There's a well-known story that, while developing the atom bomb, the scientists at Los Alamos determined that there was a one-in-a-million chance that setting off the bomb would cause the atmosphere to ignite in a nuclear chain reaction, destroying all life on Earth.

I know how that number would have been calculated: by assuming that a self-sustaining chain reaction would occur, determining what values for nuclear properties would be required to produce it, and comparing those values to the size of the error bars on the measured values.

Yes, there was a serious concern among Manhattan Project scientists that a self-sustaining nitrogen-nitrogen fusion reaction might occur. A paper by Konopinski, Marvin, and Teller, Ignition of the Atmosphere with Nuclear Bombs, examined this possibility and concluded that it wouldn't happen

However, I've read the paper, and it doesn't come up with a chance of one in a million, or any probability at all. Instead, it calculates a "safety factor", and determines that in a worst-case scenario, with the least-favorable possible values for the nuclear properties of nitrogen*, there was a safety factor of 1.6: the reaction would lose energy 1.6 times too quickly to become self-sustaining.

So, where did the "one in a million" number come from?

* The two main uncertainties were the reaction cross-section, which was assumed to be equal to the geometric cross-section, and the distribution of reaction energy, which was assumed to go 100% to the reaction products. It's physically impossible for either value to be more wrong than this.

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    Wouldn't this be better in HSM?
    – Spencer
    Commented May 24, 2019 at 22:09
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    @Spencer, I considered it, but figured it was more of a "Manhattan Project" question than a "history of science" question, and decided to put it here.
    – Mark
    Commented May 24, 2019 at 22:11
  • Curious that only n-n reaction seemed relevant. A reaction involving humidity in the atmosphere does not seem interesting to anybody. An unbonding of hydrogen and oxygen in a "super bomb" detonation I would have thought worth some ink. There may be some reason I do not know that there was no public discussion of this.
    – J. Taylor
    Commented May 26, 2019 at 12:20
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    Can you add some source to the well-known story where the one-in-a-million figure appears ?
    – Evargalo
    Commented Jul 25, 2023 at 9:10
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    @J.Taylor Atmosphere is ~780,000 ppm nitrogen, ~210,000 ppm oxygen, and depending on humidity, only somewhere between ~2 and ~20,000 ppm hydrogen. And as the lighter element of the two, nitrogen fuses easier than oxygen. So there's no way atmospheric oxygen (let alone hydrogen) would go into a chain reaction before nitrogen did -- at which point it doesn't matter really if oxygen fuses as well, because there would be no one left to admire the difference. ;-)
    – DevSolar
    Commented Jul 25, 2023 at 9:11

3 Answers 3


The worry in numerical form may be slightly more complicated than exactly "one-in-a-million"

Whereas Serber seems to dismiss the discussion as short and Compton's concerns as overblown, Buck's interview with Compton tells a prolonged process supervised in part by Compton that eventually ruled out the scenario, but only after far more than a few hours' consideration:

During the next three months scientists in secret conference discussed the dangers of fusion but without agreement. Again Compton took the lead in the final decision. If, after calculation, he said, it were proved that the chances were more than approximately three in one million that the earth would be vaporized by the atomic explosion, he would not proceed with the project. Calculations proved the figures slightly less - and the project continued.

Dongwoo Chung: "(The Impossibility of) Lighting Atmospheric Fire", Submitted as coursework for PH241, Stanford University, Winter 2015

Referencing P. S. Buck, "The Bomb - the End of the World?" The American Weekly, 8 Mar 1959. (PDF)

That all this is not an absolute certainty at any time is evidenced by some of those involved to first speculate and worry, then calculate and calm their minds, only to be not so sure after all.
Even after the calculations seemed to say "practically impossible", project members didn't stop with their worries, until right after the blast. Knowledge was sparse, uncertainties to be weighed against optimism and pessimism. Trust in abilities of fellow humans and the possibility of simple errors looming amongst unknown variables and unforeseen and unintended consequences of risk taking.

One involved remembers:

But before going farther I need to mention a few things in my life that have shaped my opinions. The first occurred at Los Alamos during WWII when we were designing atomic bombs. Shortly before the first field test (you realize that no small scale experiment can be done - either you have a critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere. "I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen - after all, there could be no experiments at the needed energy levels. "He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, "What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?" I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, "Nevermind, Hamming, no one will ever blame you." Yes, we risked all the life we knew of in the known universe on some mathematics. Mathematics is not merely an idle art form, it is an essential part of our society.
R. W. Hamming: "Mathematics on a Distant Planet", The American Mathematical Monthly, Vol. 105, No. 7 (Aug. - Sep., 1998), pp. 640-650. (jstor)

The occasion of Fermi’s satire that evening made Bainbridge furious. It merely irritated Groves:

I had become a bit annoyed with Fermi . . . when he suddenly offered to take wagers from his fellow scientists on whether or not the bomb would ignite the atmosphere, and if so, whether it would merely destroy New Mexico or destroy the world. He had also said that after all it wouldn’t make any difference whether the bomb went off or not because it would still have been a well worth-while scientific experiment. For if it did fail to go off, we would have proved that an atomic explosion was not possible.

On the realistic grounds, the Italian laureate explained with his usual candor, that the best physicists in the world would have tried and failed. Bainbridge was furious because Fermi’s “thoughtless bravado” might scare the soldiers, who did not have the benefit of a knowledge of thermonuclear ignition temperatures and fireball cooling effects.2405 But a new force was about to be loosed on the world; no one could be absolutely certain—Fermi’s point—of the outcome of its debut. Oppenheimer had assigned Edward Teller the deliciously Tellerian task of trying to think of any imaginable trick or turn by which the explosion might escape its apparent bounds. Teller at Los Alamos that evening raised the same question Fermi had, but questioned Robert Serber, no mere uninformed GI:

Trying to find my way home in the darkness, I bumped into an acquaintance, Bob Serber. That day we had received a memo from our director . . . saying that we would have to be [at Trinity] well before dawn, and that we should be careful not to step on a rattlesnake. I asked Serber, “What will you do tomorrow about the rattlesnakes?” He said, “I’ll take a bottle of whiskey.”2406 I then went into my usual speech, telling him how one could imagine that things might get out of control in this, that, or a third manner. But we had discussed these things repeatedly, and we could not see how, in actual fact, we could get into trouble. Then I asked him, “And what do you think about it?” There in the dark Bob thought for a moment, then said, “I’ll take a second bottle of whiskey.”

Segrè at Base Camp imagined apocalypse:

The most striking impression was that of an overwhelmingly bright light. . . . I was flabbergasted by the new spectacle. We saw the whole sky flash with unbelievable brightness in spite of the very dark glasses we wore. . . . I believe that for a moment I thought the explosion might set fire to the atmosphere and thus finish the earth, even though I knew that this was not possible.

Richard Rhodes: "The Making of the Atomic Bomb", Simon & Schuster: New York, 1986.

For how this concrete number of "x-in-a-million" came into public debate with surrounding information in Hans A. Bethe: "The Road from Los Alamos: Collected Essays of Hans A. Bethe", Springer, 1991. p30 (Ultimate catastrophe). The core of it first published here:

In the November 1975 issue of the Bulletin, H. C. Dudley1 claimed that it is possible that an atomic weapon might ignite a thermonuclear reaction in the atmosphere (or the ocean) and thus destroy the Earth. This claim is nonsense. Dudley's claim is based on a report by the writer Pearl Buck of an interview with Arthur H. Compton in 1959. Had Dudley consulted the original literature, or any of the scientists conversant with the problem, he would soon have recognized that Pearl Buck had completely misunderstood Arthur H. Compton.
The basic theory of thermonuclear reactions in the atmosphere was developed in a report by E. ). Konopinski, C. Marvin, and E. Teller 2, published by the Los Alamos Laboratory. This work was done before the first nuclear test at Alamogordo in July 1945, and assured the leaders and members of the project that no danger existed that the test would set the atmosphere on fire. The report LA-602 was circulated in August 1946; it was secret until February 1973 when it was declassified.
The only "candidate" for a possible thermonuclear reaction in air was a collision between two nuclei of N because N14 is a nucleus of relatively high energy content. Several nuclear reactions are possible, of which we mention [formula] […]

So there was never any possibility of causing a thermonuclear chain reaction in the atmosphere. There was never "a probability of slightly less than three parts in a million," as Dudley claimed. Ignition is not a matter of probabilities; it is simply impossible.

1 H. C. Dudley (1975) The ultimate catastrophe, Bulletin of the Atomic Scientists, 31:9, 21-24, DOI

Hans Bethe: "Ultimate Catastrophe", Bulletin of the Atomic Scientists, 32:6, 36-37, 1976. DOI

This of course in hindsight and plainly against the worries of his own colleagues at the time. It may be the scientifically accepted and correct view on the matter, for Bethe now. But it was anachronistic to blame Dudley for 'misunderstanding'. After all, in Dudley's paper the source attribution is simply between bad formatting and plagiarism. (Compare Dudley paper with Pearl Buck, "The Bomb The End of the World!" American Weekly, March 8, 1959. Also quoted in Carl C. Gaither & Alma E. Cavazos-Gaither: "Gaither's Dictionary of Scientific Quotations", Springer, 2008.)

But as a bonus, this bulletin has the accompanying picture for illustration on Bethe's article:

enter image description here

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    That "approximately three in one million" looks to be about the same as a "six sigma (ie standard deviation)" standard, which in turn is one more than the normal "five sigma" standard for scientific acceptance. If true, that is worth noting I believe. Commented May 24, 2019 at 22:02
  • It's still in use today to mean "A really, really unlikely event which we can't rule out completely."
    – Mark Olson
    Commented Jul 25, 2023 at 0:37

Such a possibility was indeed considered, but any numerical estimate of a "chance" that it happens is nonsense. The question whether it can happen or not has a definite answer, and is asked only because of lack of knowledge. One cannot estimate the "chance" of such events. One can talk about chance or probability only if one has many trials under similar conditions.

A funny story (probably a legend) related to this possibility is the following. When the question was asked, one of the leaders of the project asked his graduate student to verify by calculation whether this can happen or not. The student obtained a negative answer but he looked very disturbed on the morning of the test. When asked why, he explained: "What if I made a mistake?!" To this the answer was: "There is nothing to worry about: if you made a mistake, nobody will learn about it anyway!"



Where did one-in-a-million chance of nuking the atmosphere come from?


During the summer of 1942, almost a year before the Manhattan Project's Los Alamos Lab opened; physicist Edward Teller expressed a concern that based on his calculations the chain reaction necessary for the first Atomic Bomb would not stop when it consumed all the Uranium/Plutonium fuel. That the chain reaction would in fact ignite the atmosphere and destroy the earth. Hans Bethe, who would go on to head the theoretical division at Los Alamos performed his own calculations and was able to demonstrate to his fellow physicists that the chances of such of an occurrence were near zero. Edward Teller today is known as the father of the Hydrogen Bomb, a bomb thousands of times more powerful than the atomic bombs developed by the Manhattan Project. In 1946 after the trinity tests and use of the atomic bombs on Japan; Teller authored a paper along with 2 other Manhattan Project scientists refuting his earlier findings. The paper was declassified in 1973.

How Oppenheimer weighed the odds of an atomic bomb test ending Earth

Still, the discussions and calculations persisted long after the Trinity test. In 1946, three Manhattan project scientists, including Teller, who would later become known as the father of the hydrogen bomb, wrote a report concluding that the explosive force of the first atomic bomb wasn’t even close to what would be required to trigger a planet-destroying chain reaction in air. The report was not declassified until 1973.

AI is like a Nuclear Weapon

The concern, as Edward Teller saw it, was quite literally the end of the world. He had run the calculations, and there was a real possibility, he told his Manhattan Project colleagues in 1942, that when they detonated the world’s first nuclear bomb, the blast would set off a chain reaction. The atmosphere would ignite. All life on Earth would be incinerated. Some of Teller’s colleagues dismissed the idea, but others didn’t. If there were even a slight possibility of atmospheric ignition, said Arthur Compton, the director of a Manhattan Project lab in Chicago, all work on the bomb should halt. “Better to accept the slavery of the Nazi,” he later wrote, “than to run a chance of drawing the final curtain on mankind.”

How Oppenheimer weighed the odds of an atomic bomb test ending Earth


From Mark: This doesn't give the source for "one in a million". The "Teller and two others" paper is the one I cite in the question, giving a 1.6 safety factor. Your other sources agree that Bethe calculated that a bomb couldn't ignite the atmosphere, but don't go into any further detail.

In truth LаngLаngС doesn't either. He cites sources which discus 3 in a million chances. Sources which are tangentially related but entirely dependent on to the exchange between Hans Bethe and Teller in 1942 which is not referred to.

The question "Where did one-in-a-million chance of nuking the atmosphere come from?" is imprecisely and colloquially worded. It is directly based on Hans Bethe's response to the concerns Edward Teller's expressed in 1942. Hans Bethe was the first to show Teller's concerns were ill founded, near zero chance. The paper's cited are more distantly related to the expression in popular culture, as they were classified for decades and entirely fore shadowed by the less formal yet widely cited exchange between Bethe and Teller. The book you cited published in the 1990's is also far removed from the origins of the expression, and again reflect on but do not directly refer to the earlier Bethe / Teller exchange.

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    This doesn't give the source for "one in a million". The "Teller and two others" paper is the one I cite in the question, giving a 1.6 safety factor. Your other sources agree that Bethe calculated that a bomb couldn't ignite the atmosphere, but don't go into any further detail.
    – Mark
    Commented Jul 25, 2023 at 20:49

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