by Göbel et al., 1978), suggesting that all of the ⁴⁰Ar is from terrestrial contamination and we assume that it is not significantly isotopically fractionated.¹¹

Their cleanest single laser step measured an argon-40 to argon-36 ratio of 1.12, "among the lowest of all Genesis Ar measurements made so far," and they attribute even that entirely to terrestrial contamination of the collector.¹¹

Put the two numbers together.  The air holds 1.649 x 10¹⁸ / 298.56 = 5.524 x 10¹⁵ moles of argon-36.  If every one of those atoms arrived from the solar nebula carrying the maximum solar ratio of 4.6 x 10^-4, the primordial argon-40 that came with it is 2.541 x 10¹² moles, which is 0.00015% of the atmosphere's argon-40.

Even a trapped chondritic ratio a thousand times higher than solar leaves the air more than 99.99% radiogenic.  There is no version of this in which a meaningful fraction of atmospheric argon is left over from the Earth's formation.

That matters because it closes the one escape a young-earth author has ever proposed.  Slusher's 1981 conclusion was that "it would seem that a large amount of Ar⁴⁰ was present in the beginning."¹  Twenty-three years later a spacecraft went and measured what was present in the beginning, and there is not enough of it by five orders of magnitude.

How much argon the Earth has made in 4.5 billion years

Potassium-40 decays two ways.  Only 10.72% of decays produce argon-40, by electron capture and positron emission; the other 89.28% produce calcium-40 by beta decay.  The half-life is 1.248 x 10⁹ years, so the total decay constant is

ln 2 / 1.248 x 10^9 yr = 5.554 x 10^-10 /yr

Those numbers, with the branch ratios good to ±0.11% absolute, come from the IAEA's evaluated nuclear data file.¹²

The one soft input is how much potassium the Earth contains.  This is a model, not a measurement, and it deserves to be flagged loudly.  Published values in live use span 150 to 280 parts per million in the bulk silicate Earth, which is everything except the core.  The canonical figure is McDonough and Sun's 240 ppm, which this article takes at second hand from Bender's paper because the original could not be obtained.¹³  Allègre, Hofmann and O'Nions put it near 250 ppm from uranium at 20 ppb and a potassium/uranium ratio of 12,700.¹⁴  Arevalo, McDonough and Luhr get about 280 ppm from a larger basalt compilation.¹⁵  And Davies and Lassiter argue for roughly 150 ppm, a point Bender's paper reports in its introduction.²  That is a factor of 1.9.  Anyone presenting the degassing efficiency below as a precise number is overclaiming.

With the bulk silicate Earth at 4.043 x 10²⁴ kg, the arithmetic runs:

The famous "about half" falls out of the calculation from scratch.  Bender states it in his own words: "It is well recognized that the atmospheric inventory comprises approximately half of the total ⁴⁰Ar produced by potassium decay over Earth history, assuming the canonical value of 240 ppm for the K content of the bulk silicate Earth."²  Ozima and Podosek put it their way: "from a simple consideration of ⁴⁰Ar budget in the Earth, we have shown that more than half of radiogenic ⁴⁰Ar has been degassed from mantle to the atmosphere."⁸

The last row is worth its own sentence.  The continental crust holds most of Earth's potassium per kilogram but very little of its mass.  At 1.5 wt % potassium the crust alone makes only about two thirds of the argon now in the air, over the whole 4.5 billion years.  Ozima and Podosek make the same point using 1% crustal potassium: the atmospheric inventory "is close to the amount of radiogenic ⁴⁰Ar (ca. 1 x 10¹⁸ moles), which can be produced by K in the crust."⁸  The rest has to come from the mantle.  That is why this whole subject became an argument about mantle layering rather than an argument about arithmetic.

One sensitivity, handled honestly.  Murthy, van Westrenen and Fei showed experimentally that potassium can partition into a sulphur-bearing metallic core.¹⁶  If it did, that potassium is locked away and can never degas, so the mainstream efficiency falls.  It does not help a young earth by any amount.  It moves potassium further from the atmosphere, not closer.

Six thousand years

Now run the same machinery for 6,000 years instead of 4.5 billion.

The model route

Take the whole bulk silicate Earth at 240 ppm potassium.  In 6,000 years at present rates, 9.676 x 10¹² moles of potassium-40 decay, and 10.72% of those produce argon:

1.037 x 10^12 mol of ⁴⁰Ar

Now assume 100% instant degassing.  Every atom made anywhere in the silicate Earth, including 2,800 kilometres down, teleports into the atmosphere the moment it forms.  That is absurdly generous.  Assume it anyway.

1.649 x 10^18 / 1.037 x 10^12 = 1.59 x 10^6

The atmosphere holds 1.6 million times more argon-40 than 6,000 years of present-rate decay can make, even with perfect instantaneous escape.  Six thousand years supplies 0.0000629% of it.

To close that, decay has to run 1.59 x 10⁶ times faster than today, averaged over the whole 6,000 years.  Compress it all into a one-year Flood, as RATE proposes, and the required factor is 9.5 x 10⁹.

The measurement route, which is the one that matters

The model route has a soft joint, and a skeptic of the mainstream is entitled to lean on it.  So here is the same test with the Earth model removed entirely.

In 2008 Michael Bender, Bruce Barnett, Gabrielle Dreyfus, Jean Jouzel and Don Porcelli measured the modern argon-40 degassing rate directly.²  Radiogenic argon leaking out of the Earth slowly raises the atmosphere's argon-40 relative to its argon-38, so old air is very slightly poorer in argon-40 than today's.  They pulled trapped air from the Vostok and EPICA Dome C ice cores back to about 779,000 years, corrected for gravitational sorting in the firn using the argon-38 to argon-36 ratio, and read the slope off a mass spectrometer.  Their result, on p. 8233: "This rate corresponds to a ⁴⁰Ar outgassing rate of 1.1 ± 0.1 x 10⁸ mol/yr."²

No potassium estimate enters that.  No mantle model.  No degassing efficiency.  It is a ratio measured on trapped gas.

1.1 x 10^8 mol/yr x 6,000 yr = 6.6 x 10^11 mol
1.649 x 10^18 / 6.6 x 10^11 = 2.5 x 10^6

Six thousand years of the directly measured argon flux delivers one part in 2.5 million of the argon that is actually in the air.

This is the load-bearing form of the argument, and the reason is worth stating flatly.  The 150 to 280 ppm spread in bulk-Earth potassium is the only genuinely uncertain input in this subject, and creationists are entitled to press on it.  But it does not touch this calculation.  Even the most favourable value in that range moves the model answer by less than a factor of two, against a shortfall of a million, and the measurement route does not use the value at all.

Two further readings fall out of the same number.  Filling the atmosphere at the modern rate would take 15.0 billion years, which is longer than the Earth has existed.  That is exactly why the mainstream reading is early catastrophic degassing from a magma ocean, followed by a slow modern trickle, a conclusion the iodine-129 to xenon-129 clock reaches independently and which Ozima and Podosek call "one of few robust constraints."⁸  And the measured outgassing of 1.1 x 10⁸ mol/yr is 64% of the 1.729 x 10⁸ mol/yr that 240 ppm of bulk-Earth potassium produces today.  The Earth currently vents about two thirds of the argon it makes.

A third route, using a number the young-earth literature published itself

There is a version of this test that requires no mainstream paper at all, and it comes from RATE volume I.

In his chapter "Geochemical Processes in the Mantle and Crust", Andrew Snelling discusses the 9-kilometre KTB borehole in Germany, where¹⁷ Drescher and colleagues measured argon isotopes in crustal fluids and found ⁴⁰Ar/³⁶Ar ratios from 550 to 37,200.  Snelling reports their conclusion twice.  On p. 149: "Drescher et al. [1998] thus estimated a loss rate or degassing flux of 1-6 x 10⁹ atoms m⁻²s⁻¹ for ⁴⁰Ar from crustal rocks, in good agreement with theoretical estimates from accumulated gases in crustal fluids."¹⁷  And again on p. 159, in his own voice: "Nevertheless, there is a steady loss of ⁴⁰Ar* from crustal rocks to the atmosphere, on the order of 1-6 x 10⁹ atoms m⁻²s⁻¹."¹⁷

He never multiplies it out.  So here it is multiplied out.

Two things follow.  Bender's ice-core figure of 1.1 x 10⁸ mol/yr sits inside the bracket that Snelling's own quoted flux gives for the whole planet, so two completely different measurements, one on Antarctic ice and one on German borehole fluids, agree to within a factor of a few.  And the most generous row still leaves 6,000 years short by 1.7 million.

Two honesty notes.  Drescher et al. 1998 was not read for this article; it is quoted only as Snelling quotes it, and their flux is a modelled loss rate from measured fluid compositions rather than a direct instrument reading.  The land area used, 1.485 x 10¹⁴ m², is the subaerial land area computed from the ETOPO 2022 relief grid for a sister article.¹⁸  Neither point changes the order of magnitude.

Melvin Cook, 1966, and Harold Slusher, 1973

Now the part that makes this article unusual.

The assumption going in was that the young-earth literature had simply never engaged the atmospheric argon inventory.  That turned out to be wrong twice over.  It engaged the inventory once, in print, and got the number backwards by about two orders of magnitude.  And the man usually blamed for that number did not invent it.  He copied it out of another creationist's book and changed what it meant on the way.

Harold S. Slusher was a physicist at the Institute for Creation Research and the author of ICR Technical Monograph No. 2, Critique of Radiometric Dating.  On p. 30 of the 1973 first edition, and again word for word on p. 39 of the 1981 second edition, as item 2 in a list of objections to potassium-argon dating, he writes:

There is far too much Ar⁴⁰ in the earth for more than a small fraction of it to have been formed by radioactive decay of K⁴⁰.  This is true even if the earth were really 4.5 billion years old.  In the atmosphere of the earth, Ar⁴⁰ constitutes 99.6% of the total argon.  This is around 100 times the amount that would be generated by radioactive decay over the hypothetical 4.5 billion years.  Certainly this is not produced by an influx from outer space.  Thus, it would seem that a large amount of Ar⁴⁰ was present in the beginning.  Since geochronologists assume that errors due to presence of initial Ar⁴⁰ are small, their results are highly questionable.¹

The page numbers were checked two ways each, because a right quote at a wrong page is the commonest citation defect in this corpus.  Both editions are in archive.org's printdisabled collection, so neither can be borrowed, but both can be read paragraph by paragraph through the search-inside endpoint.¹

This is not an isolated sentence in the middle of a technical chapter.  Slusher restates it in his own summary.  The Conclusions of both editions read: "In the potassium-argon method, it is assumed that the initial Ar content of the rock is not important, though its abundance in the lithosphere and atmosphere is about 100 times the amount that would be generated by radioactive decay over 4.5 billion years."¹  Note the widening from "in the atmosphere of the earth" to "in the lithosphere and atmosphere."  A reader who skimmed the monograph would meet the claim in that second, larger form.  So it cannot be defended as an incidental slip.

His logic is fine.  His number is not.  If the air really held a hundred times more argon-40 than potassium decay could supply, primordial argon would be the obvious explanation and potassium-argon dating would be in serious trouble.  The reasoning is sound.

The air holds about 0.47 times what 4.5 billion years of potassium decay in the bulk silicate Earth produces.  Not 100 times.  The claim is wrong by a factor of roughly 200, and it is wrong in the direction that destroys its own argument.  The atmosphere does not have a surplus of argon-40 needing an explanation.  It has a deficit, and the deficit is the thing mainstream geochemists have argued about for sixty years, because it means half the argon the Earth has made is still inside it somewhere.

Where the number came from, and what it originally said

Slusher's reference list names his source, and the source does not say what he says it says.

The 1973 edition's reference list, p. 44, gives note 21 as "Cook, Melvin A. (1966).  Op. cit., p. 66." and note 22 as "Ibid., p. 67."¹  Both point at Melvin A. Cook, Prehistory and Earth Models (London: Max Parrish, 1966), a book Slusher calls in the same monograph "his classic study."¹⁹  The same book is also the source of the young-earth atmospheric helium argument, so it is the common ancestor of two of the movement's best-known geochemical clocks.

Here is Cook's p. 67, read directly:

It is generally claimed [cf. Rankama, 1954] that the high ratio of A⁴⁰/A of about 0.996 in the atmosphere compared with the very low ratio of only about 0.005 for cosmic argon (determined from meteors) is due to the K⁴⁰ generation of A⁴⁰ in the earth.  There is, however, a serious difficulty with this conclusion.  The earth would have to be about 10¹⁰ years old and the initial K⁴⁰ content of the earth about 100 times greater than at present (about 300 ppm) to have generated the A⁴⁰ in the atmosphere.¹⁹

Cook's "100 times" is a statement about potassium, not about argon.  He is saying that to make the air's argon, the Earth would have to have started with a hundred times more potassium-40 than it now has, and to have been running for ten billion years rather than four and a half.  Slusher turned that into "there is a hundred times more argon than decay can make."  Those are different quantities, and one does not follow from the other.

Cook's own arithmetic, on the facing page, shows how different.  He works the budget out in full:

Allowing an age of 4.5·10⁹ years for the earth the K⁴⁰ at the beginning would have been about ten times higher than at present or about 2·10²⁰ g.  Hence, 1.8·10²⁰ g of K⁴⁰ would have decayed to yield about 1.5·10¹⁹ g of A⁴⁰ (branching ratio 0.085) and 1.6·10²⁰ g of Ca⁴⁰.  There are at present 6.6·10¹⁹ g A⁴⁰ in the atmosphere and hydrosphere.¹⁹

Divide 6.6 x 10¹⁹ by 1.5 x 10¹⁹ and the answer is 4.4.  A shortfall of about four.  That is the same direction as the modern answer and only a factor of two away from it.

Cook's deficit is bigger than the modern one for two identifiable reasons, and both are input errors rather than reasoning errors.  He put the Earth's present potassium-40 at 2 x 10¹⁹ g, against 1.16 x 10²⁰ g for 240 ppm of potassium in the bulk silicate Earth.  And he used a branching ratio of 0.085, against the measured 0.1072.  Put both right and his 1.5 x 10¹⁹ g of argon becomes about 1.1 x 10²⁰ g, so his ratio of 4.4 falls to about 0.6 — next door to the 0.47 this article computes from scratch.  Cook, running the calculation in 1966 with 1950s numbers, got the right sign and very nearly the right size.  What went wrong happened afterwards, in the copying.

So the number that has represented the young-earth position on atmospheric argon for over half a century is a hundredfold deficit of primordial potassium, printed as a hundredfold excess of argon.

Slusher also contradicts his own source on the same page.  His paragraph says "Certainly this is not produced by an influx from outer space."  Cook, in the sentences immediately after the ones Slusher cites, says the opposite: "Furthermore, micrometeorites are probably adding above 10⁹ g of argon to the earth's atmosphere each year.  This source of argon is at present an order of magnitude greater than the radiogenic argon."¹⁹  Cook is wrong about that too, and the Genesis measurements above are what settle it: extraterrestrial argon is nearly pure argon-36 and argon-38, so no amount of infalling dust can supply argon-40.  The point here is narrower.  Slusher denied, flatly and without argument, the very mechanism his cited authority was asserting two sentences later on the page he cited.  He was not reading Cook closely.

Henry Morris repeats it, flagged as unchecked

The claim reached its largest audience through Henry Morris's Scientific Creationism, the standard popular text of the movement, on p. 150 of the 1974 edition:⁴

Certain radioactive elements produce gases as they decay, notably Helium 4 in the case of uranium decay and Argon 40 in the case of potassium decay.  These products migrate upward through the rocks and eventually escape into the atmosphere.  Most of the argon must have been present there, or in the crust, from the beginning, since there is far too much to have been produced even in five billion years by potassium decay, assuming Cook's calculations are right.⁴

Read the last five words.  Morris names Cook as the source, exactly as the reference chain says, and then declines to vouch for the arithmetic.  The claim entered popular circulation already flagged as unverified, in 1974.  It has stayed unverified ever since.  Nobody on the young-earth side went and read Cook's p. 66.

Dalrymple's answer, 1984

Brent Dalrymple, the US Geological Survey geochronologist, quoted Slusher's paragraph in full in his 1984 reply to creationist arguments and answered it directly:⁹

This statement contains several serious errors.  First, there is not more ⁴⁰Ar in the atmosphere than can be accounted for by radioactive decay of ⁴⁰K over 4.5 billion years.  An amount of ⁴⁰Ar equivalent to all the ⁴⁰Ar now in the atmosphere could be generated in 4.5 billion years if the Earth contained only 85 ppm potassium. ... The ⁴⁰Ar content of the atmosphere is well known and is 6.6 x 10¹⁹ grams.  The estimated ⁴⁰Ar content of the crust and mantle combined is about 4 to 19 x 10¹⁹ grams.  Thus, the Earth and the atmosphere now contain about equal amounts of ⁴⁰Ar, and the total could be generated if the Earth contained only 170 ppm potassium and released half of its ⁴⁰Ar to the atmosphere.⁹

His figures hold up against the independent calculation here.  At 240 ppm the Earth produces 3.478 x 10¹⁸ mol against 1.649 x 10¹⁸ mol in the air, so the potassium content that would produce exactly the atmospheric amount is 240 x (1.649/3.478) = 114 ppm.  Dalrymple's 85 ppm is the same order, and the difference traces to his older decay constants and to his including the core in "the Earth."  His 170 ppm at 50% release gives 1.23 x 10¹⁸ mol, also the right order.  His reference for the crust-and-mantle estimate could not be resolved, because the online edition of his paper omits its reference list.

Fifty-three years of silence

Slusher's claim has never been repeated by another young-earth author, never been corrected by one, and never been withdrawn.  That is a negative finding, and a negative finding is only as good as the search behind it.  So here is the search, stated precisely enough that a hostile reader can rerun it.

The corpus.  Every International Conference on Creationism paper from 1986 to 2023 — 457 papers, downloaded as PDFs and read at full text, not by title or abstract.  The complete RATE volume I, 687 PDF pages.  All 19,057 icr.org article slugs, plus the site's own search results for argon (66 records) and helium (124 records).  creation.com's 9,588 articles, including the Journal of Creation PDF archive.  answersresearchjournal.org and answersingenesis.org.  The Creation Research Society Quarterly full-text index, Creation Matters, and GRISDA's Origins.  Fourteen creationist books from 1966 to 2010, read through archive.org's search-inside endpoint.

The controls, because a null result from a broken search looks exactly like silence.  The same full-text grep over the same 457 ICC papers returns radiocarbon in 37 papers and zircon in 27.  The endpoint works.  A zero is a real zero.

The result.  Slusher appears in ten of the 457 ICC papers.  Nine are astronomy — galaxy rotation curves, lunar crater viscosity, the Akridge-Barnes-Slusher 3 K background — and the tenth, Moore 1986, is a bare bibliography entry listing Critique of Radiometric Dating with no discussion of anything in it.  Not one of the 457 papers discusses, repeats, or corrects the atmospheric-argon claim.  Seven ICC papers do discuss atmospheric argon, and all seven are about the atmospheric-argon correction applied to argon measured in rocks.  In RATE volume I, all 86 occurrences of the word "argon" are about argon in minerals.  On creation.com, the phrase "atmospheric argon" returns two hits across 9,588 articles, and neither runs an inventory argument.

One qualification has to be made, and it cuts against the article's original wording.

An earlier draft of this article said that no young-earth author has written about the atmospheric argon inventory since Slusher.  That is false, and the correction is worth more than the original sentence was.  Larry Vardiman wrote about it twice, in 1985 and in 2005.  He never mentions Slusher, he never repeats the hundredfold claim, and he argues against Slusher's conclusion without appearing to know that it exists.

In ICR Impact No. 143, May 1985, Vardiman²⁰ tabulates the atmosphere's argon mass as 6.59 x 10¹⁹ g — the correct number, and the same one used here — and then writes:

The amount of argon in the atmosphere is assumed to be fully retained in the atmosphere after radioactive decay of potassium, and permits maximum estimates of helium flux to be made.  Unfortunately, the assumption of long ages of the earth underlies the estimates of heat flow and the accumulation of argon in the atmosphere as well.  This assumption likely affects the calculation of helium accumulation.²⁰

Twenty years later he states the position outright, in a chapter titled "Evidence for a Young Earth from the Ocean and Atmosphere":²¹

Another gas which could be used for this calculation is argon.  It is produced by the decay of uranium in the rocks of the earth.  Argon contributes the largest amount of any of the minor gases to the atmospheric composition.  It is also massive enough that it will not escape to space by any conceivable mechanism.  Its concentration should then be directly related to the amount of nuclear decay in the rocks of the earth.  However, quantifying the amount of time based on the amount of argon in the atmosphere has several complexities which make it difficult to use.  First, the rate of escape from the crust to the atmosphere is uncertain. ... Second, Vardiman et al. (2005) found that nuclear processes in rocks of the earth have been accelerated during episodes in earth history which make invalid a simple calculation of the age of the earth based only on the concentration of argon in the atmosphere divided by an assumed constant production rate.  The large amount of argon in the atmosphere argues for a large amount of nuclear decay, but not necessarily a long period of time.  And, third, like most geochronometers, the problem of the initial concentration of argon needs to be dealt with.²¹

Three things about that paragraph.

First, it is the exact inverse of Slusher's move.  Slusher said the atmosphere has too much argon-40 for radioactive decay to explain, so most of it must be primordial.  Vardiman says the atmosphere's argon-40 is evidence of a large amount of decay, and only the timescale is in doubt.  Two ICR authors, on the same datum, taking opposite positions thirty-one years apart, and neither cites the other.  Vardiman's version is the better one.  It is also, on the physics, correct as far as it goes: a large argon inventory does show a large amount of decay.

Second, the parent nuclide is wrong.  "It is produced by the decay of uranium in the rocks of the earth."  Atmospheric argon-40 comes from the electron-capture branch of potassium-40.  Uranium decay produces helium, not argon.  This is a slip by a PhD atmospheric scientist in the one paragraph of the ICR corpus that takes a position on the argon budget, and it is worth recording because of what it indicates: how little attention this inventory has had.  Slusher, by contrast, gets the parent right and the magnitude wrong.

Third, Vardiman names the objection this article answers.  "First, the rate of escape from the crust to the atmosphere is uncertain. ... Diffusion rates of argon from various minerals need to be validated."²¹  That is a fair objection, and it is exactly why the load-bearing version of the argument below runs through Bender's measured degassing flux rather than through a modelled one.  Vardiman was writing in 2005 and Bender measured it in 2008.  The objection was reasonable when he made it.  It is not reasonable now, and no young-earth publication has revisited it since the measurement was published.

So the correct claim is not "nobody engaged the atmospheric argon inventory."  It is narrower and better documented: nobody engaged Slusher's inversion, and the one author who did address the inventory argued against him without noticing.

Andrew Snelling states the anomaly and walks past it

This is the sharpest item in the section, and it is not an absence at all.

In 2016 Andrew Snelling published a 26-page technical review in Answers Research Journal, the flagship young-earth journal, devoted entirely to the decay constants and half-life of potassium-40.  The sentence quoted earlier in this article, on why von Weizsäcker proposed branched decay in the first place, comes from p. 173 of that review.  It is worth reading a second time with a different question in mind:

The possible modes of decay open to ⁴⁰K were first discussed by Von Weizsäcker (1937), who concluded that ⁴⁰K undergoes branched decay to ⁴⁰Ca and to ⁴⁰Ar, based partly on the fact that the abundance of Ar in the earth's atmosphere is about 1000 times greater than expected when compared to the cosmic abundances of the other noble gases.  Von Weizsäcker (1937) also postulated that radiogenic ⁴⁰Ar should be present in old K-bearing minerals.¹⁰

He writes down the anomaly, correctly, in the correct form, in a paper about the very isotope that produces it.  Then he moves on and never returns to it.  Searching the paper's full text returns zero occurrences of "budget", "inventory" or "degassing."

That is a stronger finding than silence.  Silence can be ignorance.  This is the leading young-earth geochemist recording, in print, that Earth's atmosphere holds roughly a thousand times more argon than a non-radiogenic origin predicts, and not asking the next question — where, on a six-thousand-year Earth, that argon came from.

And the Journal of Creation does print corrections

One more piece of evidence, because it forecloses the obvious defence that creationist journals simply never revisit anything.

They do.  In Journal of Creation 24(3), Russell Humphreys replied to a critical letter from Gary Loechelt by listing what was good about it,²² and item three reads:

(3) It points out an error of mine, for which I'm grateful.  However, as this reply will show, the helium data continue to support the short biblical timescale just as strongly as before.²²

A movement whose flagship journal prints "an error of mine, for which I'm grateful" is a movement capable of correcting itself in public.  That makes the uncorrected argon claim a choice about attention, not a structural impossibility.  Nobody looked.

The greps are reproducible.  Humphreys 2011 returns zero occurrences of "atmosphere" in its full text.  Snelling's 2016 ARJ review returns zero for "budget", "inventory" and "degassing", and all twelve of its "atmospheric" hits are about the argon-36 correction, Nier's 1950 isotope measurement, or the von Weizsäcker sentence quoted above.  Cupps's Acts & Facts article returns zero for "budget", "inventory" and "degassing", and its uses of "atmospheric" are about correcting for air argon absorbed into a sample.

So a widely known geochemical constraint has gone unanswered by the young-earth literature for over five decades.  The one number the movement did publish on it was miscopied from its own founding source and never checked.  The one author who returned to the inventory argued the opposite of the published claim and did not notice.  And the movement's leading geochemist wrote the anomaly down in the flagship journal and passed by.  That is not a rhetorical flourish and it should not be inflated into one.  It is a statement about the state of a field, and the honest thing to say about it is that a movement which wants to be taken seriously on radiometric dating has left its largest single number unaddressed.

There is a quiet irony in the corpus, too.  The excess-argon literature that occupies most young-earth writing on this element argues that argon-40 is abundant and highly mobile in the crust and mantle, and contaminates almost everything it touches.  That is a claim that a very large, very mobile reservoir of radiogenic argon exists.  It is the atmospheric argument's premise, supplied by the other side.

What accelerated decay buys, and what it does not

A young-earth reader will already have the answer ready: decay ran faster.  RATE proposes exactly this, so the objection is not an unanswerable one in principle.  It has a price, and the price has two very different parts.

It is worth noting first that the movement has never agreed decay rates varied

Accelerated decay is often treated by critics as a settled young-earth doctrine.  It is not, and the disagreement is on the record in the movement's own journal.

In 1990 the Creation Research Society Quarterly ran an eleven-part "Minisymposium on Variable Constants."  The editor, Don DeYoung, introduced it: "This issue begins a series of study articles on the constants of nature and their possible variation. ... Initial response from writers and readers has shown that this area desperately needs to be addressed."²⁴  The contributors did not converge.

Part X was R. H. Brown arguing, from radiohalos, that decay rates have been essentially fixed.²⁵  His abstract:

The identifiability of radiohalo rings with the alpha-particle sources that produced them, together with the sharpness of these rings indicate that radioisotope half-lives over a range of 21 orders of magnitude have not varied by more than a factor of two during the time the geological formations of the Earth which contain radio halos have been in existence, and probably over the entire time represented by geological formations.²⁵

Part XI, printed on the next page, was Robert Gentry — the best-known radiohalo researcher in creationism — rejecting it:²⁶ "The conclusion of the previous article (Brown, 1990) that the sharpness of halo rings established the constancy of radioactive decay rates is examined and rejected."²⁶  Gentry then states the stakes for his own side plainly:

For example, if decay rates have remained constant, then creationists need to know it, for such a view firmly establishes the basis of conventional radiometric dating for fossils as well as rocks.  It appears that many creationists have thought all old radiometric ages associated with fossils can be explained away by contamination from prior radioactive decay.²⁶

That is the situation, put by a young-earth author, in a young-earth journal, thirty-six years ago.  Either the constants held, and the conventional dating framework stands;  or they did not, and something has to be said about the consequences.  This article's consequence is a specific one, and it is the subject of the rest of this section.

The heat, computed properly

There is a trap in the framing of this calculation that is worth defusing first, because it is easy to get wrong by nearly an order of magnitude.

The electron-capture branch of potassium-40 has a Q value of 1504 keV, so it is tempting to say that making an argon-40 atom releases about 1.5 MeV.  That is wrong, because only 10.72% of potassium-40 decays make argon at all.  Making one argon-40 atom costs 9.33 decays.  The rest of the potassium goes to calcium and releases its energy anyway.

Per potassium-40 decay, weighting both branches:

total nuclear Q = 0.8928 x 1310.9 + 0.1072 x 1504.4 = 1331.6 keV
heat deposited  = 0.8928 x 560.18 + 0.1066 x 1460.82 = 655.9 keV

The second line adds the mean beta energy and the absorbed 1461 keV gamma, and drops the neutrinos, which leave the planet at the speed of light.  50.7% of potassium-40's decay energy escapes as neutrinos, so any heat calculation using the full Q value overstates the heating by a factor of two.  As a sanity check, 655.9 keV per decay implies 3.33 x 10^-9 W per kilogram of natural potassium, against the standard geophysical tables' 3.3 to 3.5 x 10^-9.

Per argon-40 atom produced, then, the cost is 12.42 MeV of nuclear Q and 6.118 MeV of heat, not 1.5 MeV.

For the whole 4.5-billion-year bulk-silicate-Earth argon inventory at 240 ppm, which is 3.245 x 10¹⁹ moles of decays:

Release that in one Flood year and radiate it from the surface and the required flux is 1.276 x 10⁸ W/m², a blackbody temperature of 6,887 K.  The Sun's photosphere is 5,772 K.

Two cross-checks say this is right.  An independent calculation done for this project's hydroplate heat article, using entirely different inputs, gives 1.95 x 10³⁰ J for 4.5 billion years of uranium, thorium and potassium in the continental crust and 6.18 x 10³⁰ J for the bulk silicate Earth.  The potassium-40-only figure of 2.05 x 10³⁰ J sits between them, as it must.  And that article's blackbody calculation for a RATE-scale budget of 1.9 x 10³⁰ J over one year gives 6,800 K, within 1.3% of the figure here.  Potassium-40 by itself reproduces the entire accelerated-decay heat problem.

But heat is not the sharp end

It would be easy to stop there, and it would be a mistake, because RATE already knows.

Russell Humphreys devotes section 13 of his RATE volume II zircon chapter to the problem³ and opens it this way:

In the previous RATE book [Humphreys, 2000, pp. 337, 369–370], my feasibility study of the accelerated decay hypothesis pointed out and discussed one of the obvious problems: nuclear decay generates heat!  I wrote that without long periods of time in which the heat could dissipate by normal mechanisms, or without some new and faster mechanism, crustal rocks would melt many times over if decay rates were accelerated.³

He then generalises it beyond his own model: "I also pointed out that heat is not merely a problem for accelerated decay, but also for all Creation or Flood models I know of.  There is simply too much geological work to be done in too short a time."³

His proposed answer is "volume cooling", meaning cooling an entire body of rock at once and faster than conduction, convection or radiation allow.  He offers Snelling and Armitage's polonium-halo timescales and Baumgardner's geothermal work as evidence that something of the kind happened.  No mechanism is derived and no number is attached, and he says so himself in the passage quoted at the top of this article: "When we can devote more time to the problem, we may see good progress on it."³

That is an honest statement of an unsolved problem.  It should be quoted as such rather than mocked, and it means the argon heat calculation above is not a new objection.  It re-derives an existing one from a different direction and shows that potassium alone is enough to produce it.  If volume cooling works, it works here too.

The sharp end is transport

Here is the part that volume cooling does not touch, and it is the strongest original point in this article.

Accelerating nuclear decay accelerates production.  It does nothing to transport.  An argon atom created inside a feldspar or mica lattice has to diffuse out of that lattice, escape the mineral grain, escape the rock, migrate through the crust, and enter the atmosphere.  Every one of those steps runs at a rate set by temperature, pressure, grain size and melting, not by a decay constant.  Multiplying the decay rate by 10⁹ leaves the diffusion coefficients exactly where they were.

Two consequences follow, and they pull against each other in a way that is fatal.

First, the crust cannot supply the atmosphere, so the whole mantle has to degas.  From the table above, the continental crust at 1.5 wt % potassium makes only about two thirds of the air's argon in 4.5 billion years.  In 6,000 years at present rates it makes 3.3 x 10¹¹ moles, about one five-millionth of what the air holds.  To put 1.65 x 10¹⁸ moles of argon into the air on a Flood timescale, essentially the entire silicate Earth has to be melted or convected and stripped of its gas, in a year, while the ocean survives and Noah's family does not cook.

Second, RATE's own flagship argument requires the exact opposite.  Humphreys' 2011 Journal of Creation paper, and the RATE zircon chapter it supports, both rest on retention.  The claim is that minerals in the Fenton Hill GT-2 borehole held on to their radiogenic gas because there was not time for it to escape.  Humphreys states it plainly:

These data say that the feldspar generated over a billion years' worth of ⁴⁰Ar, and then retained it, during a period of time that began only thousands of years ago.²⁷

Both propositions cannot be true of the same 6,000 years.  The atmospheric inventory needs radiogenic argon to have escaped its host minerals with near-total efficiency and travelled to the surface.  The Fenton Hill argument needs radiogenic argon to have stayed inside its host mineral, at 313 °C, four and a half kilometres down, for the entire period.  A model that makes argon escape fast enough to fill the atmosphere destroys the retention that the helium and argon diffusion ages depend on.  A model that keeps the argon in the rock cannot fill the atmosphere.

No creationist publication has been found that notices this, because no creationist publication has considered the two questions in the same place.  The retention argument is treated in detail in RATE and helium diffusion in zircons; this article's point is only that the two arguments cannot both be run.

The calcium that constrains nothing

There is an obvious follow-up question, and a reader who thought of it deserves to find it answered honestly rather than turned into a second talking point.

If 3.245 x 10¹⁹ moles of potassium-40 decayed, then 89.28% of those decays made calcium-40, which outnumbers the argon by 8.33 to one.  That is 2.897 x 10¹⁹ moles, or 1.158 x 10¹⁸ kg, of radiogenic calcium-40 sitting somewhere in the Earth.  Surely that leaves a mark?

It does not, and the reason is arithmetic.  The bulk silicate Earth is 3.61 wt % CaO, and calcium-40 is 96.941% of natural calcium, so the Earth already contains 2.523 x 10²⁴ moles of calcium-40.  The radiogenic addition is 0.00115% of it.

Bulk-rock calcium isotope ratios shift by about one part in 10⁵ over the whole history of the Earth.  Nobody addresses the calcium half of this budget because there is nothing to address.  It neither confirms nor refutes anything, in either direction, and that is also why potassium-calcium dating exists only for potassium-rich, calcium-poor minerals like biotite, sylvite and lepidolite, and is marginal even there.

This is a point against the argument in this article, and it is stated here rather than buried.  Half of the potassium-40 story leaves no fingerprint at all.  Only the argon half is detectable, and it is detectable only because argon is a gas that nothing else in the atmosphere competes with.

What Humphreys and Vardiman actually claim

Both should be stated fairly before being set aside, because both are about something real and neither is about this.

Humphreys' 2011 paper²⁷ reanalyses Harrison, Morgan and Blackwell's 1986 argon diffusion study of microcline feldspar from the Fenton Hill GT-2 borehole, the same hole that supplied RATE's zircons.  He reads the sample-5 age spectrum, from 4.56 km depth at 313 °C, as showing 25% argon loss rather than Harrison's 20%, applies Harrison's own equation for the time needed to lose a given fraction, and obtains 5,100 years with an uncertainty range of about 3,000 to 9,000.  He presents this as independent support for RATE's 6,000-year helium age.  His own framing requires accelerated decay: the peak of 1,160 Ma in the age spectrum shows, he says, that "over 'one billion years' worth' of ⁴⁰K to ⁴⁰Ar decay occurred in situ."²⁷

Vardiman's Acts & Facts piece the same year is a popular restatement with no new analysis.²⁸

What they address: retention.  Given measured diffusivities at 313 °C, that feldspar cannot have held its argon for a million years at present temperatures.  Whether one accepts the conclusion or not, this is real work on a real published dataset, not fabrication, and it deserves to be answered on retention grounds.

What they do not address, at all: how much argon exists.  The entire argument is about the ratio of argon lost to argon retained in one mineral separate from one borehole.  It never asks where 6.6 x 10¹⁹ grams of atmospheric argon-40 came from.  The two questions are independent, and answering one does not touch the other.

Humphreys' argon paper was answered in print, in the same journal

This has to be said, because leaving it out would be the kind of omission a hostile reader finds.

Humphreys' 2011 paper did not stand unchallenged.  Journal of Creation published a five-page letter attacking it the following year, with Humphreys' reply printed immediately after.²⁹  The critic, Gary Loechelt, is an old-earth Christian, not a young-earth author.  This is a critic's letter run by the venue with a right of reply, not a dispute between creationists, and it should not be presented as one.

Loechelt's attack is on the physical inputs.  Humphreys' 2011 reanalysis rests on his own reconstruction of the Fenton Hill thermal history, built by reading values off published figures — Loechelt calls it "eyeball interpolation ... problematic at best, since no rigorous mathematical self-consistency is imposed."²⁹  Loechelt then checks Humphreys' magma-chamber parameters against measurement.  His Table 1 caption states the result:

Comparison of the measured properties of the Valles Caldera magma chamber with the parameter values assumed by Humphreys in his "best uniformitarian" model.  Overall, the real magma chamber is smaller, deeper, and cooler than the one proposed in the model.²⁹

All four are wrong in the same direction — every one of them makes the chamber a weaker heat source than Humphreys assumed.  Loechelt then feeds the measured values back through the same conductive model and reports the borehole temperature it predicts.  With the smaller radius alone, the peak "only reaches 170°C, well short of the 230°C required to account for the thermal maximum inferred from fluid inclusion studies."  With the greater depth as well it is worse, and with the lower magma temperature too, "a peak temperature of only about 130°C is reached."²⁹  His conclusion: "Thermal conduction from a cooling body of magma beneath the Valles Caldera can neither account for the current elevated temperatures nor the fluid inclusion data at Fenton Hill."

Humphreys' reply does not engage the table.  It opens on motive: "The persistence of Gary Loechelt's many-year efforts to discredit RATE testifies to the pressure that project has put on his own worldview.  He is a uniformitarian, accepting the billions of years that secularists demand as a framework for evolutionism."²⁹  It then argues that cooler past temperatures would not rescue an old Earth anyway, on the helium-in-zircon question, and closes by noting that Loechelt's own diffusion model was never peer-reviewed.  The four measured parameters are not answered.

Two honest notes.  Loechelt's letter is about the Fenton Hill retention argument, not about the atmospheric inventory, so it does not bear on this article's central calculation.  And a reply that opens on a critic's worldview rather than his measurements is a bad sign whichever side prints it;  this project should be graded by the same standard.

Where the mainstream account is genuinely unfinished

Grading both sides by the same standard means saying where the mainstream is weak, and it is weak in one specific place.

If the bulk silicate Earth has made about 3.5 x 10¹⁸ moles of argon-40 and the air holds 1.65 x 10¹⁸, then roughly half of it is still inside the Earth.  The traditional home for the missing half is an undegassed lower mantle, which is why Allègre, Hofmann and O'Nions argued for a layered mantle with a degassed top and an unprocessed bottom.¹⁴  Bender's paper says, in its introduction, that this does not survive the seismology:

The most parsimonious explanation for the remainder is that there is a large reservoir containing undegassed Ar, which is presumably the lower mantle.  However, extensive seismic evidence has shown that oceanic plates subduct into the lower mantle while plumes rise from the core-mantle boundary to produce volcanism at the surface... Because of such observations, it is problematic to maintain that the lower mantle is undegassed.²

That is a live, unresolved problem in mainstream geochemistry, printed in a PNAS paper by the people who made the measurement.  The proposed fixes are to lower the Earth's potassium content to about 150 ppm, as Davies and Lassiter suggest, or to hide potassium in the core, as Murthy's experiments permit.  Neither is settled.

A creationist is entitled to say that mainstream geochemistry does not know how much potassium the Earth contains and cannot fully account for where its argon went.  Both are true.  What follows from it is a dispute about a factor of two in the degassing efficiency, inside a framework where the atmospheric inventory itself is not in question at all.  The young-earth position needs a factor of a million.

Objections

"The bulk-silicate-Earth potassium abundance is a model, not a measurement.  The whole calculation is circular."

Half right, and it is why the article leads with Bender rather than with McDonough and Sun.  The 240 ppm figure really is a model, built from potassium/uranium ratios in basalts and uranium abundances from meteorites, and the published spread of 150 to 280 ppm is a factor of 1.9.  But the measurement route uses none of it.  The atmospheric inventory is a mass times a mole fraction times an isotope ratio.  The degassing flux is a slope on a mass spectrometer.  Multiply the second by 6,000 years and divide into the first and you get 2.5 x 10⁶ without touching any Earth model.  If bulk-Earth potassium were zero the conclusion would not change, because the argument no longer runs through production at all.

"Argon could have been created in the atmosphere on day one."

This cannot be refuted, and it also cannot be tested, which is the problem.  Note first what it concedes: it abandons Slusher's version, which claimed the argon was primordial in the ordinary sense of inherited from the solar nebula.  Genesis mission data closed that route, and this is a different claim.

What it costs is the following.  The created argon would have to be 99.6% argon-40, which is exactly what a potassium-40 decay product looks like and is five orders of magnitude away from the argon the Genesis mission caught coming off the Sun.  It would have to be present in the exact proportion, roughly half, that 4.5 billion years of the Earth's own potassium would have generated.  And it would leave the modern degassing flux, which is measured and is currently 64% of the modern production rate, as a coincidence.  This is the same move as light created in transit: internally consistent, unfalsifiable, and buying nothing except the abandonment of the geochemical evidence as evidence.  A reader who takes this route should say plainly that he is no longer making a scientific argument, because he is not.

"The 47% degassing efficiency is itself a fitted parameter."

It is not fitted, it is a quotient.  The numerator is measured, the denominator is modelled, and the quotient is whatever it is.  Nobody chose 47%; it fell out of 1.649 divided by 3.478.  The literature reports it as "about half" because the denominator is uncertain, and at 280 ppm it drops to 41% while at 150 ppm it rises above 70%.  That range is honestly reported by the people who use it.  More to the point, the efficiency plays no part in the six-thousand-year calculation, which assumes 100% instant degassing on the model route and does not use an efficiency at all on the measurement route.

"Bender's flux depends on the ice-core age scale, which assumes an old Earth.  It is circular."

The sharpest objection here, and it lands partly.  Bender's slope is argon-40 enrichment per unit time, and the time axis comes from the EPICA Dome C ice-core chronology, which runs back about 779,000 years.  A young-earth reader can reject that axis, and if he does, the slope becomes uninterpretable.

Two answers.  First, the flux is confirmed by a completely different route with no ice-core chronology in it: Drescher's KTB borehole degassing flux, quoted approvingly in RATE volume I, gives 2.7 x 10⁷ to 1.6 x 10⁸ mol/yr over the whole Earth, bracketing Bender's 1.1 x 10⁸.  Second, and more decisively, rejecting the ice-core timescale does not help.  The young-earth model needs the argon flux to have been about a million times larger than anything measured today, and no measurement of any kind, on ice or rock or borehole fluid, shows a flux remotely that large.  Deleting the time axis deletes the constraint in the direction of not knowing, not in the direction of a young earth.

"RATE never claimed to have solved the heat problem, so this is attacking a position nobody holds."

Correct, and the article says so.  Humphreys concedes the heat problem in print, calls it a problem for every Flood model he knows of, and describes volume cooling as an approach to try rather than a result.  The heat calculation here is offered as a cross-check, not as a refutation, and it earns its place by showing that potassium-40 alone reproduces the whole difficulty from an independent direction.

The position actually under attack is different and narrower.  It is that accelerated decay, whatever it does about heat, does nothing at all about transport.  Volume cooling is a proposal about removing energy.  It is not a proposal about moving argon atoms out of feldspar lattices and through forty kilometres of crust in twelve months, and no such proposal exists in the young-earth literature.  That is the gap.

"Excess argon proves argon moves through the crust freely, so filling the atmosphere fast is not a problem."

This is the best available young-earth move, and it is worth taking seriously, but it goes the wrong way.  The excess-argon literature argues that argon-40 migrates into minerals from outside and contaminates them.  For that to be true there must already be a large, mobile reservoir of radiogenic argon in the crust and mantle, which is the atmospheric argument's own premise.  More importantly, mobility is not the constraint.  Snelling's own quoted crustal flux is an estimate of the rate at which that mobile argon actually reaches the air, and it is 10⁷ to 10⁸ moles a year, not 10¹⁸.  Demonstrating that argon moves does not demonstrate that it can move a billion times faster.

"Decay constants and isotope abundances could have been different, so the whole calculation is built on present-day physics."

Granted, and this is exactly what accelerated decay proposes.  The response is that this is not an escape from the calculation, it is a restatement of what the calculation costs.  Present-rate decay is short by 1.6 x 10⁶ on the model route.  To close it the average decay rate over 6,000 years must have been 1.6 million times today's, or 9.5 billion times today's if compressed into a Flood year, and the heat that comes with it has to go somewhere.  The number in this article is the size of the miracle required, stated precisely.  It is not a proof that no miracle occurred.

Where the young-earth case is strongest here

Three places, and they are real but small.  Naming them accurately matters more than the rhetorical cost.

The Earth's potassium content is genuinely soft.  From 150 to 280 ppm is a factor of 1.9, the low end is proposed by mainstream authors rather than creationists, and it is proposed precisely because the argon budget is awkward.  A creationist is entitled to say the mainstream does not know how much potassium the Earth contains.

The mainstream degassing story has an admitted hole, stated in PNAS by the people who made the measurement, and no consensus fix.

Humphreys 2011 is legitimate work on its own narrow question.  He reads a published age spectrum, applies the original authors' own equation, gets a retention timescale, and shows his working.  It should be answered on retention grounds, not waved away.

Where it fails

The inventory.

There is no published young-earth account of where 6.6 x 10¹⁹ grams of radiogenic argon-40 came from.  The one attempt to make the inventory an argument asserted a fact that is wrong by two orders of magnitude, was miscopied from its own cited source, was corrected in print by an outsider within three years, and was never withdrawn or revisited.  The one author who returned to the inventory, Vardiman, concluded that it shows a great deal of decay and cannot date anything, which is a different position and one this article's calculation does not dispute.  Every other creationist treatment of argon has been about individual rocks or individual boreholes, and every one of them is silent on the global number.

And the escape route that accelerated decay offers for other radiometric evidence does not work here, for a reason that has nothing to do with heat.  Fast decay makes argon fast.  It does not move it.  The transport problem is unaddressed, and the only young-earth mechanism that would address it, whole-mantle degassing in a year, contradicts the retention premise that RATE's own best-known argument depends on.

Verdict

The atmospheric argon inventory is the hardest single number in this subject, and it runs against a young earth.

The measurement is clean, confirmed four ways, and independent of any Earth model.  The isotopic evidence that it is radiogenic is direct, and comes from a spacecraft that went and sampled the alternative.  The shortfall over 6,000 years is a factor of 2.5 million on a route that uses no model at all, and the one genuinely uncertain input in the field cannot move it.

The error should be stated as plainly as everything else, and so should where it came from.  Melvin Cook ran the calculation honestly in 1966 and got a deficit of about four, which is close to the truth.  Harold Slusher copied it out of Cook's book seven years later and turned a statement about primordial potassium into a statement about present-day argon, reversing its sign and inflating it two-hundredfold.  Henry Morris printed the result for a mass audience with a hedge attached.  Nobody in the fifty-three years since has opened Cook's p. 66.  Neither man was dishonest.  Repeating the claim now would not be empiricism, and correcting it is worth more than any point available on the other side.

What a young-earth reader can take from this is not a win.  It is a research agenda, and it is specific.  Somebody has to write the paper that says where the argon came from, how it got out of the rock, and how that is compatible with the retention arguments RATE has already published.  Nobody has.  Until somebody does, this is the strongest evidence for an old Earth that this project has yet examined, and saying otherwise would be dishonest.

Companion pages

• The literature — every source consulted, with what it measured, its access route, and which way it cuts.
• RATE and helium diffusion in zircons — the retention argument from the same borehole, in detail.
• Radiometric concordance — excess argon as a potassium-argon failure mode, which is a different question from the global inventory.
• Hydroplate heat — the accelerated-decay heat problem worked in full, against which the potassium-40 figures here are cross-checked.

Sources